bear v2.7.7
(Please note: bear is not available from CRAN Repository website any more since v2.6.5)

the data analysis tool for average
bioequivalence
(ABE) and bioavailability (BA)

originally created by Hsin-ya Lee and Yung-jin Lee (mobilepk at gmail.com)
Kaohsiung Veterans General Hospital (HY) &
ptpc, inc. (YJ),
Kaohsiung, Taiwan 80794

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Introduction
This package was designed to analyze average bioequivalence (ABE) data from noncompartmental analysis (NCA) to ANOVA (using lm() for a 2x2x2 crossover and parallel study; lme() for replicate crossover study). Study design of ABE can be 2x2x2 crossover or repeated crossover (2x2x2, 2x2x3,...2x2x6) or a parallel study. The dosing can be single- or multiple-dose. The statistical analysis for bioavailability (BA) measurements (AUCs and Cmax) was based on the two one-sided tests (Schuirmann, 1987). ABE involves the calculation of 90% confidence intervals for the ratio of the averages of the measures for the test and reference products. The BE will be concluded based on the calculated 90%CIs falling within 80-125% (or up to user's defined). You can browse bebac Forum - R for BE/BA to get more information about the development of bear.  We received a lots of great suggestions from the experts of bebac Forum - R for BE/BA. bear is developed under GPL (> 2) and is open sourced freeware.  Please do NOT write to us to ask how to purchase it.

Installation & Upgrade: bear (stands for BE/BA for R) is an R package.  However, it is not available directly from R repository website since v2.6.5. Please go to here. Read the content following the file list panel for more details first. No need to download the file README.md again since it has been displayed on screen.  The file - NEWS is the change history.

Remove bear: Simply go to the directory of R where you installed and then go to the sub-directory of /library, delete bear.

What bear can do:
This package includes three parts. First is doing “sample size estimation.” Users can choose 80 or 90% power and defined upper BE acceptance criteria to conduct a ABE between these two formulations. Sample size also depends on the magnitude of variability. Variance estimates can be obtained from the biomedical literature or pilot studies. For crossover designs, we provide two kinds of methods for different data (raw and log-transformed) (Liu, et al. 1992; Hauschke, et al.1992). This function will provide information about how many numbers of subjects should be included. Second part is to perform NCA.  We provide NCA approach to compute AUC0-t, AUC0-inf and terminal elimination rate constant (λz) with time-Cp profile. λz, the terminal phase rate constant, will be estimated from the slope of linear regression with various approaches (manual selection of the exact 3 data points, adjusted R2 (ARS), AIC, Two-Times-Tmax (TTT), TTT-ARS, TTT-AIC, etc).  All these approaches do not include the data point of (Tmax, Cmax).  Linear trapezoidal rule is used to calculate AUC0-t (AUC from time 0 to the last measurable Cp).  The extrapolated AUC (from time of the last measurable Cp to infinity) will be estimated from the last measurable Cp divided by λz.  AUC0-inf (AUC from time 0 to infinity) equals to AUC0-t plus the extrapolated AUC(AUCt-inf).  Cmax is obtained from observed time-Cp profile. All plots from NCA will be stored in a pdf file (like this .pdf) and all reports, including NCA reports (like this NCA PK) and pharmacokinetic summaries (Cmax, Tmax, AUC0-t, AUC0-inf, AUC0-t/AUC0-inf*100%, ln(Cmax), ln(AUC0-t), ln(AUC0-inf), MRT0-inf, T1/2, Vd/F, λz, Cl/F). Please refer to some pharmacokinetic textbooks about how to calculate these parameters with NCA.  Final step is to perform ANOVA (lm in R). For non-replicated crossover designs, FDA guidance (FDA, 2001) recommends parametric procedures to analyze log-transformed BA measures. It continues to perform ANOVA and calculate 90%CIs, and finally to conclude if it is bioequivalent with three pivotal BE parameters. This package also supplies ANOVA stat reports (like this ANOVA stat) or results of linear mixed effects (lme_stat.txt for replicate or parallel BE studies) and summaries (like this statistical summaries). All results obtained from outlier detection analysis (now only for 2x2x2 crossover BE study) will be also appearing in ANOVA_stat; and all plots from outlier detection analysis will be stored in this ODplots.pdf.

How to use it:
bear was complied and tested under R v3.2.2. So, please install or upgrade R program to the latest version. Data input: The fastest and the easiest way to use bear is to import your data into it.  You can choose "NCA --> ANOVA" from the menu and then import your data with .csv (comma-separated values) format. Please note that the readily imported file (.csv) should be placed on R accessible path.  In Windows XP/Vista, the file path is set by default on the directory of "C:\Documents and Settings\UserName\My Documents" for XP,  or "C:\UserName\My Documents" for Vista.  UserName here indicates the user's name. Thus, it can be different on each computer.  User can type "getwd()" in R console to examine your default file path.   All output files (.txt, .pdf, .csv or .RData) generated by bear will also be placed in this directory.   Now, you can import a .csv file into bear for ANOVA.   If you like to do NCA first, followed by ANOVA, you can import bear generated NCA output file which can be a .RData or a .csv format into bear for ANOVA.  You can also provide your own data file (.csv file format) now.  Then pick three time-Cp data points from each plot by clicking it with your mouse.  Here is flash demo for the selection of three Cp to estimate λ and a sample data (.csv) (right click your mouse and use "Save as..." function) which can be imported into bear for analysis (also see the following).  The sequences of column must be followed (i.e. subject# -> study sequence -> study period -> sampling time -> measured drug concentration from the left to the right).  However, you can change the column name. For example, you can change "prd" as "period" if you like.  We have presumably defined the study sequence in bear as "1" when a subject takes the reference product first, followed by test product and "2" in reversed. This is very critical to remember when using bear. If it is a BA study, only NCA will be performed. Required other computer software: With bear for R, all computer software you need is a spreadsheet, such as MS-Excel (if it's available for your computer) or LibreOffice Calc (which is a very nice freeware!) or even a plain ascii (.txt) editor which can create your .csv format for your data.  Validation:  We have tested bear with one of BE dataset and found that all output results to be the same as those generated by commercial software. Here is the validation results (pdf) done on 2009.

Sample size estimation

          <<Sample Size Estimation>>

 Upper acceptance limit = 125 %
 Lower acceptance limit = 80 %
     Expected ratio T/R = 95.00 %
           Target power = 80.00 %
Inter- or Intra-subj CV = 20.0 %

 study    2x2x1         2x2x2        2x2x3        2x2x4
design   parallel     crossover   replicated   replicated
------- ----------- ------------ ------------ ------------
   N       36            20           16           10

Estimated power = 80.99398 % (for parallel study)
Estimated power = 83.46802 % (for crossover/replicate study)
where 2x2x2 means 2-treatment, 2-sequence, and 2-period crossover study.

Sample file of the imported data format (.csv): Please note that this format is not for ANOVA or lme data.
This is the format ONLY for the raw data of a 2x2x2 crossover (A), replicate (2x2x3/2x2x4...2x2x6) (B), and
the parallel study (C).

subj,seq,prd,time,conc
1,2,2,0.00,0.00
1,2,2,0.25,36.1
1,2,2,0.50,125
1,2,2,0.75,567
1,2,2,1.00,932
1,2,2,1.50,1343
1,2,2,2.00,1739
1,2,2,3.00,1604
1,2,2,4.00,1460
(...)
subj,seq,prd,tmt,time,conc 1,2,2,1,0,0 1,2,2,1,0.25,36.1 1,2,2,1,0.5,125 1,2,2,1,0.75,567 1,2,2,1,1,932 1,2,2,1,1.5,1343 1,2,2,1,2,1739 1,2,2,1,3,1604 1,2,2,1,4,1460
(...)
subj,drug,time,conc 1,2,0,0 1,2,0.25,36.1 1,2,0.5,125 1,2,0.75,567 1,2,1,932 1,2,1.5,1343 1,2,2,1739 1,2,3,1604 1,2,4,1460
(...)
  (A)                                              (B)                                                      (C)

where "subj", "seq", "prd", "tmt" (or "drug"), "time" and "conc" represents subject#, sequence, period, treatment (or drug), sampling time and drug concentration, respectively.  Users can use different column names as wished.  Please note that:
  • Users must follow the column sequence as shown above; However, the column name can be different.
  • We have internally defined the study sequence in bear as "1" (no double quote, please) when a subject
    takes the reference product first, followed by test product and "2" in reversed.
  • In coding "tmt" or "drug", please set drug or tmt ="1" for the Reference, and drug or tmt = "2" for the Test.
  • All data should be entered only as the numerical format, not the text format (not double quote!);
  • When a drug plasma/serum/blood concentration is near the end of sampling time and is below LLOQ, this value (entire row) can be deleted (IndivDP_output function can not be used in this case); The recommended way is to input these data values as 'NA' since bear will handle it properly. However, the first data point at (time = 0, Cp = 0) must be included.
  • User can decide the terminal 2-6 data points for estimation of λz; not necessary to choose exact 3 data points. It can be difficult for multiple-dosed study sometimes to choose exact 3 data points. The max. data points will be set to 6 since v2.5.4. User can click "Stop" on the graphic window (on the upper left corner) and then click "Stop locator" to stop further selection if less than 4 data points is selected since v2.5.4.
  • Starting v2.6.2, all settings of running bear is pre-set. Users need to change these settings carefully; otherwise, it can cause bear crashed. For example, the input dataset is not matched with study design, such as defining a single-dose study, but the dataset is obtained from a multiple-dose study.
  • Known bugs (for v2.6.3): (3) In Mac OS X (Darwin) if using R.app, the "Current Settings" (on R console) won't be able to refresh promptly once the set-up files have been changed. Under the terminal or RStudio there is no such problem. So it may not be a bug. I don't have any idea about how to fix this so far.
  • Any fixed version of bear can be downloaded from here. This version will be updated from time to time until submitting to CRAN.
  • If there is any question about using bear, please report it to bebac forum. I will respond asap.






*****  Update History (Feb. 11, 2016) & References

v2.7.7 (for R v3.3.0,***personal release***) up to 2016/05/04
     - added new logo for 2016;
     - fixed imported package; switched from 'gWidgets2' to 'gWidgets' since
       the package 'gWidgets2RGtk2' has been archived;
     - also fixed 'preinst.r' (v1.4);
     
v2.7.6 (for R v3.2.3,***personal release***) up to 2016/02/11
     - kept all data points with conc.= 0 when doing AUC & AUMC calculations;
       modified ARS(), aic(), NCA(), TTT(), TTTAIC(), and TTTARS() for trapezoidal
       calculation; all-linear is fine; if linear-up/log-down; it will switch back
       to linear when (1) C[i-1]=0 or C[i]=0; (2) C[i]>C[i-1]; and (3) C[i]=C[i-1];
     - kept NCAplot() unchanged; no way to plot log(0) if there is any; it will be
       excluded;
     - fixed check.nca.data() without assigning conc. = 0 as 'NA'; instead to
       see if enough data points are available for £fz estimation; also fixed 
       NCAanalyze(), NCA.BANOVAanalyze(), RepNCAanalyze(), and demomenu() & 
       demomenu1();
     - fixed title of input GUI for D. Labes' randomizeBE;
     - fixed go2menu() with the list of the Top menu;
     - fixed check.nca.data(); to add more explanations for the list of subject data;
     - fixed Singlego() to delete the file of 'bear.current.setting' from the second-
       level menu;
       
v2.7.5 (for R v3.2.3,***personal release***) up to 2015/12/31
     - added GUI for D. Labes' randomizeBE;
     
v2.7.4 (for R v3.2.3,***personal release***) up to 2015/12/24
     - fixed 'lambda_z estimate' display with the menu of '*edit set-up file'; this
       '£fz estimate' only works on Win7; not working on/Win10/linux-pc/Mac OSX; however
       the display of '£fz estimate' on R console in OK for all platforms;

v2.7.3 (for R v3.2.3,***personal release***) up to 2015/12/23
     - switched all packages in the package list of 'Imports' in DESCRIPTION to 'importFrom()'
       in NAMESPACE to fix the warning messages as v2.7.2;
     - update 'Multipledata.rda' (subj#15) in directory of 'inst/extdata' to be able to 
       analyze with ARS/AIC; also fixed demomenu1() & demo_datasets_gen() with readRDS() 
       due to "Error: bad restore file magic number..."
     - fixed check.nca.data() to skip manual selection of data points ('5') or loading 
       dataset from previous manual selection ('6', *.RData).
       
v2.7.2 (for R v3.2.3, ***personal release***) up to 2015/12/22
     - fixed description_version() with adding win.version() for Win OS detection; this
       function starts from R v3.2.3;
     - fixed NCAanalyze() & NCA.BANOVAanalyze() with adding 'lambda_z_calc' to check.nca.data();
     - fixed the warning message when loading bear (...) after upgrading ggplot2 to v2.0.0
       as follows:
       ---
       Warning messages:
       1: replacing previous import by ¡¥grid::arrow¡¦ when loading ¡¥bear¡¦ 
       2: replacing previous import by ¡¥grid::unit¡¦ when loading ¡¥bear¡¦ 
       ---
       by removing 'grid' from "Imports" in DESCRIPTION (package 'grid' has been included in 
       R base) and instead using 'grid::grid.raster' in the codes;
       
v2.7.1 (for R v3.2.3, ***personal release***)
     - fixed "Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...):
       NA/NaN/Inf in 'y'" when calculating λz if there is any zero conc. included; replaced
       '0' with 'NA' now; codes included NCAanalyze(), NCA.BANOVAanalyze(), RepNCAanalyze(),
       demomenu() and demomenu1();
     - fixed demomenu() & demomenu1() again; last time did not complete add check.nca.data();
     - fixed BANOVAdata(); to delete 'bear.Current.setting.rds' if end run;
     - fixed NCAplot() to remove 'NA' of conc. originally coming from zero conc.;
     - added 'news(Version=="2.7.1",package="bear")' to browse update logs (about.bear());
       not working yet in compiled mode (portable package), but in R console;
     - tested on new released R v3.2.3; seemed ok...
     - fixed NCAoutput(); first time to use '\u03BBz'(λz) to replace 'lambda_z' in NCA output
       file;
     - fixed NCA(), NCAselect(), ARS(), aic(), TTT(), TTTAIC() & TTTARS().
     
v2.7.0 (for R v3.2.2; ***personal release***)
     - added check.nca.data() for checking if the data points are proper 
       enough to calculate the terminal elimination rate constant (lambda_z);
     - fixed ARS(), aic(), TTT(), TTTAIC() & TTTARS() accordingly;
     - modified NCAanalyze(), RepNCAanalyze() & NCA.BANOVAanalyze();
     - fixed the top menu again; removed linux warning message;
     - fixed check.nca.data(); made it to check the dataset based on the selected
       lambda_z calculation methods;
     - fixed demomenu() & demomenu1() also;

v2.6.9 (for R v3.2.2; ***personal release***)
     - fixed readline(...) to show only red color;
     - move package gdata and nlme from 'Depends' to 'Imports' to suppress noised message when
       doing library(bear); and it still runs fine;
     - fixed NCAoutput() for stat output on screen simultaneously;
     
v2.6.8 (for R v3.2.2; ***personal release***)
     - fixed sizemenu() and logdata(); it used to be that sizemenu() would stop run 
       if replicate; and logdata() kept looping;
     - fixed some rd files;
     
v2.6.7 (for R v3.2.2; personal release)
     - switched 'show()' into 'print(*, row.names=FALSE)'; forced not to print the row
       numbering;
     - changed 'Current Setting' to display only related info; hiding all 'no' settings;
     - fixed NCAoutput() for sink(., split=TRUE) (i.e., to display output contents on the
       screen simultaneously); also simplified the code; added text for reminding user if 
       it is a metabolite (the analyte);
     - fixed aic(), ARS(), TTT(), TTTAIC(), TTTARS(), NCA(); not to display from these but
       only to generate 'TotalData';
     - fixed NCAselect() and NCA(); not to stop after manual selection of data points;
     - changed 'NaN' to "NA" when assigning Cl/F and Vd/F if it is a metabolite;
     - improve the display of "Current Setting" again; remove all "no" settings from list;
     - still working.... (Sept. 01, 2015)
     
v2.6.6 (for R v3.2.2; personal release)
     - simplified setting schemes; no more separated plot setting since this ver.;
     - forced 'dose' to be input as 'mg' now; will be converted based on the unit of 
       measured drug plasma/serum conc. (mcg/mL, ng/mL or pg/mL);
     - added "is metabolite?" setting; when it is a metabolite, some of PK parameters
       will not be able to calculate, such as Cl/F and Vd/F; the volume term is always
       fixed as the unit of 'mL' now;
     - label for y axis does not need to put conc. unit there; it will be added 
       automatically;
     - changed logo of bear for 2015.
     
