Change Log (Sept. 21, 2009) & References
bear
v2.4.1
(uploaded to CRAN on Sept. 18, 2009) -
the
data analysis tool for average
bioequivalence
(ABE)
and bioavailability (BA)
in
R
originally created by Hsin-ya Lee and Yung-jin Lee (mobilePK@gmail.com)
Chunghwa Pharmaceutical Research Foundation (YJ),
Introduction
This package was designed to analyze average bioequivalence (ABE)
data from noncompartmental analysis (NCA) to ANOVA (using lm() for a 2x2x2
crossover; otherwise lme()). 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 got 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 one of
R
packages. Thus, users have to
download and install
R first, and then run it.
Under R Console, users can click
"Packages"
from the menu then ->"Install package(s)..." --> select a CRAN mirror site near
you and you will see the list of currently available
R packages.
Just select "bear" from the list and click "OK" to start
installation. Then it's done! If you want to
upgrade from
previous version of bear when a new version is released, please go the menu and
click
"Packages", and then select "Update packages...". then
select a CRAN mirror site near you and click "OK". Done! Pretty easy to upgrade.
If you're running Linux PC or Mac OS X, you may not see the menu
but
the R Console. You can read this
R
Installation and Administration (pdf ) for detailed information. You
can also type help("INSTALL") or help("install.packages") in R Console for
information on how to install packages from this directory. Don't worry
about this. You only need
to do this once. After these installation, you now can run stab by simply typing
"library(stab) (enter)"
under R Console.
Remove bear: Simply go to the directory of R where you
installed and then go to the sub-directory of /library, delete bear.
Methods
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
.
How to use it (To
install and use bear correctly, please
read this section first.)
installation: For how to install bear, please read
this
for more detailed information about how to use R. Users have to follow the installation procedures
as indicated to correctly install bear. This is because bear
will call some other R packages (reshape,
nlme,
sciplot and more) when running. These packages will be
installed automatically when you're installing bear
at the same time. Bear was complied and tested under R v2.9.2.
So, please install R with the latest version. Data input: The fastest and the easist 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
OpenOffice
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 (like NCA using
WinNonlin and
ANOVA with
SAS).
Sample size estimationn
|
<<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 (...) |
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
1. Users must follow the column sequence as shown above; However, the column name can be different..
2. 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.
3. In coding "tmt" or "drug", please set drug or tmt ="1" for the Reference, and
drug or tmt
= "2" for the Test.
4. All data should be entered only as the numerical
format, not the text format (not double quote!);
5. When a drug plasma/serum/blood concentration is near the end of sampling time and is below LLOQ,
this value (entire row) should be deleted; otherwise, it can affect the estimation of λz (auto mode), and
6. Please also delete the entire row for a missing sample or a missing data.
Do not enter zero (0) for missing
data.
Output files
NCA output
~~~ This report is generated using bear v2.3.0 for R. ~~~
Authors: Hsin-ya Lee, Yung-jin Lee
College of Pharmacy, Kaohsiung Medical University
Kaohsiung, Taiwan 80708
E-mail: hsinyalee@gmail.com,mobilePK@gmail.com
bear's website: http://pkpd.kmu.edu.tw/bear
R website: http://www.r-project.org
---------------------------------------------------
Lambda_z is calculated using the Akaike information criterion (AIC) method
without including the data point of (Tmax, Cmax).
