bioequivalence (ABE) and bioavailability
for
Created by Hsin-ya Lee (hsinyalee@gmail.com)
Yung-jin Lee (pkpd.taiwan@gmail.com)
bear
v2.0.2 -
data analysis tool for average
bioequivalence
(ABE)
and bioavailability
for
Created by Hsin-ya Lee (hsinyalee@gmail.com)
Yung-jin Lee (pkpd.taiwan@gmail.com)
Introduction
This package is used to analyze average bioequivalence (ABE) data
from noncompartmental analysis (NCA) to ANOVA (lm in R). Study design of
ABE should be a 2-treatment, 2-sequence, 2-period, crossover design.
The statistical analysis for bioavailability (BA) measurements (AUCs and Cmax) is
based on the two one-sided tests (Schuirmann, 1987). ABE involves the
calculation of 90% confidence intervals (90%CIs) 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%. Currently,
bear should not be used to
analyze data obtained from replicated ABE studies. We are now
working on
ANOVA with linear mixed effect (lme from nlme package) model. You
can also browse the Forum
at bebac to get more information about the development of
bear. We get a
lots of supports from many experts of
bebac Forum.
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 AUCs and terminal elimination rate constants (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 will not include the data point of (Tmax, Cmax). Linear trapezoidal rule is used to calculate AUC0t (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. AUC0inf (AUC from time 0 to infinity) equals to AUC0t plus the
extrapolated AUC. Cmax is obtained from observed time-Cp profile. All plots 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, AUC0t, AUC0inf, AUC0t/AUC0inf, ln(Cmax),
ln(AUC0t), ln(AUC0inf), MRT0inf, 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) and summaries (like this
statistical
summaries).
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, and
sciplot) when running. These packages will be
installed automatically when you're installing bear
at the same time. Bear is complied and tested under R v2.7.2.
So, please install R with the latest version (>v2.7.2). data input: The fastest 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 of the imported data format (.csv):-
Please note that this format is not for ANOVA.
This is the format for the raw data of a BE study.
| 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 (...) |
where "subj", "seq", "prd", "time" and "conc" mean subject#,
sequence, period, sampling time and drug concentration.
Output files
NCA output
~~~ This report is generated by bear v2.0.1 for R ~~~
Authors: Hsin-ya Lee, Yung-jin Lee
#100, Shih-chuan 1st Rd.
College of Pharmacy,
Kaohsiung Medical University,
Kaoshiung, Taiwan 80708
E-mail: hsinyalee@gmail.com,
pkpd.taiwan@gmail.com
bear's website: http://pkpd.kmu.edu.tw/bear
R website: www.r-project.org
---------------------------------------------------
Reference
---------------------------------------------------
<< NCA Output:- Subject# 1 (Ref.)>>
--------------------------------------------------------------------------
subj time conc AUC(0-t) AUMC(0-t)
1 1 0.25 36.1 0.0000 0.000000
2 1 0.50 125.0 20.1375 8.940625
3 1 0.75 567.0 106.6375 69.909375
4 1 1.00 932.0 294.0125 239.565625
5 1 1.50 1343.0 862.7625 976.190625
6 1 2.00 1739.0 1633.2625 2349.315625
7 1 3.00 1604.0 3304.7625 6494.315625
8 1 4.00 1460.0 4836.7625 11820.315625
9 1 8.00 797.0 9350.7625 36252.315625
10 1 12.00 383.0 11710.7625 58196.315625
11 1 24.00 72.0 14440.7625 96140.315625
|
ANOVA (lm) output
(...) Statistical analysis (ANOVA(lm), 90%CI...)