v2.6.5 (for R v3.2.1; personal release)
     - fixed helper.func() with suggested package (plyr) using requireNamespace();
     - fixed BANOVAcsv() & NCA.BANOVAdata() to keep 'NA' after loading data;
     - fixed RepMIXanalyze(), RepMIXoutput(), RepMIX(), MultipleParaMIX(), 
       MultipleParaMIXoutput(), MultipleParaMIXanalyze(), ParaMIX() and ParaMIXoutput()
       for parameter transfer between functions; place all partial AUC parameters to the
       last; BANOVA() and its related functions should be fine.
     - tested bear with R v3.2.0 (Full of ingredient); all seem fine;
     - fixed the dataset of 'SingleRep_stat_demo.csv' in both demoBANOVA() and 
       demo_datasets_gen();
     - add option of 'na.action=na.exclude' to every lme() and lm();
     - remove (remark)'TotalData<-na.omit(TotalData)' to keep all NAs; these NA will be 
       ignored when doing lm() or lme(); and
     - fixed lm.mod() for Type III SS.
       
v2.6.4 (for R v3.1.2)
     - modified lme() in RepMIX(), NCAoutput() & lme_lm.mod() with 
       lmeControl(opt='optim', msMaxIter=1000);
     - added R version into description_version() (as part of outputs);
     - modified DESCRIPTION - Title;
     - added warning for the writing permission of working path at the beginning;
     - added citation into output files;
     - added the message of showing the folder name for all output files at 
       the beginning; and
     - added warning for invalid selection of 'conc' for lambda_z estimation using 
       ARS(), aic(), TTT(), TTTAIC(), and TTTARS(); not necessary for NCAselect().
           
v2.6.3 (for R v3.1.0)
     - added the tests for carryover effects and the direct formulation effects with
       lm.mod() for 2x2x2 crossover study based on the textbook of Clinical 
       Trial Data Analysis Using R, Chen, D-G (Din); Peace KE. CRC Press, Taylor 
       & Fracis Group, 2010; ISBN-10: 1439840202; Ch. 10 - "Analysis of Bioequivalence 
       Clincial Trials"; pp.269-274. Amazon
     - took care of switching pAUC to be FALSE when running 'statistical analysis only';
       since the demo dataset for 'statistical analysis only' does not include any
       pAUC parameter (demoBANOVA());
     - fixed BANOVA() again to simplify the codes;
     - started working with new release of R v3.0.3;
     - fixed BANOVAcsv() for dataset input if doing pAUC;
     - demo dataset do not have any pAUC example for statistical-only runs;
     - BANOVA() for pAUC stats. and 2x2x2 crossover with multiple-dose stats.;
     - fixed default values for 'pAUC_start' and 'pAUC_end' with '121' & '128' (for
       multiple-dose), instead of '1' & '8' (for single-dose) respectively; since 
       the 'pAUC_start' & 'pAUC_end' counts from time zero, not from one dosing 
       interval, especially for multiple-dose; otherwise, it will cause error, 
       such as 'Na/NaN/Inf -> y...'
     - fixed NCAplot() hopefully to speed-up plotting and enhance efficiency; 
     - changed parallel study in NCAoutput() as lme(); in RepMix() the parallel
       uses lm(); but the results are the same.
       
v2.6.2 (for R 3.0.2)
    - added lme_lm.mod() to simplify original RepMix();
    - added lm.mod() to simplify original BANOVA(); also fixed an error in original 
      BANOVA(); btw, fixed the output format of BANOVA();
    - fixed BANOVAanalyze() to run BANOVAoutput() once and RepMixanalyze() to run
      RepMIXOutput() once; no more run 'BANOVA() -> BANOVAoutput()' since BANOVAoutput()
      will call BANOVA(); and also no more 'RepMix() -> RepMixOutput()' since
      RepMIXoutput() will call RepMIX(); more efficient now; otherwise; BANOVA() & RepMix()
      will run/be called twice.
    - fixed some typo in the display of setting guide;
    - re-coded with NCAcsv(), BANOVAcsv() & NCA.BANOVAcsv(); more efficient hopefully;
    - excluded the parallel study from icd_check(); how can I forget this? and kept 
      the replicated crossover study; 
    - added 'input data' to description_version(); it only works for Windows OS;
    - added 'input dataset' and the name of OS platform to NCAoutput();
    - fixed icd_check() and abandoned using 'stop()' from it; icd.check()
      can be detected icd earlier than previous version since it will get
      work done once the dataset is loaded; only for nca data; not for anova
      dataset.
    - added 'run.demo','study.type' and 'dose.type' into setting items to
      reduce menu levels;
    - fixed 'dosing interval' in bear setting; forgot to change in the last
      release (v2.6.1); so this can cause error for multiple-dose;
    - disable dataset output for demo runs; all can be done from the top menu;
    - fixed CV_inter of BANOVA() when occurring negative variance components;
    - corrected typo in RepMix() to show CV(intra);
    - also fix NCAoutput() as adding ODA setting function;
    - integrate ODA into setting file; modify the top menu;
    - changed bear setup cheatsheet mode as a graphic display;
    - fixed setting display screen;
    - fixed output format for RepMIX();
    - re-assigned column names for 'statistical analysis' (BANOVA()) if the imported
      .csv was not originally generated by bear;
    - change RepMIX()'s lme() with lmeControl(opt='optim') since the
      default 'nlminb' fails to converge frequently;
    - fixed the inconsistency of 90% CI for replicate crossover in 'stat_sum_output' 
      and 'lme_output' with NCAoutput() and RepMIX();
     
v2.6.1 (for R 3.0.2)
    - added function to avoid the errors due to dummy input;
    - re-organize the information about how to setup bear using file.show();
      testing on Windows, linux and iMac OS X platforms; iMac will work with 
      R.app or RStudio,but not TK GUI;
    - added license (GPL-2|GPL-3) announcement for bear on all output or display 
      pages;
    - added the output function of individual data points (IDP output) with mean 
      & sd for each time point;
    - removed formfeed with NCAoutput(); it does not print correctly with a 
      pdf printer; don't know why.
    - fixed on-screen display content when it is pAUC;
    - fixed some typo;
    
v2.6.0 (for R 3.0.2)
    - decided not to implement data point interpolation for missing data value (C*)
      when doing partial AUC or truncated AUC analysis in bear; users may consider 
      to use an estimate/interpolation/extrapolation for missing data when 
      necessary beforehand; further ref. included:
      (1) http://forum.bebac.at/mix_entry.php?id=4655#p4681
      (2) http://forum.bebac.at/mix_entry.php?id=1933&page=0&category=0&order
                 =last_answer&descasc=DESC#p2323
    - added analysis for pAUC or truncated AUC;
    - fixed AUMC to comply with linear-up/log-down trapezoidal rule as AUC.
    - added "study tracer" (footprint) to the selected menu;
    - create the export module for demo dataset;
    - enable demo dataset export through NCA and ANOVA for later testing purposes;
    - add 'plot.setup.rds'; plus original 'bear.setup.rds' of setup file for
      bear;
    - fixed export/import .csv and .Rdata file for 'statistical analysis' in 
      NCAoutput();
    - added bear.setup() for setup files generation; new features.
    - moved AUC calc. method to NCA.BANONAanalyze(); this has been changed later;
    - corrected some typos again;
    - fixed BANOVA() with no "abs()" for CV_intra values;
    - fixed descriptionTOST() using paste() for better display;
    
v2.5.8 (for R v3.0.2)
    - fixed BE criteria with percentage (/100); sorry about this error;
    - disable warning message with options(warn=-1) from very beginning;
    - add the function of NCA saved pivotal parameters back again with automatically
      saving as .RData (NCAoutput()); it was disabled before, though it has been
      saved as .csv format;
    - added more output info of study design for NCAoutput(); not just multiple-
      dose or single-dose; now also include if it is parallel or if it is replicated;
    - added LL/UL as data.frame() input for replicated study as the non-replciated;
    - fixed AIC crashed when running multiple-dose study; and
    - fixed plots of regression lines (ARS, AIC, etc.) for hiding the first
      empty (null) plot window.
      
v2.5.7 (for R v3.0.1)
    - added LL/UL as data.frame() input; not just LL.
    - fixed abnormal on-screen text display with Mac OS X using data.frame() input.
    - fixed BANOVAdata() & BANOVAcsv() with graphic menu; and also spelling check.
    - removed abs() from CV_intra calculation.
    
v2.5.6 (for R v3.0.1)
    - added csv outputs for data point selections of linear regression to calculate
      lambda_z with ARS, AIC, TTT, TTTAIC & TTTARS now; it used to be only available
      for manual selection of data points; It's most easy function to implement so far
      which I cannot figure out how to do this long time ago.
    - fixed R^2 display on linear regression plots for terminal elim. constant (lambda_z)
      estimation; just a mathematical annotation (squared 2), it took me two whole
      nights to complete; Wow, it's not easy for this little thing...
    - fixed NCAselect() & NCAregplot() with plot(...,lab=c(15,15,40),...) for better
      looking.
    - fixed selection of all linear or lin-up/log-down calc. for AUC with manual selection
      of data points; others (AIC, ARS, TTT & etc. have been fixed last time); previously
      the selection does not work effectively, even the 'all linear' is selected.
    - corrected some typos; Is it cont. or cont'd? Answer: In formal writing use cont'd.
      ref. link: http://wiki.answers.com/Q/Is_it_cont_or_cont%27d (used in NCA Output). 
      fine.
    - fixed 'description_pointselect()' to give more details about Windows, Linux/unix
      or ubuntu, and Mac OS X.
    - added lin-up/log-down trapezoidal AUC calc; the in-up/log-down trapezoidal method
      is default method now;
    - fix graphics in linux/unix (ubuntu), Mac OS X; use 'dev.new()' instead of 
      'windows(record=TRUE)'; original codes won't work any more for R v3.0 or above;
    - set options(digits=5) as default;

v2.5.5 (for R v3.0.0)
    - NCA plots are switched from plot() to ggplot() now; better graphics looking;
    - use some helper functions from "Cookbook for R" authored by Winston Chang to
      use ggplot() (website);
    - remove console plotting now; all plots will be logged into .pdf of NCA plots;
      this will remove 5 R scripts from previous version;
    - add test/demo functions; separate from original /R directory;
    - add 'page break' '\f' for xxx_nca_outputs.txt;
    - fix bugs for the section containing the means (SD) for each formulation 
      (by time point) in NCA output file. (thanks to Elba Romero). This is only
      for the situations of running NCA demo or NCA;
    - improve data point selection methods with correct subject labeling;
    - add bear cover page for nca plot and ODA plot pdf files (using library(png));
    - fixed the part of data point manual selection logged as .pdf. With R3.0.0, it
      is still a problem; however, it is OK with R2.15.3 (miss it so much). Porbably
      in R3.0.0 the graphic windows have been changed as stated in its update doc. Now
      it should be fine. Quite different from ARS, AIC, TTT, etc.. my mistake;
    - remove the function to save 'TotalData' again after NCA as a .RData. It does not
      make any sense to do this;
    - remove DOA on-screen plots since all plots have been logged into a .pdf file.
      It's a redundancy procedure, just like on-screen NCA plots;
    - improve pivotal_output.csv; now it is much better than previously;
    - now manual data selection from previously saved .RData can also be plotted into
      pdf now, as well as plots of on-screen data point selection;
    - fix 'Tmax_ss' for multiple dose BE; the original one should be subtracted with
      TlastD (the time of the final dose be given);
    - fix NCAselect again; try to improve graphic looking for multiple dose BE dataset,
      especially the setting of ylim(); done.
    - fixed the section containing the means (SD) for each formulation (by time point) 
      in NCA output file; it was the same for the ref. & test products in the previous
      version. Sorry about this;
    - hide on-screen linear regression plots, but still save all plots as one .pdf file;
    - set 'ylim=c(1e-3, 1e+5)' in all linear regression plots for lambda_z estimations; it
      looks much better in this case; and
    - all selection menu -> 'graphics=TRUE' now.
    
v2.5.4
    - please note that the previous saved .RData (before v2.5.4) will not be able to be supported
      in this release; users need to import the raw data from .cvs files or re-selected data points
      for linear regression to estimate lambda_z; sorry about that.
    - mostly based on BE/BA forums (with the topic of bear feature request).
    - grouping each run with random batch# and system date marked; more outputs from this version. 
      and no more overwrite previous outputs now.
    - outlier detection analysis (ODA) is taken away from routine run; and also ODA outputs
      is separated;
    - max. data point selections for lambda_z estimation was increased to 6 (range: 2-6);
    - single plot for point selection now (used to be 2x2 plots), old-man version?
    - fix inconsistent outputs for unbalanced dataset;
    - incomplete dataset will be blocked before being analyzed (hopefully);
    - use "file.choose()" for data file loading;
    - total lambda_z selections outputs as .csv format (as requested by sarawuto);
    - pivotal and misc pk parameters output as .csv format (as requested by sarawuto);
    - change data() for demo functions; to adapt future R (with R v3.0);
    - add "extdata" directory to store demo data files as .rda format;
    - add linear regression line plots for lambda_z estimation for manual data points selections.
    - change save() and load() to saveRDS() and readRDS() for convenient scripting.
    - add mean (sd) plots on semilog scale (Helmut).
    - add alarm() and readline("...") for methods of estimation lambda_z to alert user what 
      they should know before next step.(as requested by d_labes)
    - add a section containing the means (SD) for each formulation (by time point) in NCA output 
      file (as requested by Helmut).
    - modify some output files.
    - add plots of linear regression lines for lambda_z estimation for ARS, AIC, TTT,TTT-AIC &
      TTT-ARS.

v2.5.3
    - generalized SAS-like outputs (such as ANOVA and Type III SS) with 2x2x2 crossover;
    - added variance model into lme() and fixed random effect in lme() for replicate study
      as suggested by D. Labes posted at bebac forum (browse this thread at bebac forum);
    - the maximum data points that can be chosen to estimation of λz is set to 4, at 
      least 2 data points are required. The "Select the exact 3 data points" has been changed 
      to "Select 2-4 data point"; and
    - other minor changes.
    
v2.5.2
    - changed anova model back to lm(log(PK)~ seq + subj:seq + prd + drug , data) as with 
      v2.4.0; if not, this will result in error in calculation of 90% CI, as well as point
      estimates (thanks to Jiří Hofmann, Czech Republic).
      
v2.5.1
    - re-compiled again to change the requirement with R v2.10.0 to enable installation in MacOSX;
      however, bear was still compiled with R v2.11.0.
      
v2.5.0
    - added Welch t tests (also 90% CI) for a parallel BE study (thanks to Helmut Schütz);
    - added CVintra (intra-subject CV) calculation for a replicate BE study (lme_stat.txt)
      right after classical 90% CI;
    - hide ln(PK) list in the report of ANOVA_stat.txt/lm_stat.txt/lme_stat.txt;
    - completed the function of a parallel BE study with multiple-dosed (used to be single-dosed only);
      and
    - some other bugs fixed
    
v2.4.4
    - fixed the output file, Statistical_summaries.txt; i.e., Table 2: remove n1, n2 list from
      non-replicate or replicate crossover BE study; They only appear in Parallel BE study.
      
