skyee1 / replicateBE Public

forked from Helmut01/replicateBE

Notifications You must be signed in to change notification settings
Fork 0
Star 0

Comparative BA-calculation for the EMA's Average Bioequivalence with Expanding Limits (ABEL)

0 stars 3 forks Branches Tags Activity

Notifications

Name		Name	Last commit message	Last commit date
Latest commit History 340 Commits
R		R
data		data
documentation		documentation
inst/extdata		inst/extdata
man		man
stuff		stuff
tests		tests
vignettes		vignettes
.Rbuildignore		.Rbuildignore
.gitignore		.gitignore
DESCRIPTION		DESCRIPTION
NAMESPACE		NAMESPACE
NEWS.md		NEWS.md
README.Rmd		README.Rmd
README.md		README.md

Repository files navigation

replicateBE

Introduction
Examples
Installation
Session Information
Contributors
Disclaimer

Version 1.1.0 built 2021-06-24 with R 4.1.0 (stable release on CRAN 2021-06-21).

Comparative BA-calculation for the EMA’s Average Bioequivalence with Expanding Limits (ABEL)

Introduction

The library provides data sets (internal .rda and in CSV-format in /extdata/) supporting users in a black-box performance qualification (PQ) of their software installations. Users can analyze own data imported from CSV- and Excel-files. The methods given by the EMA for reference-scaling^1,² are implemented.
Potential influence of outliers on the variability of the reference can be assessed by box plots of studentized and standardized residuals as suggested at a joint EGA/EMA workshop.³
Health Canada’s approach⁴ requiring a mixed-effects model is approximated by intra-subject contrasts.
Direct widening of the acceptance range as recommended by the Gulf Cooperation Council⁵ (Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, United Arab Emirates) is provided as well.
In full replicate designs the variability of test and reference treatments can be assessed by s_wT/s_wR and the upper confidence limit of σ_wT/σ_wR (required for the WHO’s approach⁶ for reference-scaling of AUC).

Methods

Estimation of CV_wR (and CV_wT in full replicate designs)

Called internally by functions method.A() and method.B(). A linear model of log-transformed pharmacokinetic (PK) responses and effects
sequence, subject(sequence), period
where all effects are fixed (i.e., ANOVA). Estimated by the function lm() of library stats.

modCVwR <- lm(log(PK) ~ sequence + subject%in%sequence + period,
                        data = data[data$treatment == "R", ])
modCVwT <- lm(log(PK) ~ sequence + subject%in%sequence + period,
                        data = data[data$treatment == "T", ])

Method A

Called by function method.A(). A linear model of log-transformed PK responses and effects
sequence, subject(sequence), period, treatment
where all effects are fixed (e.g., by an ANOVA). Estimated by the function lm() of library stats.

modA <- lm(log(PK) ~ sequence + subject%in%sequence + period + treatment,
                     data = data)

Method B

Called by function method.B(). A linear model of log-transformed PK responses and effects
sequence, subject(sequence), period, treatment
where subject(sequence) is a random effect and all others are fixed.
Three options are provided:

Estimated by the function lmer() of library lmerTest. method.B(..., option = 1) employs Satterthwaite’s approximation of the degrees of freedom equivalent to SAS’ DDFM=SATTERTHWAITE, Phoenix WinNonlin’s Degrees of Freedom Satterthwaite, and Stata’s dfm=Satterthwaite. Note that this is the only available approximation in SPSS.

modB <- lmer(log(PK) ~ sequence + period + treatment + (1|subject),
                       data = data)

Estimated by the function lme() of library nlme. method.B(..., option = 2) employs degrees of freedom equivalent to SAS’ DDFM=CONTAIN, Phoenix WinNonlin’s Degrees of Freedom Residual, STATISTICA’s GLM containment, and Stata’s dfm=anova. Implicitly preferred according to the EMA’s Q&A document and hence, the default of the function.

modB <- lme(log(PK) ~ sequence +  period + treatment, random = ~1|subject,
                      data = data)

Estimated by the function lmer() of library lmerTest. method.B(..., option = 3) employs the Kenward-Roger approximation equivalent to Stata’s dfm=Kenward Roger (EIM) and SAS’ DDFM=KENWARDROGER(FIRSTORDER) i.e., based on the expected information matrix. Note that SAS with DDFM=KENWARDROGER and JMP calculate Satterthwaite’s [sic] degrees of freedom and apply the Kackar-Harville correction, i.e., based on the observed information matrix.

modB <- lmer(log(PK) ~ sequence + period + treatment + (1|subject),
                       data = data)

Average Bioequivalence

Called by function ABE(). The model is identical to Method A. Conventional BE limits (80.00 – 125.00%) are employed by default. Tighter limits (90.00 – 111.11%) for narrow therapeutic index drugs (EMA and others) or wider limits (75.00 – 133.33%) for C_max according to the guideline of South Africa⁷ can be specified.