--------------------------------------------------------------------------
Reference
---------------------------------------------------
<< NCA Outputs:- Subj.# 1 , Seq 2 , Prd 2 (Ref.)>>
--------------------------------------------------------------------------
subj time conc AUC(0-t) AUMC(0-t)
1 1 0.00 0.0 0.000 0.000
2 1 0.25 36.1 4.513 1.128
3 1 0.50 125.0 24.650 10.069
4 1 0.75 567.0 111.150 71.037
5 1 1.00 932.0 298.525 240.694
6 1 1.50 1343.0 867.275 977.319
7 1 2.00 1739.0 1637.775 2350.444
8 1 3.00 1604.0 3309.275 6495.444
9 1 4.00 1460.0 4841.275 11821.444
10 1 8.00 797.0 9355.275 36253.444
11 1 12.00 383.0 11715.275 58197.444
12 1 24.00 72.0 14445.275 96141.444
--------------------------------------------------
subj seq prd drug time conc code
8 1 2 2 1 3 1604 2
9 1 2 2 1 4 1460 2
10 1 2 2 1 8 797 2
11 1 2 2 1 12 383 2
12 1 2 2 1 24 72 2
----------------------------
R sq. = 0.9979083
Adj. R sq. (ARS) = 0.997211
AIC = -25.53606
lambda_z = 0.1498811
Cmax = 1739
Tmax = 2
Cl/F = 5.359898
Vd/F = 35.76101
T1/2(z) = 4.624648
AUC(0-t) = 14445.27
AUC(0-inf) = 14925.66
AUMC(0-t) = 96141.44
AUMC(0-inf) = 110875.7
MRT(0-t) = 6.655563
MRT(0-inf) = 7.428529
----------------------------
<< NCA Outputs:- Subj.# 1 , Seq 2 , Prd 3 (Ref.)>>
--------------------------------------------------------------------------
subj time conc AUC(0-t) AUMC(0-t)
1 1 0.00 0 0.000 0.000
2 1 0.25 29 3.625 0.906
3 1 0.50 125 22.875 9.625
4 1 0.75 567 109.375 70.594
5 1 1.00 800 280.250 223.750
6 1 1.50 1343 816.000 927.375
7 1 2.00 1650 1564.250 2256.000
8 1 3.00 1604 3191.250 6312.000
9 1 4.00 1432 4709.250 11582.000
10 1 8.00 600 8773.250 32638.000
11 1 12.00 383 10739.250 51430.000
12 1 24.00 69 13451.250 88942.000
<>
--------------------------------------------------
subj seq prd drug time conc code
20 1 2 3 1 3 1604 3
21 1 2 3 1 4 1432 3
22 1 2 3 1 8 600 3
23 1 2 3 1 12 383 3
24 1 2 3 1 24 69 3
(...)
|
Outputs of ANOVA (lm) (same as SAS PROC GLM) or lme (same as SAS PROC MIXED)
(...) Data Summary of BA measurement
--------------------------------------------------------------------------
subj drug seq prd Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 1 2 2 1739 14445.27 14925.656 7.461066 9.578123 9.610837
2 2 1 1 1 1481 12516.14 13134.553 7.300473 9.434774 9.483002
3 3 1 2 2 1780 15371.40 15999.744 7.484369 9.640264 9.680328
4 4 1 1 1 1374 11063.10 11647.240 7.225481 9.311371 9.362824
5 5 1 2 2 1555 13971.45 14556.963 7.349231 9.544771 9.585825
6 6 1 1 1 1756 15376.35 15950.591 7.470794 9.640586 9.677251
(...)
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 lnCmax lnAUC0t lnAUC0INF
1 1 1602.071 14109.25 14713.39 7.37045 9.538976 9.582570
2 2 1589.786 13357.85 13970.66 7.36052 9.487205 9.532541
SUBJECT SEQUENCE Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 2 1686.0 13369.59 13950.10 7.429620 9.497491 9.540791
2 2 1 1659.0 13907.39 14645.04 7.408181 9.535147 9.586510
3 3 2 1926.5 15277.70 15838.53 7.560560 9.634131 9.670149
4 4 1 1501.5 12522.38 13133.29 7.310602 9.428436 9.476462
5 5 2 1470.0 12911.54 13523.30 7.291343 9.462496 9.509240
6 6 1 1639.0 14607.04 15146.74 7.399287 9.587870 9.624130
(...)