v2.4.3
    - changed the statistical model from linear mixed model(lme()) to linear model (lm())(similar to 
      SAS GLM) for a parallel BE study; basically, the results obtained from lme() or lm() are the same.
      However, to meet the regulatory requirements (both FDA and EU), lm() has been adopted since this
      version. Later, the Welch t-test will be added for a parallel BE study for unequal variances in
      the next release. See more discussion: Post#01 and Post#02.
    - recompiled bear under R v.2.11.0.
    
v2.4.2
    - fixed NCA outputs for the unbalanced parallel BE study
    - fixed TOST descriptions
    - recompiled with R v2.10.1
    
v2.4.1
    - add time/date stamp on the header or title page of text or pdf (plots) outputs (11.10(e) of 21 CRF 
      Part 11); more to be made for Part 11...
    - set .pdf output format as A4 paper size.
    - modify all .Rd files to fit R v2.9.2 requirements
    - change of the name "seq:subj" to "subj(seq)" in anova with the mode of "Y ~ seq + subj:seq +
      per + trt" in order to be conveniently cross validated with SAS (thanks to Elmaestro)
    - mostly minor changes with this release
    
v2.4.0
    - add data analysis of multiple-dose (MD) ABE data
    - add Cook's distance for outlier detection with various criteria
    - fixed y-axis scaling problem
    
v2.3.1
    - fixed NCA plots of  Time scale (with auto-scale)
    - used the difference of lsmeans between the Ref. and the Test to calculate 90% CIs for 
      Cmax and AUCs
      
v2.3.0
    - add sample size estimation and lme analysis for the parallel BE study
    - add References into bear's output (such as ANOVA)
    - label outliers' subjects number for boxplot only if there is any (see crossover demo)
    - add input data summary of BA measurement (class level information, means, etc.)
    - add interpretations for some statistical tests (such as Hotelling T2 test)
    - add add Two One-Sided Tests (TOST) and Anderson-Hauck's tests (just for educational 
      purposes ONLY)
    - allow users to change BE acceptance range now (not fixed on 80%-125% any more!); different
      countries have different regulatory basis...
    - show MSResidual and MSSubject(seq) values when calculating inter- and intra-subject CV
    - change Hotelling T2 test layout

v 2.2.0
    - add point estimate along with 90% CI in output file called 'Statistical_summaries.txt 
      (suggested by D. Labes).
    - add sample size estimation for replicate BE study, and output re-arrangement.
    - add Hotelling T2 function and boxplot for outlier detection
    - add Quantiles for intrasubject and intersubject (with boxplot)
    - add replicated study for 2*2*3, 2*2*4, 2*2*5, and 2*2*6 (using lme to analyze replicated
      BE study)
    - add sample size estimation for replicated study (using 2*2*2 sample size estimation extended 
      to 2*2*n sample size of replicate crossover design)

v.2.1.0
    - we add 'analysis of outliers detection' since this release.  These include some normality 
      tests, and some diagnostic plots for this functions, such as QQ plots and intra- and 
      inter-subject residual plots.
    - fix intra-subject CV calculation based on ref. #6. (thanks to Helmut Schütz).

v1.5.0~2.0.3
   - now λz can be estimated from three methods: manual selections of the 3 exact data points,
     computer selection based on adjusted R sq. (ARS), and the Two-Times-Tmax (TTT) Method.
   - re-structure all codes of bear since v2.0.0.
   - add R sq. in NCA output; the original one is adjusted R sq. & changed T1/2 to T1/2(z) in NCA 
     output file
   - corrected some typo errors appearing in the output files or console display
   - rearrange the output files with better styles: such as 3-decimal digits for 'power', etc.
   - built-in the data file (.RData) required for demo purposes; user doesn't need to enter/import
     /load it again
   - manual selection of the 3 exact data points can be saved now.  user does not have to redo it 
     next time.
   - displayed the method used to estimate λz in NCA output
   - changed '0.693' to ln(2) when estimating T1/2(z) (= ln(2)/λz) in NCA algorithm
   - changed LSM-ref and LSM-test to LSMEAN-ref and LSMEAN-test, respectively, in the output file 
     of 'Statistical_Summaries.txt'
   - and many more that I just cannot remember right now...

v1.1.5
   - fixed the anova (lm) calculation due to the import of a .csv file. (thanks to Jiří Hofmann, 
     Czech Republic)
   - added Type III SS (suggested by EIMaestro)
   - changed upper bound of sample size estimation from 105% to 95% (more conservative; suggested 
     by Helmut Schütz)

v1.1.4
   - fixed the compatibility for iMac and Linux (thanks to Koji Shimamoto, Tokyo, Japan; also for 
     his testing bear on iMac)

v1.1.3-1.1.0
   - removed the function of "Sample size estimation (raw data)"; also improve the function of 
     "Sample size estimation (Log Transform)."
   - fixed the rounding error in the display of "Sample size estimation (Log transform)" (thanks
     to Helmut Schütz)
   - fixed some the format (comma, semicolon, etc.) of import data file (thanks to Helmut Schütz); users 
     now can choose their favorite formats.
   - display the PATH where bear will import from and will output the all results to.
   - display only one graphic devices (using PageDown & PageUp to change plots) (thanks to Helmut Schütz)
   - display semilog (not linear) plots when choosing data points to do linear regression for 
     λz in NCA (thanks to Helmut Schütz)
   - calculate CV_intra & CV_inter now (thanks to Helmut Schütz)
   - output both the .csv and the .RData file formats obtained from NCA; users can choose either 
     one for anova.
   - use "Tests of SUBJECT(SEQUENCE) as an error term" in ANOVA output (thanks to Helmut Schütz)
   - changed ANOVA(GLM) to ANOVA (lm) in the menu title (thanks to ElMaestro)
   
-----

References
-----
1. Hauschke D, Steinijans VW, Diletti E and Burke M. Sample size determination for bioequivalence
    assessment using a multiplicative model. J. Pharmacokin. Biopharm. 20:557-561, 1992. 
2. U.S. Dept of Health and Human Services, Food and Drug Administration, Center for Drug Evaluation and
    Research.  Guidance for industry. Statistical approaches to establishing bioequivalence, 2001.
3. Liu JP and Chow SC. Sample size determination for the twp one-sided tests procedure in bioequivalence.
    J. Pharmacokin. Biopharm. 20:101-104, 1992. 
4. Schuirmann DJ. A comparison of the two one-sided tests procedure and the power approach for assessing
    the equivalence of average bioavailability. J. Pharmacokin. Biopharm. 15:657-680, 1987. 
5. Chow SC, Liu JP. Design and Analysis of Bioavailability and Bioequivalence Studies. 2009; 3rd. ed., CRC
    Press, Chapman & Hall/CRC.
6. Hauschke D, Steinijans V, Pigeot I. Bioequivalence Studies in Drug Development: Mehtods and
    Applications, 2007; John Wiley & Sons Ltd. 
****
Output files

NCA output


..................................................

 .b                                                
 88                                                
 888oooo    .ooooo.   eoooo.   oooood8b            
 d88    88 d8(   )8b       )8b  888  8)            
 888    88 888ooo88b o8o89888   888                
 888    88 888       88(   88   888                
   o8ooo8   88bod8P   doooo8b  d888b             

 This report was generated using bear v2.6.2
 on:- Tue Feb 25 14:42:23 2014 
 running on: Windows - build 7601, Service Pack 1 
 7 x64 , x86-64 
 user id: XXXXXX

 bear is developed by Hsin-ya Lee & Yung-jin Lee.
 contact: Yung-jin Lee  
 Kaohsiung Veterans General Hospital (HY) &
 ptpc inc. (YJ), Kaohsiung, Taiwan

 bear is under license of GPL-2|GPL-3.

..................................................

 input data: Single2x2x2_demo.csv 

 -------------------  Project Settings ------------------

               Methods                  Settings
                ------										------               
              run demo                       yes
          study design           2x2x2 crossover
 single-/multiple-dose               single-dose
     lambda_z estimate          adj. R sq. (ARS)
       trapezoidal AUC        linear-up/log-down
     BE criterion (LL)               lower limit
                  dose            (demo default)
                ------  								  ------
      dosing interval*       *multiple-dose only
                Tlast*       *multiple-dose only
                ------										------                
           pAUC_start# the starting time of pAUC
             pAUC_end#      the end time of pAUC
                ------										------             
            IDP output                       yes

 --------------------------------------------------------


***(1) All BE pivotal parameters have been saved in
    -> (4073225_2014-02-25_pivotal.csv)
***(2) All misc. PK parameters have been saved in
    -> (4073225_2014-02-25_misc_pk.csv)
 Summary of Mean Conc. (SD) vs. time by Formulation:-
-----------------------------------------------------
--- Test ---

  Time  Test_Mean  Test_SD
  0.00      0.000    0.000
  0.25     43.229   20.820
  0.50    161.286   96.869
  0.75    541.643  245.173
  1.00    887.643  242.692
  1.50   1236.286  243.607
  2.00   1520.143  250.017
  3.00   1541.357  235.864
  4.00   1345.643  263.043
  8.00    762.929  198.689
 12.00    445.857  154.877
 24.00     81.707   20.864

--- Ref ---

  Time  Ref_Mean  Ref_SD
  0.00     0.000   0.000
  0.25    59.811  28.441
  0.50   121.550  66.002
  0.75   431.857 185.171
  1.00   880.786 197.139
  1.50  1260.429 200.746
  2.00  1454.000 274.581
  3.00  1408.000 274.505
  4.00  1249.500 250.827
  8.00   686.500 117.907
 12.00   399.857  70.143
 24.00    81.964  14.318
-----------------------------------------------------


------------------------<<   NCA Summary and Outputs  >>-------------------

1. Lambda_z is calculated using the adj. R squared (ARS) method
   without including the data point of (Tmax, Cmax).

2. The linear-up/log-down trapezoidal rule is used to calculate
   AUC and AUMC.

3. This is a 2x2x2 crossover, single-dose study.
---------------------------------------------------------------------------


                    Reference                      
---------------------------------------------------

<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    1  0.00    0.0     0.000     0.000
    1  0.25   36.1     4.513     1.128
    1  0.50  125.0    24.650    10.069
    1  0.75  567.0   111.150    71.037
    1  1.00  932.0   298.525   240.694
    1  1.50 1343.0   867.275   977.319
    1  2.00 1739.0  1637.775  2350.444
    1  3.00 1604.0  3308.366  6515.672
    1  4.00 1460.0  4839.237 11861.724
    1  8.00  797.0  9220.268 37269.259
    1 12.00  383.0 11480.032 59319.783
    1 24.00   72.0 13712.933 95942.940
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
    1   2   2    1    3 1604
    1   2   2    1    4 1460
    1   2   2    1    8  797
    1   2   2    1   12  383
    1   2   2    1   24   72

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9979083 
Adj. R sq. (ARS) = 0.9972111 
        lambda_z = 0.1498811 
            Cmax = 1739 
            Tmax = 2 
            Cl/F = 5.636457 
            Vd/F = 37.60619 
         T1/2(z) = 4.624648 
        AUC(0-t) = 13712.93 
      AUC(0-inf) = 14193.31 
       AUMC(0-t) = 95942.94 
     AUMC(0-inf) = 110677.2 
        MRT(0-t) = 6.99653 
      MRT(0-inf) = 7.797838 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    2  0.00    0.0     0.000     0.000
    2  0.50   69.7    17.425     8.713
    2  0.75  167.0    47.013    28.725
    2  1.00  602.0   143.137   119.631
    2  1.50 1023.0   549.388   653.756
    2  2.00 1388.0  1152.138  1731.381
    2  3.00 1481.0  2586.637  5340.881
    2  4.00 1346.0  3999.062 10273.120
    2  8.00  658.0  7844.316 32435.043
    2 12.00  336.0  9760.715 51172.900
    2 24.00   84.0 11942.070 87505.919
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
    2   1   1    1    8  658
    2   1   1    1   12  336
    2   1   1    1   24   84

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9930725 
Adj. R sq. (ARS) = 0.986145 
        lambda_z = 0.1256205 
            Cmax = 1481 
            Tmax = 3 
            Cl/F = 6.343794 
            Vd/F = 50.49968 
         T1/2(z) = 5.517788 
        AUC(0-t) = 11942.07 
      AUC(0-inf) = 12610.75 
       AUMC(0-t) = 87505.92 
     AUMC(0-inf) = 108877.3 
        MRT(0-t) = 7.327534 
      MRT(0-inf) = 8.633688 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
    3  0.00    0.0     0.000      0.000
    3  0.50   38.2     9.550      4.775
    3  0.75  277.0    48.950     33.131
    3  1.00  631.0   162.450    137.975
    3  1.50 1002.0   570.700    671.475
    3  2.00 1780.0  1266.200   1937.225
    3  3.00 1776.0  3044.199   6381.890
    3  4.00 1618.0  4739.973  12303.932
    3  8.00  782.0  9339.120  38793.846
    3 12.00  466.0 11780.834  62791.525
    3 24.00   89.7 14521.356 107797.292
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    3   2   2    1    8 782.0
    3   2   2    1   12 466.0
    3   2   2    1   24  89.7

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9998651 
Adj. R sq. (ARS) = 0.9997302 
        lambda_z = 0.1357918 
            Cmax = 1780 
            Tmax = 2 
            Cl/F = 5.269423 
            Vd/F = 38.80516 
         T1/2(z) = 5.104484 
        AUC(0-t) = 14521.36 
      AUC(0-inf) = 15181.93 
       AUMC(0-t) = 107797.3 
     AUMC(0-inf) = 128515.6 
        MRT(0-t) = 7.423362 
      MRT(0-inf) = 8.465036 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    4  0.00    0.0     0.000     0.000
    4  0.50   37.2     9.300     4.650
    4  0.75  306.0    52.200    35.663
    4  1.00  758.0   185.200   159.100
    4  1.50 1124.0   655.700   770.100
    4  2.00 1374.0  1280.200  1878.600
    4  3.00 1129.0  2527.693  4976.929
    4  4.00 1043.0  3613.125  8768.776
    4  8.00  576.0  6759.237 27026.407
    4 12.00  325.0  8513.615 44237.337
    4 24.00   75.9 10568.884 78343.313
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    4   1   1    1    8 576.0
    4   1   1    1   12 325.0
    4   1   1    1   24  75.9

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9987868 
Adj. R sq. (ARS) = 0.9975735 
        lambda_z = 0.1254065 
            Cmax = 1374 
            Tmax = 2 
            Cl/F = 7.159403 
            Vd/F = 57.08959 
         T1/2(z) = 5.527205 
        AUC(0-t) = 10568.88 
      AUC(0-inf) = 11174.12 
       AUMC(0-t) = 78343.31 
     AUMC(0-inf) = 97695.04 
        MRT(0-t) = 7.412638 
      MRT(0-inf) = 8.742978 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    5  0.00    0.0     0.000     0.000
    5  0.25   37.9     4.737     1.184
    5  0.50  171.0    30.850    13.056
    5  0.75  795.0   151.600    98.275
    5  1.00 1167.0   396.850   318.681
    5  1.50 1403.0  1039.350  1136.556
    5  2.00 1541.0  1775.350  2433.181
    5  3.00 1555.0  3323.350  6306.681
    5  4.00 1292.0  4742.792 11252.822
    5  8.00  716.0  8646.113 33909.175
    5 12.00  412.0 10846.393 55508.694
    5 24.00   80.1 13278.270 95467.064
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    5   2   2    1    8 716.0
    5   2   2    1   12 412.0
    5   2   2    1   24  80.1