Tested designs

Four period (full) replicates

TRTR | RTRT
TRRT | RTTR
TTRR | RRTT
TRTR | RTRT | TRRT | RTTR
TRRT | RTTR | TTRR | RRTT

Three period (full) replicates

TRT | RTR
TRR | RTT

Two period (full) replicate

TR | RT | TT | RR (Balaam’s design; not recommended due to poor power characteristics)

Three period (partial) replicates

TRR | RTR | RRT
TRR | RTR (Extra-reference design; biased in the presence of period effects, not recommended)

Cross-validation

Details about the reference datasets:

help("data", package = "replicateBE")
?replicateBE::data

Results of the 30 reference datasets agree with ones obtained in SAS (9.4), Phoenix WinNonlin (6.4 – 8.1), STATISTICA (13), SPSS (22.0), Stata (15.0), and JMP (10.0.2).⁸

Examples

Evaluation of the internal reference dataset 01⁹ by Method A.

library(replicateBE) # attach the library
res <- method.A(verbose = TRUE, details = TRUE,
                print = FALSE, data = rds01)
# 
# Data set DS01: Method A by lm() 
# ----------------------------------- 
# Type III Analysis of Variance Table
# 
# Response: log(PK)
#                   Df   Sum Sq  Mean Sq  F value     Pr(>F)
# sequence           1   0.0077 0.007652  0.00268  0.9588496
# period             3   0.6984 0.232784  1.45494  0.2278285
# treatment          1   1.7681 1.768098 11.05095  0.0010405
# sequence:subject  75 214.1296 2.855061 17.84467 < 2.22e-16
# Residuals        217  34.7190 0.159995                    
# 
# treatment T – R:
#   Estimate Std. Error    t value   Pr(>|t|) 
# 0.14547400 0.04650870 3.12788000 0.00200215 
# 217 Degrees of Freedom
cols <- c(12, 17:21)           # extract relevant columns
# cosmetics: 2 decimal places acc. to the GL
tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
names(tmp) <- names(res)[cols]
tmp  <- cbind(tmp, res[22:24]) # pass|fail
print(tmp, row.names = FALSE)
#  CVwR(%)  L(%)   U(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
#    46.96 71.23 140.40   107.11   124.89 115.66 pass pass pass

The same dataset evaluated by Method B, Satterthwaite approximation of degrees of freedom.

res  <- method.B(option = 1, verbose = TRUE, details = TRUE,
                 print = FALSE, data = rds01)
# 
# Data set DS01: Method B (option = 1) by lmer() 
# ---------------------------------------------- 
# Response: log(PK)
# Type III Analysis of Variance Table with Satterthwaite's method
#             Sum Sq  Mean Sq NumDF    DenDF F value    Pr(>F)
# sequence  0.001917 0.001917     1  74.7208 0.01198 0.9131536
# period    0.398078 0.132693     3 217.1188 0.82881 0.4792840
# treatment 1.579332 1.579332     1 216.9386 9.86464 0.0019197
# 
# treatment T – R:
#   Estimate Std. Error    t value   Pr(>|t|) 
#  0.1460900  0.0465130  3.1408000  0.0019197 
# 216.939 Degrees of Freedom (equivalent to SAS’ DDFM=SATTERTHWAITE)
cols <- c(12, 17:21)
tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
names(tmp) <- names(res)[cols]
tmp  <- cbind(tmp, res[22:24])
print(tmp, row.names = FALSE)
#  CVwR(%)  L(%)   U(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
#    46.96 71.23 140.40   107.17   124.97 115.73 pass pass pass