PERIOD Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 1632.714 13855.25 14531.50 7.390958 9.52988 9.577774
2 2 1559.143 13611.85 14152.54 7.340011 9.49630 9.537337
DRUG Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 1539.643 13171.14 13781.86 7.32951 9.474286 9.519987
2 2 1652.214 14295.97 14902.19 7.40146 9.551895 9.595125
Statistical analysis (ANOVA(lm), 90%CI...)
--------------------------------------------------------------------------
Dependent Variable: lnCmax
Type I SS
Analysis of Variance Table
Response: lnCmax
Df Sum Sq Mean Sq F value Pr(>F)
seq 1 0.000017 0.000017 0.0011 0.9743
prd 1 0.027294 0.027294 1.7187 0.2144
drug 1 0.025583 0.025583 1.6110 0.2284
seq:subj 12 0.255270 0.021273 1.3395 0.3103
Residuals 12 0.190565 0.015880
Type III SS
Single term deletions
Model:
lnCmax ~ seq + subj:seq + prd + drug
Df Sum of Sq RSS AIC F value Pr(F)
0.191 -107.719
prd 1 0.027 0.218 -105.971 1.7187 0.2144
drug 1 0.026 0.216 -106.192 1.6110 0.2284
seq:subj 12 0.255 0.446 -107.920 1.3395 0.3103
Tests of Hypothesis for SUBJECT(SEQUENCE) as an error term
Error: subj
Df Sum Sq Mean Sq F value Pr(>F)
prd:drug 1 0.000017 0.000017 8e-04 0.9778
Residuals 12 0.255270 0.021273
Error: Within
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
Residuals 12 0.190565 0.015880
Intra_subj. CV = 100*sqrt(abs(exp(MSResidual)-1)) = 13.4025 %
Inter_subj. CV = 100*sqrt(abs(exp((MSSubject(seq)-MSResidual)/2)-1)) = 5.4059 %
MSResidual = 0.01780339
MSSubject(seq) = 0.0236397
(...)
(...) Statistical analysis (lme, 90%CI...) - replicate BE study
--------------------------------------------------------------------------
Dependent Variable: lnCmax
Linear mixed-effects model fit by REML
Data: TotalData
AIC BIC logLik
-45.23532 -29.93913 30.61766
Random effects:
Formula: ~1 | subj
(Intercept) Residual
StdDev: 0.07591504 0.096394
Fixed effects: lnCmax ~ seq + prd + drug
Value Std.Error DF t-value p-value
(Intercept) 7.372429 0.04264797 38 172.86705 0.0000
seq2 -0.009494 0.04806556 12 -0.19753 0.8467
prd2 -0.062443 0.03643351 38 -1.71389 0.0947
prd3 0.017159 0.03643351 38 0.47097 0.6404
prd4 0.027577 0.03643351 38 0.75691 0.4538
drug2 0.046554 0.02576238 38 1.80705 0.0787
Correlation:
(Intr) seq2 prd2 prd3 prd4
seq2 -0.564
prd2 -0.427 0.000
prd3 -0.427 0.000 0.500
prd4 -0.427 0.000 0.500 0.500
drug2 -0.302 0.000 0.000 0.000 0.000
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-1.9923453 -0.4759801 0.1513995 0.5975501 1.5432336
Number of Observations: 56
Number of Groups: 14
Type I Tests of Fixed Effects
numDF denDF F-value p-value
(Intercept) 1 38 94465.47 <.0001
seq 1 12 0.04 0.8467
prd 3 38 2.45 0.0785
drug 1 38 3.27 0.0787
Type III Tests of Fixed Effects
numDF denDF F-value p-value
(Intercept) 1 38 29883.017 <.0001
seq 1 12 0.039 0.8467
prd 3 38 2.449 0.0785
drug 1 38 3.265 0.0787
(...) BE Summary Report
--------------------------------------------------------------------------
Dependent Variable: lnCmax
--------------------------------------------------------------------------
n1(R=>T) = 7
n2(T=>R) = 7
N(n1+n2) = 14
Lower criteria = 80 %
Upper criteria = 125 %
MEAN-ref = 7.32951
MEAN-test = 7.40146
MSE = 0.01780339
SE = 0.05043155
Diff. (test-ref) = 0.07195028
**************** Classical (Shortest) 90% C.I. for lnCmax ****************
CI90_lower Point_estimated CI90_upper
1 98.223 107.460 117.566
---------------------- Two One-Sided Tests (TOST) -------------------------
TOST T value P value
1 T_lower -5.8514 0.0000
2 T_upper -2.9980 0.0056
**Interpretation:
Ho: Theta =< 0.8 or Theta >= 1.25
Ha: 0.8 < Theta < 1.25
Theta = Mean_test/Mean_ref
Because all P values are less than 0.05, we will reject the null hypothesis (Ho).