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9999939 
Adj. R sq. (ARS) = 0.9999879 
        lambda_z = 0.136803 
            Cmax = 1555 
            Tmax = 3 
            Cl/F = 5.770431 
            Vd/F = 42.18057 
         T1/2(z) = 5.066753 
        AUC(0-t) = 13278.27 
      AUC(0-inf) = 13863.78 
       AUMC(0-t) = 95467.06 
     AUMC(0-inf) = 113799.4 
        MRT(0-t) = 7.189721 
      MRT(0-inf) = 8.208391 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
    6  0.00    0.0     0.000      0.000
    6  0.50  213.0    53.250     26.625
    6  0.75  799.0   179.750    114.844
    6  1.00  987.0   403.000    313.125
    6  1.50 1301.0   975.000   1047.750
    6  2.00 1756.0  1739.250   2413.625
    6  3.00 1665.0  3449.346   6681.283
    6  4.00 1529.0  5045.381  12256.072
    6  8.00  772.0  9476.268  37839.829
    6 12.00  461.0 11889.054  61554.849
    6 24.00   82.6 14529.993 104760.021
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    6   1   1    1    8 772.0
    6   1   1    1   12 461.0
    6   1   1    1   24  82.6

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9995815 
Adj. R sq. (ARS) = 0.9991631 
        lambda_z = 0.1405159 
            Cmax = 1756 
            Tmax = 2 
            Cl/F = 5.291766 
            Vd/F = 37.65956 
         T1/2(z) = 4.932875 
        AUC(0-t) = 14529.99 
      AUC(0-inf) = 15117.83 
       AUMC(0-t) = 104760 
     AUMC(0-inf) = 123051.4 
        MRT(0-t) = 7.209915 
      MRT(0-inf) = 8.139492 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    7  0.00    0.0     0.000     0.000
    7  0.25   72.3     9.037     2.259
    7  0.50   15.5    18.258     5.432
    7  0.75  403.0    70.571    44.182
    7  1.00 1114.0   260.196   221.214
    7  1.50 1566.0   930.196  1086.964
    7  2.00 1488.0  1693.530  2421.173
    7  3.00 1471.0  3173.014  6118.466
    7  4.00 1249.0  4529.988 10849.386
    7  8.00  657.0  8216.082 32181.991
    7 12.00  411.0 10313.757 52831.937
    7 24.00   82.1 12764.188 93153.649
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    7   2   2    1    8 657.0
    7   2   2    1   12 411.0
    7   2   2    1   24  82.1

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9993315 
Adj. R sq. (ARS) = 0.998663 
        lambda_z = 0.1309619 
            Cmax = 1566 
            Tmax = 1.5 
            Cl/F = 5.974122 
            Vd/F = 45.61725 
         T1/2(z) = 5.292738 
        AUC(0-t) = 12764.19 
      AUC(0-inf) = 13391.09 
       AUMC(0-t) = 93153.65 
     AUMC(0-inf) = 112986.1 
        MRT(0-t) = 7.298047 
      MRT(0-inf) = 8.437412 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    8  0.00    0.0     0.000     0.000
    8  0.25   29.2     3.650     0.912
    8  0.50  145.0    25.425    10.887
    8  0.75  282.0    78.800    46.388
    8  1.00  727.0   204.925   163.700
    8  1.50 1360.0   726.675   855.450
    8  2.00 1939.0  1551.425  2334.950
    8  3.00 1614.0  3322.959  6736.717
    8  4.00 1238.0  4740.659 11667.369
    8  8.00  648.0  8386.225 32759.539
    8 12.00  392.0 10423.513 52792.519
    8 24.00   77.3 12749.502 91040.048
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    8   1   1    1    8 648.0
    8   1   1    1   12 392.0
    8   1   1    1   24  77.3

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9997916 
Adj. R sq. (ARS) = 0.9995832 
        lambda_z = 0.1334435 
            Cmax = 1939 
            Tmax = 2 
            Cl/F = 6.002053 
            Vd/F = 44.97825 
         T1/2(z) = 5.194314 
        AUC(0-t) = 12749.5 
      AUC(0-inf) = 13328.77 
       AUMC(0-t) = 91040.05 
     AUMC(0-inf) = 109283.5 
        MRT(0-t) = 7.140675 
      MRT(0-inf) = 8.199068 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    9  0.00    0.0     0.000     0.000
    9  0.25   33.3     4.162     1.041
    9  0.50  118.0    23.075     9.456
    9  0.75  320.0    77.825    46.831
    9  1.00 1118.0   257.575   216.581
    9  1.50 1469.0   904.325  1046.956
    9  2.00 1475.0  1640.325  2335.331
    9  3.00 1200.0  2973.100  5644.368
    9  4.00 1126.0  4135.707  9707.328
    9  8.00  645.0  7588.832 29788.038
    9 12.00  377.0  9585.089 49394.976
    9 24.00   70.2 11775.348 85300.516
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
    9   2   2    1    4 1126.0
    9   2   2    1    8  645.0
    9   2   2    1   12  377.0
    9   2   2    1   24   70.2

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9999516 
Adj. R sq. (ARS) = 0.9999274 
        lambda_z = 0.1387153 
            Cmax = 1475 
            Tmax = 2 
            Cl/F = 6.513905 
            Vd/F = 46.95879 
         T1/2(z) = 4.996904 
        AUC(0-t) = 11775.35 
      AUC(0-inf) = 12281.42 
       AUMC(0-t) = 85300.52 
     AUMC(0-inf) = 101094.5 
        MRT(0-t) = 7.243991 
      MRT(0-inf) = 8.231502 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
   10  0.00    0.0     0.000     0.000
   10  0.25   55.9     6.987     1.747
   10  0.50  153.0    33.100    13.056
   10  0.75  420.0   104.725    61.994
   10  1.00 1033.0   286.350   230.494
   10  1.50 1388.0   891.600  1009.244
   10  2.00 1279.0  1557.979  2173.136
   10  3.00 1205.0  2799.611  5271.051
   10  4.00 1113.0  3958.002  9317.754
   10  8.00  770.0  7681.974 31205.283
   10 12.00  438.0 10035.868 54303.884
   10 24.00   90.1 12675.976 97815.270
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
   10   1   1    1    8 770.0
   10   1   1    1   12 438.0
   10   1   1    1   24  90.1

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9998077 
Adj. R sq. (ARS) = 0.9996154 
        lambda_z = 0.1335572 
            Cmax = 1388 
            Tmax = 1.5 
            Cl/F = 5.992243 
            Vd/F = 44.86649 
         T1/2(z) = 5.18989 
        AUC(0-t) = 12675.98 
      AUC(0-inf) = 13350.59 
       AUMC(0-t) = 97815.27 
     AUMC(0-inf) = 119057.2 
        MRT(0-t) = 7.716587 
      MRT(0-inf) = 8.917748 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time conc AUC(0-t) AUMC(0-t)
   11  0.00    0    0.000     0.000
   11  0.25   81   10.125     2.531
   11  0.50  213   46.875    18.375
   11  0.75  387  121.875    67.969
   11  1.00 1012  296.750   230.750
   11  1.50 1127  831.500   906.375
   11  2.00 1029 1370.129  1846.934
   11  3.00  889 2327.423  4228.507
   11  4.00  750 3144.954  7078.290
   11  8.00  445 5482.124 20696.475
   11 12.00  325 7009.575 35811.245
   11 24.00   54 8821.434 65334.924
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
   11   2   2    1    2 1029
   11   2   2    1    3  889
   11   2   2    1    4  750
   11   2   2    1    8  445
   11   2   2    1   12  325
   11   2   2    1   24   54

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9941775 
Adj. R sq. (ARS) = 0.9927219 
        lambda_z = 0.1312836 
            Cmax = 1127 
            Tmax = 1.5 
            Cl/F = 8.6648 
            Vd/F = 66.00064 
         T1/2(z) = 5.279771 
        AUC(0-t) = 8821.434 
      AUC(0-inf) = 9232.758 
       AUMC(0-t) = 65334.92 
     AUMC(0-inf) = 78339.77 
        MRT(0-t) = 7.406383 
      MRT(0-inf) = 8.484981 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
   12  0.00    0.0     0.000      0.000
   12  0.25  112.2    14.025      3.506
   12  0.50  169.0    49.175     17.575
   12  0.75  532.0   136.800     78.013
   12  1.00  759.0   298.175    222.762
   12  1.50 1425.0   844.175    946.888
   12  2.00 1318.0  1529.577   2144.112
   12  3.00 1542.0  2959.577   5775.112
   12  4.00 1386.0  4422.191  10881.263
   12  8.00  786.0  8653.350  35472.478
   12 12.00  511.0 11208.001  60653.448
   12 24.00   97.9 14207.959 109907.360
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
   12   1   1    1    4 1386.0
   12   1   1    1    8  786.0
   12   1   1    1   12  511.0
   12   1   1    1   24   97.9

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9987163 
Adj. R sq. (ARS) = 0.9980745 
        lambda_z = 0.1318477 
            Cmax = 1542 
            Tmax = 3 
            Cl/F = 5.350998 
            Vd/F = 40.58469 
         T1/2(z) = 5.25718 
        AUC(0-t) = 14207.96 
      AUC(0-inf) = 14950.48 
       AUMC(0-t) = 109907.4 
     AUMC(0-inf) = 133359.6 
        MRT(0-t) = 7.735619 
      MRT(0-inf) = 8.920086 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc AUC(0-t) AUMC(0-t)
   13  0.00    0.0    0.000     0.000
   13  0.25   80.4   10.050     2.513
   13  0.50  170.0   41.350    15.650
   13  0.75  385.0  110.725    62.369
   13  1.00  864.0  266.850   206.463
   13  1.50 1235.0  791.600   885.587
   13  2.00 1130.0 1382.461  1917.408
   13  3.00  983.0 2437.255  4542.145
   13  4.00  862.0 3358.431  7756.180
   13  8.00  508.0 6036.324 23353.726
   13 12.00  269.0 7540.012 38074.069
   13 24.00   75.6 9368.486 68725.818
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
   13   2   2    1    2 1130.0
   13   2   2    1    3  983.0
   13   2   2    1    4  862.0
   13   2   2    1    8  508.0
   13   2   2    1   12  269.0
   13   2   2    1   24   75.6

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9942339 
Adj. R sq. (ARS) = 0.9927923 
        lambda_z = 0.1240478 
            Cmax = 1235 
            Tmax = 1.5 
            Cl/F = 8.017696 
            Vd/F = 64.6339 
         T1/2(z) = 5.587741 
        AUC(0-t) = 9368.486 
      AUC(0-inf) = 9977.929 
       AUMC(0-t) = 68725.82 
     AUMC(0-inf) = 88265.39 
        MRT(0-t) = 7.335851 
      MRT(0-inf) = 8.846064 
-----------------------------



<< NCA Outputs:-  (Ref.)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
   14  0.00    0.0     0.000      0.000
   14  0.50   64.1    16.025      8.012
   14  0.75  406.0    74.787     50.081
   14  1.00  627.0   203.912    166.519
   14  1.50  880.0   580.663    653.269
   14  2.00 1120.0  1080.662   1543.269
   14  3.00 1598.0  2439.662   5060.269
   14  4.00 1481.0  3978.421  10436.175
   14  8.00  851.0  8526.659  36889.871
   14 12.00  492.0 11147.416  62621.147
   14 24.00  116.0 14270.148 114467.906
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
   14   1   1    1    8  851
   14   1   1    1   12  492
   14   1   1    1   24  116

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9992821 
Adj. R sq. (ARS) = 0.9985642 
        lambda_z = 0.1235951 
            Cmax = 1598 
            Tmax = 3 
            Cl/F = 5.260148 
            Vd/F = 42.55953 
         T1/2(z) = 5.608211 
        AUC(0-t) = 14270.15 
      AUC(0-inf) = 15208.7 
       AUMC(0-t) = 114467.9 
     AUMC(0-inf) = 144586.8 
        MRT(0-t) = 8.021494 
      MRT(0-inf) = 9.506851 
-----------------------------

                         Test                      
---------------------------------------------------

<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    1  0.00    0.0     0.000     0.000
    1  0.25   84.5    10.562     2.641
    1  0.50  192.0    45.125    17.281
    1  0.75  629.0   147.750    88.250
    1  1.00  873.0   335.500   256.344
    1  1.50 1246.0   865.250   941.844
    1  2.00 1633.0  1585.000  2225.594
    1  3.00 1375.0  3085.305  5954.866
    1  4.00 1006.0  4266.212 10057.341
    1  8.00  616.0  7446.702 28622.356
    1 12.00  379.0  9398.481 47825.381
    1 24.00   84.4 11752.192 86783.133
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
    1   2   1    2    4 1006.0
    1   2   1    2    8  616.0
    1   2   1    2   12  379.0
    1   2   1    2   24   84.4

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9999566 
Adj. R sq. (ARS) = 0.9999349 
        lambda_z = 0.1240003 
            Cmax = 1633 
            Tmax = 2 
            Cl/F = 6.434574 
            Vd/F = 51.89158 
         T1/2(z) = 5.589881 
        AUC(0-t) = 11752.19 
      AUC(0-inf) = 12432.83 
       AUMC(0-t) = 86783.13 
     AUMC(0-inf) = 108607.6 
        MRT(0-t) = 7.384421 
      MRT(0-inf) = 8.735547 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
    2  0.00    0.0     0.000      0.000
    2  0.25   30.1     3.763      0.941
    2  0.50  211.0    33.900     15.069
    2  0.75 1221.0   212.900    142.725
    2  1.00 1485.0   551.150    442.819
    2  1.50 1837.0  1381.650   1502.944
    2  2.00 1615.0  2243.459   3006.486
    2  3.00 1621.0  3861.459   7052.986
    2  4.00 1411.0  5375.032  12332.996
    2  8.00  763.0  9591.065  36770.589
    2 12.00  424.0 11899.053  59401.054
    2 24.00  109.0 14681.768 105821.292
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
    2   1   2    2    8  763
    2   1   2    2   12  424
    2   1   2    2   24  109

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9968462 
Adj. R sq. (ARS) = 0.9936924 
        lambda_z = 0.1196762 
            Cmax = 1837 
            Tmax = 1.5 
            Cl/F = 5.130652 
            Vd/F = 42.87113 
         T1/2(z) = 5.791856 
        AUC(0-t) = 14681.77 
      AUC(0-inf) = 15592.56 
       AUMC(0-t) = 105821.3 
     AUMC(0-inf) = 135290.7 
        MRT(0-t) = 7.207667 
      MRT(0-inf) = 8.676622 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
    3  0.00    0.0     0.000      0.000
    3  0.25   32.8     4.100      1.025
    3  0.50  181.0    30.825     13.363
    3  0.75  271.0    87.325     50.081
    3  1.00  402.0   171.450    125.737
    3  1.50  783.0   467.700    519.862
    3  2.00 2073.0  1181.700   1849.987
    3  3.00 1842.0  3136.926   6718.808
    3  4.00 1610.0  4860.324  12731.374
    3  8.00  883.0  9701.631  40815.661
    3 12.00  389.0 12112.134  64269.287
    3 24.00   75.8 14410.174 102033.145
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
    3   2   1    2    3 1842.0
    3   2   1    2    4 1610.0
    3   2   1    2    8  883.0
    3   2   1    2   12  389.0
    3   2   1    2   24   75.8

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9954759 
Adj. R sq. (ARS) = 0.9939679 
        lambda_z = 0.1536559 
            Cmax = 2073 
            Tmax = 2 
            Cl/F = 5.367872 
            Vd/F = 34.93437 
         T1/2(z) = 4.511035 
        AUC(0-t) = 14410.17 
      AUC(0-inf) = 14903.48 
       AUMC(0-t) = 102033.1 
     AUMC(0-inf) = 117083.1 
        MRT(0-t) = 7.080632 
      MRT(0-inf) = 7.856087 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    4  0.00    0.0     0.000     0.000
    4  0.25   30.8     3.850     0.963
    4  0.50  198.0    32.450    14.300
    4  0.75  395.0   106.575    63.706
    4  1.00  906.0   269.200   213.988
    4  1.50 1413.0   848.950   970.362
    4  2.00 1629.0  1609.450  2314.738
    4  3.00 1501.0  3173.577  6214.390
    4  4.00 1383.0  4614.772 11248.740
    4  8.00  713.0  8659.879 34632.514
    4 12.00  403.0 10833.240 55955.017
    4 24.00   87.2 13308.918 96867.812
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    4   1   2    2    8 713.0
    4   1   2    2   12 403.0
    4   1   2    2   24  87.2