The same dataset evaluated by Method B, Kenward-Roger approximation of degrees of freedom. Outlier assessment, recalculation of CV_wR after exclusion of outliers, new expanded limits.

res  <- method.B(option = 3, ola = TRUE, verbose = TRUE,
                 details = TRUE, print = FALSE, data = rds01)

# 
# Outlier analysis
#  (externally) studentized residuals
#  Limits (2×IQR whiskers): -1.717435, 1.877877
#  Outliers:
#  subject sequence  stud.res
#       45     RTRT -6.656940
#       52     RTRT  3.453122
# 
#  standarized (internally studentized) residuals
#  Limits (2×IQR whiskers): -1.69433, 1.845333
#  Outliers:
#  subject sequence stand.res
#       45     RTRT -5.246293
#       52     RTRT  3.214663
# 
# Data set DS01: Method B (option = 3) by lmer() 
# ---------------------------------------------- 
# Response: log(PK)
# Type III Analysis of Variance Table with Kenward-Roger's method
#             Sum Sq  Mean Sq NumDF    DenDF F value    Pr(>F)
# sequence  0.001917 0.001917     1  74.9899 0.01198 0.9131528
# period    0.398065 0.132688     3 217.3875 0.82878 0.4792976
# treatment 1.579280 1.579280     1 217.2079 9.86432 0.0019197
# 
# treatment T – R:
#   Estimate Std. Error    t value   Pr(>|t|) 
#  0.1460900  0.0465140  3.1408000  0.0019197 
# 217.208 Degrees of Freedom (equivalent to Stata’s dfm=Kenward Roger EIM)
cols <- c(27, 31:32, 19:21)
tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
names(tmp) <- names(res)[cols]
tmp  <- cbind(tmp, res[22:24])
print(tmp, row.names = FALSE)
#  CVwR.rec(%) L.rec(%) U.rec(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
#        32.16    78.79   126.93   107.17   124.97 115.73 pass pass pass

The same dataset evaluated according to the conditions of the GCC (if CV_wR > 30% widened limits 75.00 – 133.33%, GMR-constraint 80.00 – 125.00%).

res <- method.A(regulator = "GCC", details = TRUE,
                print = FALSE, data = rds01)
cols <- c(12, 17:21)
tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
names(tmp) <- names(res)[cols]
tmp  <- cbind(tmp, res[22:24])
print(tmp, row.names = FALSE)
#  CVwR(%)  L(%)   U(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
#    46.96 75.00 133.33   107.11   124.89 115.66 pass pass pass

The same dataset evaluated according to the conditions of South Africa (if CV_wR > 30% fixed limits 75.00 – 133.33%).

res <- ABE(theta1 = 0.75, details = TRUE,
           print = FALSE, data = rds01)
tmp <- data.frame(as.list(sprintf("%.2f", res[12:17])))
names(tmp) <- names(res)[12:17]
tmp <- cbind(tmp, res[18])
print(tmp, row.names = FALSE)
#  CVwR(%) BE.lo(%) BE.hi(%) CL.lo(%) CL.hi(%)  PE(%)   BE
#    46.96    75.00   133.33   107.11   124.89 115.66 pass

Evaluation of the internal reference dataset 05.¹⁰ Tighter limits for the NTID phenytoin.

res <- ABE(theta1 = 0.90, details = TRUE,
           print = FALSE, data = rds05)
cols <- c(13:17)
tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
names(tmp) <- names(res)[cols]
tmp  <- cbind(tmp, res[18])
print(tmp, row.names = FALSE)
#  BE.lo(%) BE.hi(%) CL.lo(%) CL.hi(%)  PE(%)   BE
#     90.00   111.11   103.82   112.04 107.85 fail

Installation

The package requires R ≥3.5.0. However, for the Kenward-Roger approximation method.B(..., option = 3) R ≥3.6.0 is required.

Install the released version from CRAN:

install.packages("replicateBE", repos = "https://cloud.r-project.org/")

To use the development version, please install the released version from CRAN first to get its dependencies right (readxl ≥1.0.0, PowerTOST ≥1.5.3, lmerTest, nlme, pbkrtest).