BE acceptance range is set at 80 % - 125 % .
------------------------ Anderson-Hauck Test ------------------------------
P value = 0.005515
**Interpretation:
Ho: Theta =< 0.8 or Theta >= 1.25
Ha: 0.8 < Theta < 1.25
Theta = Mean_test/Mean_ref
Because all P values are less than 0.05, we will reject the null hypothesis (Ho).
BE acceptance range is set at 80 % - 125 % .
---------------------------------------------------------------------------
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).
--------------------------------------------------------------------------
(...)
(...) Data Summary of BA measurement
--------------------------------------------------------------------------
subj drug seq prd Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 1 2 2 1739 14445 14933 7.46 9.58 9.61
2 2 1 1 1 1481 12516 13185 7.30 9.43 9.49
3 3 1 2 2 1780 15371 16032 7.48 9.64 9.68
4 4 1 1 1 1374 11063 11668 7.23 9.31 9.36
5 5 1 2 2 1555 13971 14557 7.35 9.54 9.59
(...)
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 4 1 2 3 4
--------
DRUG 1: the Ref. product; DRUG 2: the Test product
--------------------------------------------------
Means
--------------------------------------------------------------------------
SEQUENCE Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 1580.286 13793.89 14472.89 7.357143 9.520714 9.568571
2 2 1591.214 13351.86 13970.64 7.358929 9.483929 9.529643
SUBJECT SEQUENCE Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 2 1678.25 13195.75 13770.00 7.4225 9.4825 9.5225
2 2 1 1656.50 13910.75 14725.00 7.4050 9.5325 9.5875
3 3 2 1931.50 15348.75 15931.00 7.5600 9.6375 9.6725
4 4 1 1496.50 12468.00 13081.50 7.3050 9.4225 9.4675
5 5 2 1467.75 12826.00 13465.00 7.2875 9.4525 9.5050
(...)
PERIOD Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 1632.714 13856.64 14540.71 7.391429 9.529286 9.580000
2 2 1537.714 13307.43 13930.00 7.330000 9.482143 9.527143
3 3 1538.500 13294.71 13898.86 7.323571 9.475000 9.518571
4 4 1634.071 13832.71 14517.50 7.387143 9.522857 9.570714
DRUG Cmax AUC0t AUC0INF lnCmax lnAUC0t lnAUC0INF
1 1 1537.536 13155.25 13764.75 7.326071 9.470000 9.517143
2 2 1633.964 13990.50 14678.79 7.390000 9.534643 9.581071
(...) |
Statistical Summary output
Statistical Summaries for Pivotal Parameters of Bioequivalence Study (N= 14)
--------------------------------------------------------------------------
Parameters Test_Mean Test_SD Ref_Mean Ref_SD
1 Cmax 1662.536 181.868 1589.643 186.703
2 AUC0-t 13742.526 1945.507 13124.974 1994.792
3 AUC0-inf 14479.338 2230.335 13721.289 2068.855
4 ln(Cmax) 7.411 0.106 7.365 0.120
5 ln(AUC0-t) 9.519 0.143 9.470 0.163
6 ln(AUC0-inf) 9.570 0.152 9.515 0.161
Statistical Summaries for Pivotal Parameters of Bioequivalence Study (N= 14)
--------------------------------------------------------------------------
Parameters CI90_lower Point_estimated CI90_upper
1 ln(Cmax) 100.312 104.765 109.416
2 ln(AUC0-t) 98.529 104.875 111.629
3 ln(AUC0-inf) 99.080 105.534 112.409
-------------------------------------------------------------------------
CI90: 90% confidence interval