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.999467 
Adj. R sq. (ARS) = 0.9989339 
        lambda_z = 0.1304601 
            Cmax = 1629 
            Tmax = 2 
            Cl/F = 5.723557 
            Vd/F = 43.87209 
         T1/2(z) = 5.313097 
        AUC(0-t) = 13308.92 
      AUC(0-inf) = 13977.32 
       AUMC(0-t) = 96867.81 
     AUMC(0-inf) = 118032.9 
        MRT(0-t) = 7.278414 
      MRT(0-inf) = 8.444603 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    5  0.00    0.0     0.000     0.000
    5  0.25   25.8     3.225     0.806
    5  0.50  151.0    25.325    11.050
    5  0.75  523.0   109.575    69.519
    5  1.00 1031.0   303.825   247.425
    5  1.50 1294.0   885.075   990.425
    5  2.00 1385.0  1554.825  2168.175
    5  3.00 1291.0  2892.274  5503.966
    5  4.00 1143.0  4107.773  9745.881
    5  8.00  571.0  7404.496 28769.607
    5 12.00  334.0  9172.335 46133.492
    5 24.00   83.3 11338.689 82211.929
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    5   2   1    2    8 571.0
    5   2   1    2   12 334.0
    5   2   1    2   24  83.3

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9990564 
Adj. R sq. (ARS) = 0.9981129 
        lambda_z = 0.1192508 
            Cmax = 1385 
            Tmax = 2 
            Cl/F = 6.646055 
            Vd/F = 55.73172 
         T1/2(z) = 5.812514 
        AUC(0-t) = 11338.69 
      AUC(0-inf) = 12037.22 
       AUMC(0-t) = 82211.93 
     AUMC(0-inf) = 104834.2 
        MRT(0-t) = 7.250567 
      MRT(0-inf) = 8.709175 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    6  0.00    0.0     0.000     0.000
    6  0.50  140.0    35.000    17.500
    6  0.75  643.0   132.875    86.531
    6  1.00  909.0   326.875   260.438
    6  1.50 1073.0   822.375   890.062
    6  2.00 1252.0  1403.625  1918.438
    6  3.00 1522.0  2790.625  5453.438
    6  4.00 1375.0  4237.881 10506.585
    6  8.00  795.0  8472.486 35144.725
    6 12.00  403.0 10780.386 57705.034
    6 24.00   74.1 13110.915 95884.394
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
    6   1   2    2    4 1375.0
    6   1   2    2    8  795.0
    6   1   2    2   12  403.0
    6   1   2    2   24   74.1

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9990527 
Adj. R sq. (ARS) = 0.998579 
        lambda_z = 0.1466877 
            Cmax = 1522 
            Tmax = 3 
            Cl/F = 5.875411 
            Vd/F = 40.05386 
         T1/2(z) = 4.725325 
        AUC(0-t) = 13110.92 
      AUC(0-inf) = 13616.07 
       AUMC(0-t) = 95884.39 
     AUMC(0-inf) = 111451.8 
        MRT(0-t) = 7.313326 
      MRT(0-inf) = 8.185317 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    7  0.00    0.0     0.000     0.000
    7  0.50  151.0    37.750    18.875
    7  0.75  510.0   120.375    76.125
    7  1.00 1023.0   312.000   251.812
    7  1.50 1477.0   937.000  1061.438
    7  2.00 1643.0  1717.000  2436.812
    7  3.00 1524.0  3299.754  6383.783
    7  4.00 1126.0  4614.731 10953.086
    7  8.00  577.0  7899.282 29933.788
    7 12.00  339.0  9689.287 47517.988
    7 24.00   77.3 11813.610 82724.145
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    7   2   1    2    8 577.0
    7   2   1    2   12 339.0
    7   2   1    2   24  77.3

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9997564 
Adj. R sq. (ARS) = 0.9995128 
        lambda_z = 0.1250707 
            Cmax = 1643 
            Tmax = 2 
            Cl/F = 6.435182 
            Vd/F = 51.45235 
         T1/2(z) = 5.542042 
        AUC(0-t) = 11813.61 
      AUC(0-inf) = 12431.66 
       AUMC(0-t) = 82724.14 
     AUMC(0-inf) = 102499 
        MRT(0-t) = 7.002444 
      MRT(0-inf) = 8.244994 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t) AUMC(0-t)
    8  0.00    0.0     0.000     0.000
    8  0.25   55.8     6.975     1.744
    8  0.50  132.0    30.450    11.738
    8  0.75  401.0    97.075    57.581
    8  1.00  762.0   242.450   190.425
    8  1.50 1118.0   712.450   800.175
    8  2.00 1598.0  1391.450  2018.425
    8  3.00 1615.0  2997.950  6038.925
    8  4.00 1480.0  4544.468 11440.490
    8  8.00  854.0  9098.303 37933.011
    8 12.00  386.0 11455.707 60889.513
    8 24.00   56.2 13509.554 94126.255
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
    8   1   2    2    4 1480.0
    8   1   2    2    8  854.0
    8   1   2    2   12  386.0
    8   1   2    2   24   56.2

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9983398 
Adj. R sq. (ARS) = 0.9975097 
        lambda_z = 0.1654067 
            Cmax = 1615 
            Tmax = 3 
            Cl/F = 5.776456 
            Vd/F = 34.92274 
         T1/2(z) = 4.190563 
        AUC(0-t) = 13509.55 
      AUC(0-inf) = 13849.32 
       AUMC(0-t) = 94126.25 
     AUMC(0-inf) = 104334.8 
        MRT(0-t) = 6.967384 
      MRT(0-inf) = 7.53357 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
    9  0.00    0.0     0.000      0.000
    9  0.50   57.0    14.250      7.125
    9  0.75  544.0    89.375     61.688
    9  1.00  975.0   279.250    234.562
    9  1.50 1217.0   827.250    934.688
    9  2.00 1126.0  1412.705   1957.339
    9  3.00 1759.0  2855.205   5721.839
    9  4.00 1564.0  4514.796  11514.161
    9  8.00  867.0  9240.517  38944.498
    9 12.00  510.0 11931.667  65382.213
    9 24.00  101.9 14972.615 115421.481
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time  conc
    9   2   1    2    8 867.0
    9   2   1    2   12 510.0
    9   2   1    2   24 101.9

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9999947 
Adj. R sq. (ARS) = 0.9999894 
        lambda_z = 0.1339045 
            Cmax = 1759 
            Tmax = 3 
            Cl/F = 5.084658 
            Vd/F = 37.97226 
         T1/2(z) = 5.176428 
        AUC(0-t) = 14972.61 
      AUC(0-inf) = 15733.6 
       AUMC(0-t) = 115421.5 
     AUMC(0-inf) = 139368.3 
        MRT(0-t) = 7.708839 
      MRT(0-inf) = 8.858003 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time conc  AUC(0-t) AUMC(0-t)
   10  0.00    0     0.000     0.000
   10  0.50   93    23.250    11.625
   10  0.75  769   131.000    89.531
   10  1.00 1024   355.125   289.625
   10  1.50 1135   894.875   971.250
   10  2.00 1483  1549.375  2138.375
   10  3.00 1260  2917.848  5540.983
   10  4.00 1013  4049.860  9482.459
   10  8.00  523  7014.661 26622.638
   10 12.00  373  8789.793 44174.337
   10 24.00   92 11198.726 84268.353
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
   10   1   2    2    8  523
   10   1   2    2   12  373
   10   1   2    2   24   92

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9966286 
Adj. R sq. (ARS) = 0.9932573 
        lambda_z = 0.1104668 
            Cmax = 1483 
            Tmax = 2 
            Cl/F = 6.649182 
            Vd/F = 60.19169 
         T1/2(z) = 6.274712 
        AUC(0-t) = 11198.73 
      AUC(0-inf) = 12031.56 
       AUMC(0-t) = 84268.35 
     AUMC(0-inf) = 111795.5 
        MRT(0-t) = 7.524816 
      MRT(0-inf) = 9.291854 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time   conc  AUC(0-t)  AUMC(0-t)
   11  0.00    0.0     0.000      0.000
   11  0.25   42.8     5.350      1.337
   11  0.50  136.0    27.700     11.175
   11  0.75  442.0    99.950     61.112
   11  1.00  751.0   249.075    196.425
   11  1.50 1227.0   743.575    844.300
   11  2.00 1682.0  1470.825   2145.425
   11  3.00 1517.0  3068.906   6126.879
   11  4.00 1379.0  4515.809  11179.542
   11  8.00  791.0  8747.426  35789.251
   11 12.00  548.0 11395.764  61949.353
   11 24.00   91.1 14451.410 111741.522
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
   11   2   1    2    3 1517.0
   11   2   1    2    4 1379.0
   11   2   1    2    8  791.0
   11   2   1    2   12  548.0
   11   2   1    2   24   91.1

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9951984 
Adj. R sq. (ARS) = 0.9935979 
        lambda_z = 0.1337319 
            Cmax = 1682 
            Tmax = 2 
            Cl/F = 5.286592 
            Vd/F = 39.53126 
         T1/2(z) = 5.18311 
        AUC(0-t) = 14451.41 
      AUC(0-inf) = 15132.62 
       AUMC(0-t) = 111741.5 
     AUMC(0-inf) = 133184.5 
        MRT(0-t) = 7.732223 
      MRT(0-inf) = 8.801152 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time conc  AUC(0-t) AUMC(0-t)
   12  0.00    0     0.000     0.000
   12  0.50  114    28.500    14.250
   12  0.75  419    95.125    60.656
   12  1.00  650   228.750   181.188
   12  1.50 1023   647.000   727.312
   12  2.00 1247  1214.500  1734.438
   12  3.00 1129  2401.523  4692.162
   12  4.00  987  3457.933  8377.767
   12  8.00  564  6481.435 25957.707
   12 12.00  316  8193.811 42752.635
   12 24.00   65 10098.507 74143.657
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
   12   1   2    2    3 1129
   12   1   2    2    4  987
   12   1   2    2    8  564
   12   1   2    2   12  316
   12   1   2    2   24   65

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9996462 
Adj. R sq. (ARS) = 0.9995282 
        lambda_z = 0.1361725 
            Cmax = 1247 
            Tmax = 2 
            Cl/F = 7.564409 
            Vd/F = 55.55019 
         T1/2(z) = 5.090213 
        AUC(0-t) = 10098.51 
      AUC(0-inf) = 10575.84 
       AUMC(0-t) = 74143.66 
     AUMC(0-inf) = 89105.09 
        MRT(0-t) = 7.342041 
      MRT(0-inf) = 8.425342 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
   subj  time   conc  AUC(0-t)  AUMC(0-t)
   13  0.00    0.0     0.000      0.000
   13  0.50   50.0    12.500      6.250
   13  0.75  216.0    45.750     29.625
   13  1.00  762.0   168.000    145.125
   13  1.50 1144.0   644.500    764.625
   13  2.00 1238.0  1240.000   1812.625
   13  3.00 1605.0  2661.500   5458.125
   13  4.00 1472.0  4199.041  10828.438
   13  8.00  880.0  8801.967  37660.119
   13 12.00  511.0 11517.437  64325.225
   13 24.00  112.6 14678.238 116611.742
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time   conc
   13   2   1    2    4 1472.0
   13   2   1    2    8  880.0
   13   2   1    2   12  511.0
   13   2   1    2   24  112.6

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9998215 
Adj. R sq. (ARS) = 0.9997322 
        lambda_z = 0.1285206 
            Cmax = 1605 
            Tmax = 3 
            Cl/F = 5.143251 
            Vd/F = 40.0189 
         T1/2(z) = 5.393279 
        AUC(0-t) = 14678.24 
      AUC(0-inf) = 15554.36 
       AUMC(0-t) = 116611.7 
     AUMC(0-inf) = 144455.7 
        MRT(0-t) = 7.944533 
      MRT(0-inf) = 9.287152 
----------------------------



<< NCA Outputs:-  (Test)>>
--------------------------------------------------------
 subj  time conc  AUC(0-t)  AUMC(0-t)
   14  0.00    0     0.000      0.000
   14  0.50  452   113.000     56.500
   14  0.75  600   244.500    141.000
   14  1.00  874   428.750    306.500
   14  1.50 1321   977.500   1020.375
   14  2.00 1678  1727.250   2354.750
   14  3.00 2018  3575.250   7059.750
   14  4.00 1890  5528.551  13885.638
   14  8.00 1284 11798.652  50700.251
   14 12.00  927 16181.953  94058.095
   14 24.00   34 19423.731 143246.648
--------------------------------------------------------

<< Selected data points for lambda_z calculations >>
----------------------------------------------------
 subj seq prd drug time conc
   14   1   2    2    8 1284
   14   1   2    2   12  927
   14   1   2    2   24   34

  << Final PK Parameters >>
-----------------------------
           R sq. = 0.9741755 
Adj. R sq. (ARS) = 0.9483509 
        lambda_z = 0.2381544 
            Cmax = 2018 
            Tmax = 3 
            Cl/F = 4.088622 
            Vd/F = 17.16794 
         T1/2(z) = 2.910495 
        AUC(0-t) = 19423.73 
      AUC(0-inf) = 19566.5 
       AUMC(0-t) = 143246.6 
     AUMC(0-inf) = 147272.5 
        MRT(0-t) = 7.374827 
      MRT(0-inf) = 7.526767 
----------------------------




<< PK Parameter Summaries >>

              Cmax                  
-----------------------------------
 subj Test  Ref Ratio
    1 1633 1739 0.939
    2 1837 1481 1.240
    3 2073 1780 1.165
    4 1629 1374 1.186
    5 1385 1555 0.891
    6 1522 1756 0.867
    7 1643 1566 1.049
    8 1615 1939 0.833
    9 1759 1475 1.193
   10 1483 1388 1.068
   11 1682 1127 1.492
   12 1247 1542 0.809
   13 1605 1235 1.300
   14 2018 1598 1.263
 summary     Test      Ref  Ratio
  LSMEAN 1652.214 1539.643  1.093
    S.D.  222.416  220.015  0.204
  C.V(%)   13.462   14.290 18.704

-----------------------------------

              Tmax                    
-----------------------------------
 subj Test Ref Ratio
    1  2.0 2.0 1.000
    2  1.5 3.0 0.500
    3  2.0 2.0 1.000
    4  2.0 2.0 1.000
    5  2.0 3.0 0.667
    6  3.0 2.0 1.500
    7  2.0 1.5 1.333
    8  3.0 2.0 1.500
    9  3.0 2.0 1.500
   10  2.0 1.5 1.333
   11  2.0 1.5 1.333
   12  2.0 3.0 0.667
   13  3.0 1.5 2.000
   14  3.0 3.0 1.000
summary   Test    Ref  Ratio
 LSMEAN  2.321  2.143  1.167
   S.D.  0.541  0.602  0.408
 C.V(%) 23.301 28.102 34.985

-----------------------------------

              AUC0t                     
-----------------------------------
 subj     Test       Ref Ratio
    1 11752.19 13712.933 0.857
    2 14681.77 11942.070 1.229
    3 14410.17 14521.356 0.992
    4 13308.92 10568.884 1.259
    5 11338.69 13278.270 0.854
    6 13110.92 14529.993 0.902
    7 11813.61 12764.188 0.926
    8 13509.55 12749.502 1.060
    9 14972.61 11775.348 1.272
   10 11198.73 12675.976 0.883
   11 14451.41  8821.434 1.638
   12 10098.51 14207.959 0.711
   13 14678.24  9368.486 1.567
   14 19423.73 14270.148 1.361
summary      Test       Ref  Ratio
 LSMEAN 13482.075 12513.325  1.108
   S.D.  2310.463  1848.046  0.284
 C.V(%)    17.137    14.769 25.615