You need tools for building R packages from sources on your machine. For Windows users:
- Download Rtools from CRAN and follow the suggestions of the installer.
- Install devtools and build the development version by:

install.packages("devtools", repos = "https://cloud.r-project.org/")
devtools::install_github("Helmut01/replicateBE")

Session Information

Inspect this information for reproducibility. Of particular importance are the versions of R and the packages used to create this workflow. It is considered good practice to record this information with every analysis.

options(width = 59)
devtools::session_info()
# - Session info ------------------------------------------
#  setting  value                       
#  version  R version 4.1.0 (2021-05-18)
#  os       Windows 7 x64 SP 1          
#  system   x86_64, mingw32             
#  ui       RTerm                       
#  language EN                          
#  collate  German_Germany.1252         
#  ctype    German_Germany.1252         
#  tz       Europe/Vienna               
#  date     2021-06-24                  
# 
# - Packages ----------------------------------------------
#  package       * version    date       lib source        
#  backports       1.2.1      2020-12-09 [1] CRAN (R 4.1.0)
#  boot            1.3-28     2021-05-03 [1] CRAN (R 4.1.0)
#  broom           0.7.7      2021-06-13 [1] CRAN (R 4.1.0)
#  cachem          1.0.5      2021-05-15 [1] CRAN (R 4.1.0)
#  callr           3.7.0      2021-04-20 [1] CRAN (R 4.1.0)
#  cellranger      1.1.0      2016-07-27 [1] CRAN (R 4.1.0)
#  cli             2.5.0      2021-04-26 [1] CRAN (R 4.1.0)
#  colorspace      2.0-1      2021-05-04 [1] CRAN (R 4.1.0)
#  crayon          1.4.1      2021-02-08 [1] CRAN (R 4.1.0)
#  cubature        2.0.4.2    2021-05-13 [1] CRAN (R 4.1.0)
#  desc            1.3.0      2021-03-05 [1] CRAN (R 4.1.0)
#  devtools        2.4.2      2021-06-07 [1] CRAN (R 4.1.0)
#  digest          0.6.27     2020-10-24 [1] CRAN (R 4.1.0)
#  dplyr           1.0.7      2021-06-18 [1] CRAN (R 4.1.0)
#  ellipsis        0.3.2      2021-04-29 [1] CRAN (R 4.1.0)
#  evaluate        0.14       2019-05-28 [1] CRAN (R 4.1.0)
#  fansi           0.5.0      2021-05-25 [1] CRAN (R 4.1.0)
#  fastmap         1.1.0      2021-01-25 [1] CRAN (R 4.1.0)
#  fs              1.5.0      2020-07-31 [1] CRAN (R 4.1.0)
#  generics        0.1.0      2020-10-31 [1] CRAN (R 4.1.0)
#  ggplot2         3.3.4      2021-06-16 [1] CRAN (R 4.1.0)
#  glue            1.4.2      2020-08-27 [1] CRAN (R 4.1.0)
#  gtable          0.3.0      2019-03-25 [1] CRAN (R 4.1.0)
#  highr           0.9        2021-04-16 [1] CRAN (R 4.1.0)
#  htmltools       0.5.1.1    2021-01-22 [1] CRAN (R 4.1.0)
#  knitr           1.33       2021-04-24 [1] CRAN (R 4.1.0)
#  lattice         0.20-44    2021-05-02 [1] CRAN (R 4.1.0)
#  lifecycle       1.0.0      2021-02-15 [1] CRAN (R 4.1.0)
#  lme4            1.1-27     2021-05-15 [1] CRAN (R 4.1.0)
#  lmerTest        3.1-3      2020-10-23 [1] CRAN (R 4.1.0)
#  magrittr        2.0.1      2020-11-17 [1] CRAN (R 4.1.0)
#  MASS            7.3-54     2021-05-03 [1] CRAN (R 4.1.0)
#  Matrix          1.3-4      2021-06-01 [1] CRAN (R 4.1.0)
#  memoise         2.0.0      2021-01-26 [1] CRAN (R 4.1.0)
#  