--------------------------------------------------------------------------
Summaries for Misc. Pharmacokinetic Parameters (N= 14 )
Test Reference
------------------------------------------------------
Parameters Mean SD CV Mean SD CV
1 Cl/F 5.654 0.855 15.124 5.975 1.031 17.258
2 Lambda_z 0.134 0.015 11.386 0.136 0.007 5.173
3 Tmax 2.321 0.541 23.301 2.161 0.585 27.080
4 T1/2(z) 5.268 0.672 12.757 5.119 0.265 5.185
5 Vd/F 42.676 6.746 15.808 44.214 8.550 19.337
6 MRT0inf 8.200 0.824 10.054 8.027 0.397 4.951
7 AUCratio 95.053 1.811 1.905 95.634 0.685 0.717
-----------------------------------------------------
AUCratio: (AUC0-t/AUC0-inf)*100
----------------------------------------------------- |
Analysis of outliers detection and related plots
(...)Intra-subject and Inter-subject Residuals
--------------------------------------------------------------------------
subj Obs Exp Intra Stud_Intra Inter Stud_Inter
1 1 9.470745 9.598578 -0.127834 -1.054118 0.016499 0.084320
2 2 9.483002 9.569159 -0.086158 -0.710458 0.007879 0.040268
3 3 9.659970 9.727936 -0.067967 -0.560454 0.275215 1.406519
4 4 9.362824 9.459112 -0.096287 -0.793987 -0.212216 -1.084554
5 5 9.432655 9.567027 -0.134372 -1.108037 -0.046603 -0.238169
(...)
13 13 9.699149 9.528906 0.170243 1.403827 -0.122846 -0.627819
14 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).
---------------------------------------------------------------------
(...)
****************************************************************************
Analysis of Outlier Detection
****************************************************************************
Test for Normality Assumption (Shapiro-Wilk)
--------------------------------------------------------------------------
Parameter Test P value
1 lnCmax_Stud_Intra 0.91950 0.2163
2 lnCmax_Stud_Inter 0.94222 0.4475
3 lnAUC0t_Stud_Intra 0.90395 0.1287
4 lnAUC0t_Stud_Inter 0.87428 0.0482
5 lnAUC0INF_Stud_Intra 0.88242 0.0629
6 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).
---------------------------------------------------------------------
Test for Normality Assumption (Pearson)
--------------------------------------------------------------------------
Parameter Test P value
1 lnCmax -0.27517 0.3410
2 lnAUC0t -0.50957 0.0627
3 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).
-------------------------------------------------------------------------
Test for Normality Assumption (Spearman)
--------------------------------------------------------------------------
Parameter Test P value
1 lnCmax -0.37143 0.1917
2 lnAUC0t -0.41099 0.1458
3 lnAUC0INF -0.43736 0.1198
-------------------------------------------------
Spearman: Spearman's rank correlation coefficient
-------------------------------------------------------------------------
Hotelling T^2 with Chi-square test
--------------------------------------------------------------------------
subj Cmax P value lnCmax P value
1 1 0.92550 0.62955 0.87200 0.64662
2 2 0.89118 0.64045 0.85392 0.65249
3 3 6.64221 0.03611 5.56026 0.06203
4 4 0.59125 0.74407 0.52257 0.77006
(...)