-----------------------------------

             AUC0inf              
-----------------------------------
 subj     Test       Ref Ratio
    1 12432.83 14193.314 0.876
    2 15592.56 12610.751 1.236
    3 14903.48 15181.926 0.982
    4 13977.32 11174.116 1.251
    5 12037.22 13863.784 0.868
    6 13616.07 15117.827 0.901
    7 12431.66 13391.088 0.928
    8 13849.32 13328.773 1.039
    9 15733.60 12281.420 1.281
   10 12031.56 13350.593 0.901
   11 15132.62  9232.758 1.639
   12 10575.84 14950.483 0.707
   13 15554.36  9977.929 1.559
   14 19566.50 15208.697 1.287
summary      Test       Ref  Ratio
 LSMEAN 14102.497 13133.104  1.104
   S.D.  2243.522  1912.741  0.277
 C.V(%)    15.909    14.564 25.060

-----------------------------------

        (AUC0t/AUC0inf)*100        
-----------------------------------
   subj   Test    Ref   Ratio
    1 94.525 96.615  97.837
    2 94.159 94.698  99.431
    3 96.690 95.649 101.088
    4 95.218 94.584 100.671
    5 94.197 95.777  98.351
    6 96.290 96.112 100.186
    7 95.028 95.319  99.696
    8 97.547 95.654 101.979
    9 95.163 95.879  99.253
   10 93.078 94.947  98.032
   11 95.498 95.545  99.951
   12 95.487 95.033 100.477
   13 94.367 93.892 100.506
   14 99.270 93.829 105.799
summary   Test    Ref   Ratio
 LSMEAN 95.466 95.252 100.233
   S.D.  1.580  0.806   1.984
 C.V(%)  1.655  0.846   1.980

-----------------------------------

             ln(Cmax)              
-----------------------------------
 subj  Test   Ref Ratio
    1 7.398 7.461 0.992
    2 7.516 7.300 1.030
    3 7.637 7.484 1.020
    4 7.396 7.225 1.024
    5 7.233 7.349 0.984
    6 7.328 7.471 0.981
    7 7.404 7.356 1.007
    8 7.387 7.570 0.976
    9 7.473 7.296 1.024
   10 7.302 7.236 1.009
   11 7.428 7.027 1.057
   12 7.128 7.341 0.971
   13 7.381 7.119 1.037
   14 7.610 7.377 1.032
summary  Test   Ref Ratio
 LSMEAN 7.401 7.329 1.010
   S.D. 0.135 0.147 0.026
 C.V(%) 1.824 2.002 2.581

-----------------------------------

            ln(AUC0t)             
-----------------------------------
   subj  Test   Ref Ratio
    1 9.372 9.526 0.984
    2 9.594 9.388 1.022
    3 9.576 9.583 0.999
    4 9.496 9.266 1.025
    5 9.336 9.494 0.983
    6 9.481 9.584 0.989
    7 9.377 9.454 0.992
    8 9.511 9.453 1.006
    9 9.614 9.374 1.026
   10 9.324 9.447 0.987
   11 9.579 9.085 1.054
   12 9.220 9.562 0.964
   13 9.594 9.145 1.049
   14 9.874 9.566 1.032
summary  Test   Ref Ratio
 LSMEAN 9.496 9.423 1.008
   S.D. 0.164 0.159 0.027
 C.V(%) 1.729 1.689 2.676

-----------------------------------

           ln(AUC0inf)             
-----------------------------------
 subj  Test   Ref Ratio
    1 9.428 9.561 0.986
    2 9.655 9.442 1.022
    3 9.609 9.628 0.998
    4 9.545 9.321 1.024
    5 9.396 9.537 0.985
    6 9.519 9.624 0.989
    7 9.428 9.502 0.992
    8 9.536 9.498 1.004
    9 9.664 9.416 1.026
   10 9.395 9.499 0.989
   11 9.625 9.131 1.054
   12 9.266 9.612 0.964
   13 9.652 9.208 1.048
   14 9.882 9.630 1.026
summary  Test   Ref Ratio
 LSMEAN 9.543 9.472 1.008
   S.D. 0.155 0.157 0.026
 C.V(%) 1.624 1.654 2.590

-----------------------------------

            MRT0inf              
-----------------------------------
 subj  Test   Ref Ratio
    1 8.736 7.798 1.120
    2 8.677 8.634 1.005
    3 7.856 8.465 0.928
    4 8.445 8.743 0.966
    5 8.709 8.208 1.061
    6 8.185 8.139 1.006
    7 8.245 8.437 0.977
    8 7.534 8.199 0.919
    9 8.858 8.232 1.076
   10 9.292 8.918 1.042
   11 8.801 8.485 1.037
   12 8.425 8.920 0.945
   13 9.287 8.846 1.050
   14 7.527 9.507 0.792
summary  Test   Ref Ratio
 LSMEAN 8.470 8.538 0.995
   S.D. 0.558 0.431 0.083
 C.V(%) 6.591 5.051 8.315
-----------------------------------

            T1/2(z)              
-----------------------------------
   subj  Test   Ref Ratio
1     1 5.590 4.625 1.209
2     2 5.792 5.518 1.050
3     3 4.511 5.104 0.884
4     4 5.313 5.527 0.961
5     5 5.813 5.067 1.147
6     6 4.725 4.933 0.958
7     7 5.542 5.293 1.047
8     8 4.191 5.194 0.807
9     9 5.176 4.997 1.036
10   10 6.275 5.190 1.209
11   11 5.183 5.280 0.982
12   12 5.090 5.257 0.968
13   13 5.393 5.588 0.965
14   14 2.910 5.608 0.519
  summary   Test   Ref  Ratio
1  LSMEAN  5.107 5.227  0.982
2    S.D.  0.835 0.278  0.175
3  C.V(%) 16.342 5.314 17.829

-----------------------------------

              Vd/F                 
-----------------------------------
   subj   Test    Ref Ratio
1     1 51.892 37.606 1.380
2     2 42.871 50.500 0.849
3     3 34.934 38.805 0.900
4     4 43.872 57.090 0.768
5     5 55.732 42.181 1.321
6     6 40.054 37.660 1.064
7     7 51.452 45.617 1.128
8     8 34.923 44.978 0.776
9     9 37.972 46.959 0.809
10   10 60.192 44.866 1.342
11   11 39.531 66.001 0.599
12   12 55.550 40.585 1.369
13   13 40.019 64.634 0.619
14   14 17.168 42.560 0.403
  summary   Test    Ref  Ratio
1  LSMEAN 43.297 47.146  0.952
2    S.D. 11.155  9.295  0.319
3  C.V(%) 25.764 19.714 33.529

-----------------------------------

             Lambda_z            
-----------------------------------
 subj      Test       Ref     Ratio
    1 0.1240003 0.1498811 0.8273249
    2 0.1196762 0.1256205 0.9526805
    3 0.1536559 0.1357918 1.1315549
    4 0.1304601 0.1254065 1.0402980
    5 0.1192508 0.1368030 0.8716973
    6 0.1466877 0.1405159 1.0439229
    7 0.1250707 0.1309619 0.9550158
    8 0.1654067 0.1334435 1.2395266
    9 0.1339045 0.1387153 0.9653190
   10 0.1104668 0.1335572 0.8271120
   11 0.1337319 0.1312836 1.0186492
   12 0.1361725 0.1318477 1.0328016
   13 0.1285206 0.1240478 1.0360564
   14 0.2381544 0.1235951 1.9268927
summary        Test         Ref      Ratio
 LSMEAN  0.14036852 0.132962205  1.0620608
   S.D.  0.03164424 0.007264294  0.2728481
 C.V(%) 22.54368589 5.463428079 25.6904391

-----------------------------------

               Cl/F              
-----------------------------------
 subj  Test   Ref Ratio
    1 6.435 5.636 1.142
    2 5.131 6.344 0.809
    3 5.368 5.269 1.019
    4 5.724 7.159 0.799
    5 6.646 5.770 1.152
    6 5.875 5.292 1.110
    7 6.435 5.974 1.077
    8 5.776 6.002 0.962
    9 5.085 6.514 0.781
   10 6.649 5.992 1.110
   11 5.287 8.665 0.610
   12 7.564 5.351 1.414
   13 5.143 8.018 0.641
   14 4.089 5.260 0.777
summary   Test    Ref  Ratio
 LSMEAN  5.800  6.232  0.957
   S.D.  0.883  1.050  0.228
 C.V(%) 15.222 16.852 23.831

-----------------------------------
(...)

Outputs of ANOVA (lm) (same as SAS PROC GLM) or lme (same as SAS PROC MIXED)

(...)
input data: single2x2x2_stat_demo.csv 

 -------------------  Project Settings ------------------

               Methods                   Settings
                ------										 ------
              run demo                        yes
          study design            2x2x2 crossover
 single-/multiple-dose                single-dose
     lambda_z estimate           adj. R sq. (ARS)
       trapezoidal AUC         linear-up/log-down
     BE criterion (LL)                lower limit
                  dose             (demo default)
                ------										 ------
      dosing interval*        *multiple-dose only
                Tlast*        *multiple-dose only
                ------										 ------                
            AUC method                    all AUC
                ------										 ------            
           pAUC_start#  the starting time of pAUC
             pAUC_end#       the end time of pAUC
                ------										 ------             
            IDP output                        yes

 *: for multiple-dose study only.
 #: for truncated/partial AUC only.
 --------------------------------------------------------

  List of Input Data Obtained from NCA         
-----------------------------------------------
 subj drug seq prd Cmax AUC0t AUC0INF
    1    1   2   2 1739 14445   14933
    2    1   1   1 1481 12516   13185
    3    1   2   2 1780 15371   16032
    4    1   1   1 1374 11063   11668
    5    1   2   2 1555 13971   14557
    6    1   1   1 1756 15376   15964
    7    1   2   2 1566 13442   14068
    8    1   1   1 1939 13422   14001
    9    1   2   2 1475 12410   12915
   10    1   1   1 1388 13310   13985
   11    1   2   2 1127  9353    9750
   12    1   1   1 1542 15015   15757
   13    1   2   2 1235  9723   10375
   14    1   1   1 1598 14977   15916
    1    2   2   1 1633 12294   12972
    2    2   1   2 1837 15299   16209
    3    2   2   1 2073 15184   15691
    4    2   1   2 1629 13982   14650
    5    2   2   1 1385 11852   12550
    6    2   1   2 1522 13838   14343
    7    2   2   1 1643 12361   12979
    8    2   1   2 1615 14347   14681
    9    2   2   1 1759 15804   16565
   10    2   1   2 1483 11711   12544
   11    2   2   1 1682 15371   16029
   12    2   1   2 1247 10609   11093
   13    2   2   1 1605 15428   16308
   14    2   1   2 1718 17803   18870


  Class Level Information                  
-------------------------------------------------------
  Class       Levels      Values
  SUBJECT      14          1 2 3 4 5 6 7 8 9 10 11 12 13 14 
  DRUG          2          1 2 
  SEQUENCE      2          1 2 
  PERIOD        2          1 2 
-----------
DRUG 1: the Ref. product; DRUG 2: the Test product
SEQUENCE 1:  Ref. -> Test, and SEQUENCE 2: Test -> Ref.
-------------------------------------------------------


 Means                  
------------------------------------------------
 SEQUENCE    Cmax    AUC0t  AUC0INF
        1 1580.64 13804.86 14490.43
        2 1589.79 13357.79 13980.29


 SUBJECT SEQUENCE   Cmax   AUC0t AUC0INF
       1        2 1686.0 13369.5 13952.5
       2        1 1659.0 13907.5 14697.0
       3        2 1926.5 15277.5 15861.5
       4        1 1501.5 12522.5 13159.0
       5        2 1470.0 12911.5 13553.5
       6        1 1639.0 14607.0 15153.5
       7        2 1604.5 12901.5 13523.5
       8        1 1777.0 13884.5 14341.0
       9        2 1617.0 14107.0 14740.0
      10        1 1435.5 12510.5 13264.5
      11        2 1404.5 12362.0 12889.5
      12        1 1394.5 12812.0 13425.0
      13        2 1420.0 12575.5 13341.5
      14        1 1658.0 16390.0 17393.0


 PERIOD    Cmax    AUC0t  AUC0INF
      1 1632.71 13855.21 14540.71
      2 1537.71 13307.43 13930.00


 DRUG    Cmax    AUC0t  AUC0INF
    1 1539.64 13171.00 13793.29
    2 1630.79 13991.64 14677.43


*** A 2-trt,2-seq,and 2-period crossover single-dose design.

*** BE acceptance criterion: (80.000% - 125.000%.)


             Statistical analysis (ANOVA(lm))              
-----------------------------------------------------------
   Dependent Variable: Cmax                       

Analysis of Variance Table

Response: target
          Df Sum Sq Mean Sq F value Pr(>F)
prd        1  63175   63175  1.7293 0.2131
drug       1  58149   58149  1.5917 0.2311
subj(seq) 12 634325   52860  1.4469 0.2660
Residuals 12 438395   36533               

Analysis of Variance Table

Response: target
           DF    Type I SS  Mean Square  F Value  Pr > F
prd         1        63175        63175   1.7293 0.21308
drug        1        58149        58149   1.5917 0.23106
subj(seq)  12       634325        52860   1.4469 0.26599

Analysis of Variance Table

Response: target
           DF  Type III SS  Mean Square  F Value  Pr > F
prd         1        63175        63175   1.7293 0.21308
drug        1        58149        58149   1.5917 0.23106
subj(seq)  12       634325        52860   1.4469 0.26599
-----------------------------------------------------------

Tests of Hypothesis using the Type I MS for 
SUBJECT(SEQUENCE) as an error term

            Df  Sum Sq Mean Sq F value Pr(>F)
seq          1     585     585   0.013  0.911
Residuals   26 1194044   45925               

Tests of Hypothesis using the Type III MS for
SUBJECT(SEQUENCE) as an error term

            Df  Sum Sq Mean Sq F value Pr(>F)
seq          1     585     585   0.013  0.911
Residuals   26 1194044   45925               
---
Sum Sq. = Type III SS


            Statistical analysis (ANOVA(lm))               
-----------------------------------------------------------
   Dependent Variable: AUC0t                      

Analysis of Variance Table

Response: target
          Df   Sum Sq Mean Sq F value Pr(>F)
prd        1  2100484 2100484  0.3988 0.5396
drug       1  4714183 4714183  0.8950 0.3628
subj(seq) 12 35813062 2984422  0.5666 0.8308
Residuals 12 63208187 5267349               

Analysis of Variance Table

Response: target
           DF    Type I SS  Mean Square  F Value  Pr > F
prd         1      2100484      2100484  0.39877 0.53957
drug        1      4714183      4714183  0.89498 0.36279
subj(seq)  12     35813062      2984422  0.56659 0.83085

Analysis of Variance Table

Response: target
           DF  Type III SS  Mean Square  F Value  Pr > F
prd         1      2100484      2100484  0.39877 0.53957
drug        1      4714183      4714183  0.89498 0.36279
subj(seq)  12     35813062      2984422  0.56659 0.83085
-----------------------------------------------------------

Tests of Hypothesis using the Type I MS for 
SUBJECT(SEQUENCE) as an error term

            Df    Sum Sq Mean Sq F value Pr(>F)
seq          1   1399110 1399110   0.344  0.563
Residuals   26 105835916 4070612               

Tests of Hypothesis using the Type III MS for
SUBJECT(SEQUENCE) as an error term

            Df    Sum Sq Mean Sq F value Pr(>F)
seq          1   1399110 1399110   0.344  0.563
Residuals   26 105835916 4070612               
---
Sum Sq. = Type III SS


             Statistical analysis (ANOVA(lm))              
-----------------------------------------------------------
   Dependent Variable: AUC0INF                  

Analysis of Variance Table

Response: target
          Df   Sum Sq Mean Sq F value Pr(>F)
prd        1  2610804 2610804  0.4654 0.5081
drug       1  5471960 5471960  0.9754 0.3428
subj(seq) 12 38891782 3240982  0.5777 0.8226
Residuals 12 67320754 5610063               