--------------------------------------------------------------------------
Dependent Variable: Cmax
Type I SS
Analysis of Variance Table
Response: Cmax
Df Sum Sq Mean Sq F value Pr(>F)
seq 1 585 585 0.0160 0.9014
prd 1 63175 63175 1.7293 0.2131
drug 1 58149 58149 1.5917 0.2311
seq:subj 12 634325 52860 1.4469 0.2660
Residuals 12 438395 36533
Type III SS
Single term deletions
Model:
Cmax ~ seq + subj:seq + prd + drug
Df Sum of Sq RSS AIC F value Pr(F)
|
Statistical Summary output
Statistical Summaries for Bioequivalence Study (N= 14 )
--------------------------------------------------------------------------
parameters Test_Mean Test_SD Ref_Mean Ref_SD Ratio
1 Cmax 1630.786 197.522 1539.643 220.015 1.079
2 AUC0-t 13975.284 1997.852 13158.790 1971.053 1.096
3 AUC0-inf 14659.822 2092.321 13776.930 2033.362 1.097
4 ln(Cmax) 7.390 0.122 7.329 0.147 1.009
5 ln(AUC0-t) 9.535 0.145 9.473 0.161 1.007
6 ln(AUC0-inf) 9.583 0.144 9.520 0.159 1.007
Statistical Analysis
--------------------------------------------------------------------------
parameters F_value P_value CI90_lower CI90_upper power
1 Cmax 1.592 0.231 - - -
2 AUC0-t 0.884 0.366 - - -
3 AUC0-inf 0.967 0.345 - - -
4 ln(Cmax) 1.611 0.228 97.586 115.644 1.000
5 ln(AUC0-t) 0.836 0.378 94.288 120.058 1.000
6 ln(AUC0-inf) 0.912 0.358 94.635 120.023 1.000
-------------------------------------------------------------------------
Ratio = Test/Ref. (mean ratio)
F value and P value were obtained from ANOVA.
CI90: 90% confidence interval
Power: required to detect at least 20% of differences
--------------------------------------------------------------------------
Summaries for Pharmacokinetic Analysis (NCA)
Test
-------------------------------------------------
parameters Mean SD CV
1 Cl/F 5.563 0.810 14.555
2 Lambda_z 0.133 0.014 10.682
3 Tmax 2.321 0.541 23.301
4 T1/2(z) 5.283 0.530 10.025
5 Vd/F 42.532 8.460 19.891
6 MRT0inf 8.198 0.516 6.290
7 AUCratio 95.324 1.125 1.180
Reference
----------------------------------------------------
parameters Mean SD CV
1 Cl/F 5.944 1.012 17.028
2 Lambda_z 0.133 0.007 5.201
3 Tmax 2.143 0.602 28.102
4 T1/2(z) 5.216 0.262 5.023
5 Vd/F 44.873 8.896 19.825
6 MRT0inf 8.128 0.399 4.905
7 AUCratio 95.482 0.768 0.805
-----------------------------------------------------
AUC ratio: (AUC0-t/AUC0-inf)*100
-----------------------------------------------------
|
Change Log (Oct. 14, 2008)
-----
v1.5.0~2.0.1
- 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 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 testing bear on iMac machine)
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
(kel) 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)
-----
Todo Lists (Oct. 14, 2008)
-----
1. NCA:
We're working on another five: AICs, TTT-ARS, TTT-AICs, lee.function-ARS, and
lee.function-AICs
(from an R package PK). These methods are all exclude the data point of Cmax for
estimation of λz (thanks
to Ace, martin, DLabes and Helmut on bebac Forum);
the selected data points now can only be displayed on R
console, and we will try to include these information into the
output file (NAC_PK.txt).
2.calculate intra-subject residuals (a little bit tough...): we treat
this as 'outlier detection in BE/BA' (suggested
by Helmut)
3. implement the better algorithm for λz calculation (suggested by martin
and Ace; especially
Ace who provided us his R codes for this; later DLabes & Helmut) as additional options;
then we have
tested some algorithms (function.Ace, WinNonlin v5.x.x, TTT method
and even combination of TTT method
with a best fit criterion, such ajd. R sq. (ARS) or AIC. See
Bebac.forum
for details.
4. implement "lme" for ANOVA as the additional method to current "lm".
(suggested by EIMaestro)
5. implement the "Save" function for data points selection for each subjects
before doing NCA (using data.frame()?)
6. add Type III SS (this should be able to be done quickly...)
(done!)
7. add methods for replicated study... (it may take longer for this).
-----
References