13 13 2.26697 0.32191 2.47282 0.29042
14 14 3.46892 0.17650 3.00119 0.22300
subj AUC0t P value lnAUC0t P value
1 1 0.91572 0.63263 0.88935 0.64103
2 2 0.22251 0.89471 0.24628 0.88414
3 3 1.59543 0.45036 1.60903 0.44730
4 4 1.30339 0.52116 1.16065 0.55972
5 5 0.93873 0.62540 1.06203 0.58801
(...)
11 11 5.47893 0.06460 6.45905 0.03958
12 12 3.00762 0.22228 3.68832 0.15816
13 13 4.16647 0.12453 4.54473 0.10307
14 14 36.99471 0.00000 23.07303 0.00001
subj AUC0INF P value lnAUC0INF P value
1 1 0.78347 0.67588 0.76142 0.68338
2 2 0.29003 0.86501 0.32987 0.84795
3 3 1.51641 0.46851 1.53149 0.46499
4 4 1.26269 0.53188 1.12343 0.57023
(...)
12 12 3.36757 0.18567 4.09229 0.12923
13 13 3.93636 0.13971 4.18647 0.12329
14 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).
-------------------------------------------------------------------------
Test for Equality of Intra-subject variabilities between formulations
--------------------------------------------------------------------------
Parameter Test P value
1 lnCmax_Pearson -0.08448 0.7740
2 lnCmax_Pitman_Morgan 0.08626 0.7740
3 lnCmax_Spearman -0.10769 0.7156
4 lnAUC0t_Pearson 0.11349 0.6993
5 lnAUC0t_Pitman_Morgan 0.15657 0.6993
6 lnAUC0t_Spearman -0.07692 0.7966
7 lnAUC0INF_Pearson 0.07876 0.7890
8 lnAUC0INF_Pitman_Morgan 0.07490 0.7890
9 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).
--------------------------------------------------------------------------
Point and Interval Estimation of Inter- and Intra-subject Variability
--------------------------------------------------------------------------
Parameter Point_Estimate CI95_lower CI95_upper
1 lnCmax_intra 0.018 0.009 0.049
2 lnCmax_inter 0.003 -0.009 0.025
3 lnCmax_intraclass 0.141 -0.423 0.626
4 lnCmax_prob 0.31554 - -
5 lnAUC0t_intra 0.037 0.019 0.100
6 lnAUC0t_inter -0.006 -0.024 0.019
7 lnAUC0t_intraclass -0.192 -0.657 0.379
8 lnAUC0t_prob 0.74431 - -
9 lnAUC0INF_intra 0.034 0.018 0.094
10 lnAUC0INF_inter -0.006 -0.023 0.016
11 lnAUC0INF_intraclass -0.211 -0.669 0.362
12 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).
-------------------------------------------------------------------------
Quantiles for Boxplots (intrasubj)
--------------------------------------------------------------------------
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
-------------------------------------------------------------------------
Quantiles for Boxplots (intersubj)
--------------------------------------------------------------------------
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
-------------------------------------------------------------------------
|
Change Log (Sept. 21, 2009) & References
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 autoscale)
- 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 DLabes).
- 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).
v1.5.0~2.0.3
- now £fz 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 £fz in NCA output
- changed '0.693' to ln(2) when estimating T1/2(z) (= ln(2)/£fz) 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 Jiri 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)
v1.1.4
- fixed the compatibility for iMac and Linux (thanks to Koji Shimamoto, Tokyo, Japan; also for his testing bear on an 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)
- fixed some the format (comma, semicolon, etc.) of import data file (thanks to Helmut); 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)
- display semilog (not linear) plots when choosing data points to do linear regression for lambda_z in NCA
(thanks to Helmut)
- calculate CV_intra & CV_inter now (thanks to Helmut)
- 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)
- changed ANOVA(GLM) to ANOVA (lm) in the menu title (thanks to EIMaestro)
-----
To-do lists (July 23, 2009)
-----
- add configuration setup file (as .RData data frame) into bear. Use can create/edit this configuration file. Once data has been imported, don't need to enter anything... just sit back and watch.
-----
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.
|