Analysis of Variance Table

Response: target
           DF    Type I SS  Mean Square  F Value  Pr > F
prd         1      2610804      2610804  0.46538 0.50808
drug        1      5471960      5471960  0.97538 0.34284
subj(seq)  12     38891782      3240982  0.57771 0.82256

Analysis of Variance Table

Response: target
           DF  Type III SS  Mean Square  F Value  Pr > F
prd         1      2610804      2610804  0.46538 0.50808
drug        1      5471960      5471960  0.97538 0.34284
subj(seq)  12     38891782      3240982  0.57771 0.82256
-----------------------------------------------------------

Tests of Hypothesis using the Type I MS for 
SUBJECT(SEQUENCE) as an error term

            Df    Sum Sq Mean Sq F value Pr(>F)
seq          1   1821720 1821720   0.414  0.525
Residuals   26 114295300 4395973               

Tests of Hypothesis using the Type III MS for
SUBJECT(SEQUENCE) as an error term

            Df    Sum Sq Mean Sq F value Pr(>F)
seq          1   1821720 1821720   0.414  0.525
Residuals   26 114295300 4395973               
---
Sum Sq. = Type III SS


              Statistical analysis (ANOVA(lm))             
-----------------------------------------------------------
   Dependent Variable: log(Cmax)                           

Analysis of Variance Table

Response: target
          Df   Sum Sq  Mean Sq F value Pr(>F)
prd        1 0.027294 0.027294  1.7187 0.2144
drug       1 0.025583 0.025583  1.6110 0.2284
subj(seq) 12 0.255270 0.021272  1.3395 0.3103
Residuals 12 0.190565 0.015880               

Analysis of Variance Table

Response: target
           DF    Type I SS  Mean Square  F Value  Pr > F
prd         1     0.027294     0.027294   1.7187 0.21439
drug        1     0.025583     0.025583   1.6110 0.22842
subj(seq)  12     0.255270     0.021272   1.3395 0.31028

Analysis of Variance Table

Response: target
           DF  Type III SS  Mean Square  F Value  Pr > F
prd         1     0.027294     0.027294   1.7187 0.21439
drug        1     0.025583     0.025583   1.6110 0.22842
subj(seq)  12     0.255270     0.021272   1.3395 0.31028
-----------------------------------------------------------

Tests of Hypothesis using the Type I MS for 
SUBJECT(SEQUENCE) as an error term

            Df Sum Sq  Mean Sq F value Pr(>F)
seq          1 0.0000 0.000017   0.001  0.976
Residuals   26 0.4987 0.019181               

Tests of Hypothesis using the Type III MS for
SUBJECT(SEQUENCE) as an error term

            Df Sum Sq  Mean Sq F value Pr(>F)
seq          1 0.0000 0.000017   0.001  0.976
Residuals   26 0.4987 0.019181               
---
Sum Sq. = Type III SS

Intra_subj. CV = 100*sqrt(exp(MSResidual)-1) = 12.652 %
Inter_subj. CV = 100*sqrt(exp((MSSubject(seq)-MSResidual)/2)-1)
               = 5.196 %
    MSResidual = 0.01588043 
MSSubject(seq) = 0.02127254 


              Statistical analysis (ANOVA(lm))             
-----------------------------------------------------------
   Dependent Variable: log(AUC0t)     

Analysis of Variance Table

Response: target
          Df  Sum Sq  Mean Sq F value Pr(>F)
prd        1 0.01674 0.016744  0.5230 0.4834
drug       1 0.02717 0.027166  0.8485 0.3751
subj(seq) 12 0.20142 0.016785  0.5242 0.8614
Residuals 12 0.38421 0.032017               

Analysis of Variance Table

Response: target
           DF    Type I SS  Mean Square  F Value  Pr > F
prd         1     0.016744     0.016744  0.52297 0.48344
drug        1     0.027166     0.027166  0.84848 0.37513
subj(seq)  12     0.201418     0.016785  0.52424 0.86135

Analysis of Variance Table

Response: target
           DF  Type III SS  Mean Square  F Value  Pr > F
prd         1     0.016744     0.016744  0.52297 0.48344
drug        1     0.027166     0.027166  0.84848 0.37513
subj(seq)  12     0.201418     0.016785  0.52424 0.86135
-----------------------------------------------------------

Tests of Hypothesis using the Type I MS for 
SUBJECT(SEQUENCE) as an error term

            Df Sum Sq Mean Sq F value Pr(>F)
seq          1 0.0093 0.00930   0.384  0.541
Residuals   26 0.6295 0.02421               

Tests of Hypothesis using the Type III MS for
SUBJECT(SEQUENCE) as an error term

            Df Sum Sq Mean Sq F value Pr(>F)
seq          1 0.0093 0.00930   0.384  0.541
Residuals   26 0.6295 0.02421               
---
Sum Sq. = Type III SS

Intra_subj. CV = 100*sqrt(exp(MSResidual)-1) = 18.038 %
Inter_subj. CV = 100*sqrt(exp((MSSubject(seq)-MSResidual)/2)-1)
               = 0 % (due to a negative variance component)
*** the above CV_intra is estimated from lm() which may be different
    from that obtained from lme().

    MSResidual = 0.03201731 
MSSubject(seq) = 0.01678485 


              Statistical analysis (ANOVA(lm))             
-----------------------------------------------------------
   Dependent Variable: log(AUC0INF)    

Analysis of Variance Table

Response: target
          Df  Sum Sq  Mean Sq F value Pr(>F)
prd        1 0.01862 0.018624  0.6036 0.4522
drug       1 0.02842 0.028420  0.9212 0.3561
subj(seq) 12 0.19506 0.016255  0.5269 0.8595
Residuals 12 0.37023 0.030853               

Analysis of Variance Table

Response: target
           DF    Type I SS  Mean Square  F Value  Pr > F
prd         1     0.018624     0.018624  0.60364 0.45224
drug        1     0.028420     0.028420  0.92116 0.35611
subj(seq)  12     0.195062     0.016255  0.52687 0.85952

Analysis of Variance Table

Response: target
           DF  Type III SS  Mean Square  F Value  Pr > F
prd         1     0.018624     0.018624  0.60364 0.45224
drug        1     0.028420     0.028420  0.92116 0.35611
subj(seq)  12     0.195062     0.016255  0.52687 0.85952
-----------------------------------------------------------

Tests of Hypothesis using the Type I MS for 
SUBJECT(SEQUENCE) as an error term

            Df Sum Sq Mean Sq F value Pr(>F)
seq          1 0.0105 0.01055   0.448  0.509
Residuals   26 0.6123 0.02355               

Tests of Hypothesis using the Type III MS for
SUBJECT(SEQUENCE) as an error term

            Df Sum Sq Mean Sq F value Pr(>F)
seq          1 0.0105 0.01055   0.448  0.509
Residuals   26 0.6123 0.02355               
---
Sum Sq. = Type III SS

Intra_subj. CV = 100*sqrt(exp(MSResidual)-1) = 17.701 %
Inter_subj. CV = 100*sqrt(exp((MSSubject(seq)-MSResidual)/2)-1)
               = 0 % (due to a negative variance component)
*** the above CV_intra is estimated from lm() which may be different
    from that obtained from lme().

    MSResidual = 0.03085252 
MSSubject(seq) = 0.01625513 

  Pivotal Parameters of BE Study - Summary Report 
--------------------------------------------------
  Dependent Variable: log(Cmax)                   
--------------------------------------------------
        n1(R -> T) = 7 
        n2(T -> R) = 7 
          N(n1+n2) = 14 
    Lower criteria = 80.000 %
    Upper criteria = 125.000 %
          MEAN-ref = 7.330714 
         MEAN-test = 7.390714 
               MSE = 0.01588043 
                SE = 0.04763017 
Estimate(test-ref) = 0.06045413 

*** Classical (Shortest) 90% C.I. for log(Cmax) ***

        Point Estimate   CI90 lower   CI90 upper
Ratio          106.232       97.586      115.644

---------------------- Two One-Sided Tests (TOST) -------------------------

    TOST    T value   P value
 T_lower     -5.945     0.000
 T_upper     -3.425     0.003

**Interpretation:
Ho: Theta < 0.800 or  Theta > 1.25000
Ha: 0.800 < or = Theta < or = 1.25000
where Theta = Mean_Test/Mean_Ref.
Because all P values are less than 0.05,
we will reject the null hypothesis (Ho).
BE acceptance criterion is set within the range of 80.000% - 125.000%.


------------------------ Anderson-Hauck Test ------------------------------

          P value = 0.002481 

**Interpretation:
Ho: Theta < 0.800 or  Theta > 1.25000
Ha: 0.800 < or = Theta < or = 1.25000
where Theta = Mean_Test/Mean_Ref.
Because all P values are less than 0.05,
we will reject the null hypothesis (Ho).
BE acceptance criterion is set within the range of 80.000% - 125.000%.

---------------------------------------------------------------------------

             *** Intra-subject and Inter-subject Residuals ***            
--------------------------------------------------------------------------
 subj      Obs      Exp     Intra Stud_Intra     Inter Stud_Inter
    1 7.400000 7.490714 -0.090714  -1.100692  0.138571   0.727189
    2 7.300000 7.410714 -0.110714  -1.343364  0.098571   0.517279
    3 7.640000 7.620714  0.019286   0.234005  0.398571   2.091605
    4 7.230000 7.315714 -0.085714  -1.040024 -0.091429  -0.479795
    5 7.230000 7.350714 -0.120714  -1.464700 -0.141429  -0.742182
    6 7.470000 7.400714  0.069286   0.840686  0.078571   0.412324
    7 7.400000 7.440714 -0.040714  -0.494011  0.038571   0.202413
    8 7.570000 7.480714  0.089286   1.083358  0.238571   1.251964
    9 7.470000 7.445714  0.024286   0.294673  0.048571   0.254891
   10 7.240000 7.270714 -0.030714  -0.372675 -0.181429  -0.952092
   11 7.430000 7.290714  0.139286   1.690039 -0.261429  -1.371913
   12 7.340000 7.235714  0.104286   1.265362 -0.251429  -1.319435
   13 7.380000 7.310714  0.069286   0.840686 -0.221429  -1.162003
   14 7.380000 7.415714 -0.035714  -0.433343  0.108571   0.569756
--------------------------------------------------------------------------
Obs: Observed lnCmax
Exp: Expected lnCmax
Intra: Intra-subject residuals
Stud_Intra: Studentized intra-subject residuals
Inter: Inter-subject residuals
Stud_Inter: Studentized inter-subject residuals
-------------------------------------------------------------------------


            Pivotal Parameters of BE Study - Summary Report               
--------------------------------------------------------------------------
  Dependent Variable: log(AUC0t)                                          
--------------------------------------------------------------------------
        n1(R -> T) = 7 
        n2(T -> R) = 7 
          N(n1+n2) = 14 
    Lower criteria = 80.000 %
    Upper criteria = 125.000 %
          MEAN-ref = 9.473571 
         MEAN-test = 9.537857 
               MSE = 0.03201731 
                SE = 0.06763063 
Estimate(test-ref) = 0.06229652 

**************** Classical (Shortest) 90% C.I. for lnAUC0t ****************

        Point Estimate   CI90 lower   CI90 upper
Ratio          106.428       94.342      120.061

---------------------- Two One-Sided Tests (TOST) -------------------------

    TOST    T value   P value
 T_lower     -4.250     0.001
 T_upper     -2.349     0.018

**Interpretation:
Ho: Theta < 0.800 or  Theta > 1.25000
Ha: 0.800 < or = Theta < or = 1.25000
where Theta = Mean_Test/Mean_Ref.
Because all P values are less than 0.05,
we will reject the null hypothesis (Ho).
BE acceptance criterion is set within the range of 80.000% - 125.000%.

------------------------ Anderson-Hauck Test ------------------------------

          P value = 0.017829 

**Interpretation:
Ho: Theta < 0.800 or  Theta > 1.25000
Ha: 0.800 < or = Theta < or = 1.25000
where Theta = Mean_Test/Mean_Ref.
Because all P values are less than 0.05,
we will reject the null hypothesis (Ho).
BE acceptance criterion is set within the range of 80.000% - 125.000%.

---------------------------------------------------------------------------

             *** Intra-subject and Inter-subject Residuals ***            
--------------------------------------------------------------------------
 subj      Obs      Exp     Intra Stud_Intra     Inter Stud_Inter
    1 9.420000 9.555714 -0.135714  -1.151388  0.025714   0.151250
    2 9.430000 9.526429 -0.096429  -0.818092  0.021429   0.126042
    3 9.630000 9.690714 -0.060714  -0.515095  0.295714   1.739373
    4 9.310000 9.421429 -0.111429  -0.945350 -0.188571  -1.109165
    5 9.380000 9.515714 -0.135714  -1.151388 -0.054286  -0.319305
    6 9.640000 9.581429  0.058571   0.496915  0.131429   0.773055
    7 9.420000 9.520714 -0.100714  -0.854451 -0.044286  -0.260486
    8 9.500000 9.526429 -0.026429  -0.224218  0.021429   0.126042
    9 9.670000 9.605714  0.064286   0.545394  0.125714   0.739444
   10 9.500000 9.426429  0.073571   0.624174 -0.178571  -1.050346
   11 9.640000 9.445714  0.194286   1.648303 -0.194286  -1.142776
   12 9.620000 9.436429  0.183571   1.557404 -0.158571  -0.932707
   13 9.640000 9.465714  0.174286   1.478625 -0.154286  -0.907499
   14 9.610000 9.691429 -0.081429  -0.690833  0.351429   2.067081
--------------------------------------------------------------------------
Obs: Observed lnAUC0t
Exp: Expected lnAUC0t
Intra: Intra-subject residuals
Stud_Intra: Studentized intra-subject residuals
Inter: Inter-subject residuals
Stud_Inter: Studentized inter-subject residuals
-------------------------------------------------------------------------


            Pivotal Parameters of BE Study - Summary Report               
--------------------------------------------------------------------------
  Dependent Variable: log(AUC0INF)                                        
--------------------------------------------------------------------------
        n1(R -> T) = 7 
        n2(T -> R) = 7 
          N(n1+n2) = 14 
    Lower criteria = 80.000 %
    Upper criteria = 125.000 %
          MEAN-ref = 9.522857 
         MEAN-test = 9.584286 
               MSE = 0.03085252 
                SE = 0.06638902 
Estimate(test-ref) = 0.06371814 

**************** Classical (Shortest) 90% C.I. for lnAUC0INF **************

        Point Estimate   CI90 lower   CI90 upper
Ratio          106.579       94.686      119.967

---------------------- Two One-Sided Tests (TOST) -------------------------

    TOST    T value   P value
 T_lower     -4.286     0.001
 T_upper     -2.436     0.016

**Interpretation:
Ho: Theta < 0.800 or  Theta > 1.25000
Ha: 0.800 < or = Theta < or = 1.25000
where Theta = Mean_Test/Mean_Ref.
Because all P values are less than 0.05,
we will reject the null hypothesis (Ho).
BE acceptance criterion is set within the range of 80.000% - 125.000%.

------------------------ Anderson-Hauck Test ------------------------------

          P value = 0.015169 

**Interpretation:
Ho: Theta < 0.800 or  Theta > 1.25000
Ha: 0.800 < or = Theta < or = 1.25000
where Theta = Mean_Test/Mean_Ref.
Because all P values are less than 0.05,
we will reject the null hypothesis (Ho).
BE acceptance criterion is set within the range of 80.000% - 125.000%.

---------------------------------------------------------------------------

             *** Intra-subject and Inter-subject Residuals ***            
--------------------------------------------------------------------------
 subj      Obs      Exp     Intra Stud_Intra     Inter Stud_Inter
    1 9.470000 9.597143 -0.127143  -1.106594  0.011429   0.067982
    2 9.490000 9.585714 -0.095714  -0.833054  0.034286   0.203947
    3 9.660000 9.727143 -0.067143  -0.584381  0.271429   1.614582
    4 9.360000 9.470714 -0.110714  -0.963607 -0.195714  -1.164199
    5 9.440000 9.572143 -0.132143  -1.150111 -0.038571  -0.229441
    6 9.680000 9.620714  0.059286   0.515996  0.104286   0.620339
    7 9.470000 9.567143 -0.097143  -0.845487 -0.048571  -0.288925
    8 9.550000 9.565714 -0.015714  -0.136770 -0.005714  -0.033991
    9 9.720000 9.652143  0.067857   0.590598  0.121429   0.722313
   10 9.550000 9.490714  0.059286   0.515996 -0.155714  -0.926260
   11 9.680000 9.492143  0.187857   1.635023 -0.198571  -1.181194
   12 9.670000 9.485714  0.184286   1.603939 -0.165714  -0.985745
   13 9.700000 9.532143  0.167857   1.460952 -0.118571  -0.705317
   14 9.680000 9.760714 -0.080714  -0.702501  0.384286   2.285908
--------------------------------------------------------------------------
Obs: Observed lnAUC0INF
Exp: Expected lnAUC0INF
Intra: Intra-subject residuals
Stud_Intra: Studentized intra-subject residuals
Inter: Inter-subject residuals
Stud_Inter: Studentized inter-subject residuals

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Ref.:
1. Chow SC and Liu JP. Design and Analysis of Bioavailability-           
   Bioequivalence Studies. 3rd ed.,Chapman & Hall/CRC,New York (2009).
2. Schuirmann DJ. On hypothesis testing to determine if the mean of a  
   normal distribution is continued in a known interval. Biometrics,37,
   617(1981).                                                           
3. Schuirmann DJ. A comparison of the two one-sided tests procedure and the 
   power approach for assessing the equivalence of average bioavailability.
   Journal of Pharmacokinetics and Biopharmaceutics,15,657-680 (1987). 
4. Anderson S and Hauck WW.  A new procedure for testing equivalence in 
   comparative bioavailability and other clinical trials. Communications 
   in Statistics-Theory and Methods,12,2663-2692 (1983).                
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(...)


Statistical Summary output

(...)
Statistical Summaries for Pivotal Parameters of Bioequivalence (N = 14 )
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   Parameters Test_Mean  Test_SD  Ref_Mean   Ref_SD
         Cmax  1652.214  222.416  1539.643  220.015
       AUC0-t 13482.075 2310.463 12513.325 1848.046
     AUC0-inf 14102.497 2243.522 13133.104 1912.741
     ln(Cmax)     7.401    0.135     7.329    0.147
   ln(AUC0-t)     9.496    0.164     9.423    0.159
 ln(AUC0-inf)     9.543    0.155     9.472    0.157


Statistical Summaries for Pivotal Parameters of Bioequivalence (N = 14 )
(cont'd)
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   Parameters  F values  P vales   PE (%)  Lo 90%CI  Up 90%CI
         Cmax     2.070    0.176        -         -         -
       AUC0-t     1.241    0.287        -         -         -
     AUC0-inf     0.698    0.728        -         -         -
     ln(Cmax)     1.328    0.316  107.460    98.223   117.566
   ln(AUC0-t)     0.638    0.776  107.563    95.127   121.626
 ln(AUC0-inf)     0.609    0.799  107.333    95.301   120.884

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 Both F values and P values were obtained from ANOVA, respectively.
 90%CI: 90% confidence interval 
 PE(%): point estimate; = squared root of (lower 90%CI * upper 90%CI)
 Please note: no posterior power calculated. Ref.: Hoenig JM and Heisey DM. 
 The abuse of power: the pervasive fallacy of power calculations for data 
 analysis. The American Statistician 55/1, 19-24 (2001). See discussions 
 at Bebac Forum --> http://forum.bebac.at for more info.
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Summaries for misc. Pharmacokinetic Parameters (N = 14 )

                  Test                  Reference          
--------------------------------------------------------------

    Parameters   Mean     SD  CV (%)   Mean    SD  CV (%)
          Cl/F  5.800  0.883  15.222  6.232 1.050  16.852
      Lambda_z  0.140  0.032  22.544  0.133 0.007   5.463
          Tmax  2.321  0.541  23.301  2.143 0.602  28.102
       T1/2(z)  5.107  0.835  16.342  5.227 0.278   5.314
          Vd/F 43.297 11.155  25.764 47.146 9.295  19.714
       MRT0inf  8.470  0.558   6.591  8.538 0.431   5.051
 AUC.index (%) 95.466  1.580   1.655 95.252 0.806   0.846

--------------------------------------------------------------
 AUC.index (%) : (AUC0-t/AUC0-inf)*100;                       
         AUC0-t: AUC from time zero to the time of the last   
                 measurable drug plasma concentrations.       
--------------------------------------------------------------


Analysis of outliers detection and related plots

      
(...)
Intra-subject and Inter-subject Residuals                 
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 subj      Obs      Exp     Intra Stud_Intra     Inter Stud_Inter
    1 9.470745 9.598578 -0.127834  -1.054118  0.016499   0.084320
    2 9.483002 9.569159 -0.086158  -0.710458  0.007879   0.040268
    3 9.659970 9.727936 -0.067967  -0.560454  0.275215   1.406519
    4 9.362824 9.459112 -0.096287  -0.793987 -0.212216  -1.084554
    5 9.432655 9.567027 -0.134372  -1.108037 -0.046603  -0.238169
(...)
   13 9.699149 9.528906  0.170243   1.403827 -0.122846  -0.627819
   14 9.673686 9.824056 -0.150371  -1.239958  0.517673   2.645629
------------------------------------------------
Obs: Observed lnAUC0INF
Exp: Expected lnAUC0INF
Intra: Intra-subject residuals
Stud_Intra: Studentized intra-subject residuals
Inter: Inter-subject residuals
Stud_Inter: Studentized inter-subject residuals
**Ref: Chow SC and Liu JP. Design and Analysis of Bioavailability-         
Bioequivalence Studies. 3rd ed., Chapman & Hall/CRC, New York (2009).    
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(...)

****************************************************************************
Analysis of Outlier Detection
****************************************************************************

Test for Normality Assumption  (Shapiro-Wilk)            
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            Parameter    Test P value
    lnCmax_Stud_Intra 0.91950  0.2163
    lnCmax_Stud_Inter 0.94222  0.4475
   lnAUC0t_Stud_Intra 0.90395  0.1287
   lnAUC0t_Stud_Inter 0.87428  0.0482
 lnAUC0INF_Stud_Intra 0.88242  0.0629
 lnAUC0INF_Stud_Inter 0.87166  0.0443

-------------------------------------------------
Stud_Intra: studentized intra-subject residuals
Stud_Inter: studentized inter-subject residuals
-------------------------------------------------
**Interpretation:
  The normality of the studentized intra-subject residuals and the
studentized inter-residuals was examined using the test of Shapiro-Wilk.
If a P value is more than 0.05, we will fail to reject the normal        
assumption hypothesis.                                                   

**Ref: Chow SC and Liu JP. Design and Analysis of Bioavailability-     
Bioequivalence Studies. 3rd ed., Chapman & Hall/CRC, New York (2009).
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Test for Normality Assumption  (Pearson)            
--------------------------------------------------------------------------
 Parameter     Test P value
    lnCmax -0.27517  0.3410
   lnAUC0t -0.50957  0.0627
 lnAUC0INF -0.49037  0.0750

-------------------------------------------------
Pearson: Pearson's correlation coefficient
-------------------------------------------------
**Interpretation:
  Either Pearson correlation coefficient or Spearman's rank correlation 
coefficient is used to examine the assumption of independence between  
intra- and inter-subject variabilities.  Thus, if a P value is more than
0.05, there is no evidence to suggest that the assumption is not true.  

**Ref: Chow SC and Liu JP. Design and Analysis of Bioavailability-         
Bioequivalence Studies. 3rd ed., Chapman & Hall/CRC, New York (2009).    
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Test for Normality Assumption  (Spearman)            
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 Parameter     Test P value
    lnCmax -0.37143  0.1917
   lnAUC0t -0.41099  0.1458
 lnAUC0INF -0.43736  0.1198

-------------------------------------------------
Spearman: Spearman's rank correlation coefficient
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  Hotelling T^2 with Chi-square test 
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 subj    Cmax P value  lnCmax P value
    1 0.92550 0.62955 0.87200 0.64662
    2 0.89118 0.64045 0.85392 0.65249
    3 6.64221 0.03611 5.56026 0.06203
    4 0.59125 0.74407 0.52257 0.77006
(...)
   13 2.26697 0.32191 2.47282 0.29042
   14 3.46892 0.17650 3.00119 0.22300

 subj    AUC0t P value  lnAUC0t P value
    1  0.91572 0.63263  0.88935 0.64103
    2  0.22251 0.89471  0.24628 0.88414
    3  1.59543 0.45036  1.60903 0.44730
    4  1.30339 0.52116  1.16065 0.55972
    5  0.93873 0.62540  1.06203 0.58801
(...)
   11  5.47893 0.06460  6.45905 0.03958
   12  3.00762 0.22228  3.68832 0.15816
   13  4.16647 0.12453  4.54473 0.10307
   14 36.99471 0.00000 23.07303 0.00001

 subj  AUC0INF P value lnAUC0INF P value
    1  0.78347 0.67588   0.76142 0.68338
    2  0.29003 0.86501   0.32987 0.84795
    3  1.51641 0.46851   1.53149 0.46499
    4  1.26269 0.53188   1.12343 0.57023
(...)
   12  3.36757 0.18567   4.09229 0.12923
   13  3.93636 0.13971   4.18647 0.12329
   14 36.26111 0.00000  23.50638 0.00001

-------------------------------------------------
**Interpretation: If subjects have relatively BIG T^2 values which
 cause P value less than 0.05, these subject may be outlying subjects.

Ref.:
1. Liu JP and Weng CS. Detection of outlying data in bioavailability-
   bioequivalence studies. Statistics in Medicine, 10, 1375-1389(1991).
2. Chow SC and Liu JP. Design and Analysis of Bioavailability-       
   Bioequivalence Studies. 3rd ed., Chapman & Hall/CRC, New York (2009).
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  Test for Equality of Intra-subject variabilities between formulations  
--------------------------------------------------------------------------
               Parameter     Test P value
          lnCmax_Pearson -0.08448  0.7740
    lnCmax_Pitman_Morgan  0.08626  0.7740
         lnCmax_Spearman -0.10769  0.7156
         lnAUC0t_Pearson  0.11349  0.6993
   lnAUC0t_Pitman_Morgan  0.15657  0.6993
        lnAUC0t_Spearman -0.07692  0.7966
       lnAUC0INF_Pearson  0.07876  0.7890
 lnAUC0INF_Pitman_Morgan  0.07490  0.7890
      lnAUC0INF_Spearman -0.05934  0.8438

-------------------------------------------------
**Interpretation:
  The standard 2*2*2 crossover design was assumed that intra-subject     
variabilities for  the Test and the Reference formulations are the same.   
Thus, if the intra-subject variabilities between formulations are different,
equivalence in average bioavailabilities between formulations does not   
imply that the two formulations are therapeutically equivalent and       
interchangeable.                                                         
  We use use both parametric (Pitman-Morgan's adjusted F test and Pearson
correlation coefficient) and nonparametric test (Spearman's rank correlation
coefficient) for testing equality of intra-subject variabilities between
formulations.  If a P value is less than 0.05, we may reject the null    
hypothesis of equality in intra-subject variabilities between formulations.

**Ref.:
 1. Chow SC and Liu JP. Design and Analysis of Bioavailability-           
    Bioequivalence Studies. 3rd ed., Chapman & Hall/CRC, New York (2009). 
 2. Haynes JD. Statistical simulation study of new proposed uniformity    
    requirements for bioequivalency studies. Journal of Pharmaceutical    
    Sciences, 70, 673-675 (1981).                                         
 3. McCulloch CE. Tests for equality of variances with paired data.       
    Communications in Statistics-Theory and Methods, 16, 1377-1391 (1987). 
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Point and Interval Estimation of Inter- and Intra-subject Variability 
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            Parameter Point_Estimate CI95_lower CI95_upper
         lnCmax_intra          0.018      0.009      0.049
         lnCmax_inter          0.003     -0.009      0.025
    lnCmax_intraclass          0.141     -0.423      0.626
          lnCmax_prob        0.31554          -          -
        lnAUC0t_intra          0.037      0.019      0.100
        lnAUC0t_inter         -0.006     -0.024      0.019
   lnAUC0t_intraclass         -0.192     -0.657      0.379
         lnAUC0t_prob        0.74431          -          -
      lnAUC0INF_intra          0.034      0.018      0.094
      lnAUC0INF_inter         -0.006     -0.023      0.016
 lnAUC0INF_intraclass         -0.211     -0.669      0.362
       lnAUC0INF_prob        0.76603          -          -

-------------------------------------------------
intra: intra-subject variability
inter: inter-subject variability
intraclass: intraclass correlation
prob: the probability for obtaining a negative estimate of inter-subject
      variability
CI95: 95% confidence interval
-------------------------------------------------
**Interpretation:
1. Prior information of inter- and intra- subject variabilities can be used  
   for sample size determination.                                           
2. Intraclass correlation shows the precision of intra-subject variability.
   A negative estimate indicates that inter- and intra- variability on the  
   subjects are negatively correlated.                                      
3. Searle(1971) provided a formula for calculation of the probability for 
   obtaining a negative estimate of inter-subject variability. In addition,  
   a negative estimate may indicate that the general model is incorrect or  
   sample size is too small.  Thus, prob provides the probability for     
   obtaining a negative estimate.  If P value is less than 0.05, the chance 
   of obtaining a negative estimate is negligible.                         

**Ref.:
 1. Chow SC and Liu JP. Design and Analysis of Bioavailability-           
    Bioequivalence Studies. 3rd ed., Chapman & Hall/CRC, New York (2009). 
 2. Searle SR. Linear Models. John Wiley & Sons, New York (1971).         
 3. Snedecor GW and Cochran WG. Statistical Methods. 7th ed.,  Iowa State 
    University Press, Ames, IA (1980).                                    
 4. Hocking RP. The Analysis of Linear Models. Brooks/Cole, Monterey, CA  
    (1985).                                                               
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Quantiles for Boxplots (intrasubj) 
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       Quantile lnCmax_Estimate lnAUC0t_Estimate lnAUC0INF_Estimate
100%   Max 100%      1.58859255        1.5645553          1.5930108
99%         99%      1.58859255        1.5645553          1.5930108
95%         95%      1.58859255        1.5645553          1.5930108
90%         90%      1.33567805        1.5411660          1.5730580
75%      Q3 75%      0.93884707        0.6873813          0.6338556
50%  Median 50%     -0.04497309       -0.2919099         -0.3120133
25%      Q1 25%     -1.06347243       -0.7792669         -0.8037332
10%         10%     -1.21551649       -1.1020990         -1.1080370
5%           5%     -1.36618557       -1.3727270         -1.2399578
1%           1%     -1.36618557       -1.3727270         -1.2399578
0%       Min 0%     -1.36618557       -1.3727270         -1.2399578
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Quantiles for Boxplots (intersubj) 
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       Quantile lnCmax_Estimate lnAUC0t_Estimate lnAUC0INF_Estimate
100%   Max 100%       1.9874004        2.6115077          2.6456287
99%         99%       1.9874004        2.6115077          2.6456287
95%         95%       1.9874004        2.6115077          2.6456287
90%         90%       1.2193723        1.4261550          1.4065194
75%      Q3 75%       0.6865071        0.4745906          0.4247924
50%  Median 50%       0.2170634       -0.2231420         -0.1773188
25%      Q1 25%      -1.0106795       -0.9256405         -0.9399940
10%         10%      -1.3212861       -1.0355480         -0.9965418
5%           5%      -1.3490155       -1.0729741         -1.0845536
1%           1%      -1.3490155       -1.0729741         -1.0845536
0%       Min 0%      -1.3490155       -1.0729741         -1.0845536
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