minqa           1.2.4      2014-10-09 [1] CRAN (R 4.1.0)
#  munsell         0.5.0      2018-06-12 [1] CRAN (R 4.1.0)
#  mvtnorm         1.1-2      2021-06-07 [1] CRAN (R 4.1.0)
#  nlme            3.1-152    2021-02-04 [1] CRAN (R 4.1.0)
#  nloptr          1.2.2.2    2020-07-02 [1] CRAN (R 4.1.0)
#  numDeriv        2016.8-1.1 2019-06-06 [1] CRAN (R 4.1.0)
#  pbkrtest        0.5.1      2021-03-09 [1] CRAN (R 4.1.0)
#  pillar          1.6.1      2021-05-16 [1] CRAN (R 4.1.0)
#  pkgbuild        1.2.0      2020-12-15 [1] CRAN (R 4.1.0)
#  pkgconfig       2.0.3      2019-09-22 [1] CRAN (R 4.1.0)
#  pkgload         1.2.1      2021-04-06 [1] CRAN (R 4.1.0)
#  PowerTOST       1.5.3.9000 2021-06-21 [1] local         
#  prettyunits     1.1.1      2020-01-24 [1] CRAN (R 4.1.0)
#  processx        3.5.2      2021-04-30 [1] CRAN (R 4.1.0)
#  ps              1.6.0      2021-02-28 [1] CRAN (R 4.1.0)
#  purrr           0.3.4      2020-04-17 [1] CRAN (R 4.1.0)
#  R6              2.5.0      2020-10-28 [1] CRAN (R 4.1.0)
#  Rcpp            1.0.6      2021-01-15 [1] CRAN (R 4.1.0)
#  readxl          1.3.1      2019-03-13 [1] CRAN (R 4.1.0)
#  remotes         2.4.0      2021-06-02 [1] CRAN (R 4.1.0)
#  replicateBE   * 1.1.0      2021-06-21 [1] CRAN (R 4.1.0)
#  rlang           0.4.11     2021-04-30 [1] CRAN (R 4.1.0)
#  rmarkdown       2.9        2021-06-15 [1] CRAN (R 4.1.0)
#  rprojroot       2.0.2      2020-11-15 [1] CRAN (R 4.1.0)
#  scales          1.1.1      2020-05-11 [1] CRAN (R 4.1.0)
#  sessioninfo     1.1.1      2018-11-05 [1] CRAN (R 4.1.0)
#  stringi         1.6.1      2021-05-10 [1] CRAN (R 4.1.0)
#  stringr         1.4.0      2019-02-10 [1] CRAN (R 4.1.0)
#  TeachingDemos   2.12       2020-04-07 [1] CRAN (R 4.1.0)
#  testthat        3.0.3      2021-06-16 [1] CRAN (R 4.1.0)
#  tibble          3.1.2      2021-05-16 [1] CRAN (R 4.1.0)
#  tidyr           1.1.3      2021-03-03 [1] CRAN (R 4.1.0)
#  tidyselect      1.1.1      2021-04-30 [1] CRAN (R 4.1.0)
#  usethis         2.0.1      2021-02-10 [1] CRAN (R 4.1.0)
#  utf8            1.2.1      2021-03-12 [1] CRAN (R 4.1.0)
#  vctrs           0.3.8      2021-04-29 [1] CRAN (R 4.1.0)
#  withr           2.4.2      2021-04-18 [1] CRAN (R 4.1.0)
#  xfun            0.24       2021-06-15 [1] CRAN (R 4.1.0)
#  yaml            2.2.1      2020-02-01 [1] CRAN (R 4.1.0)
# 
# [1] D:/Program Files/R/R-4.1.0/library

Contributors

Helmut Schütz (author) ORCID iD
Michael Tomashevskiy (contributor)
Detlew Labes (contributor) ORCID iD

Disclaimer

Package offered for Use without any Guarantees and Absolutely No Warranty. No Liability is accepted for any Loss and Risk to Public Health Resulting from Use of this R-Code.

  1. European Medices Agency. EMA/582648/2016. Annex I. 21 September 2016. ↩
  2. European Medices Agency. Committee for Medicinal Products for Human Use. CPMP/EWP/QWP/1401/98 Rev. 1/ Corr **. 20 January 2010. ↩
  3. European Generic Medicines Association. Revised EMA Bioequivalence Guideline. Questions & Answers. London, June 2010. ↩
  4. Health Canada. Guidance Document. Conduct and Analysis of Comparative Bioavailability Studies. 2018/06/08. ↩
  5. Executive Board of the Health Ministers’ Council for GCC States. The GCC Guidelines for Bioequivalence. Version 2.4. 30/3/2016. ↩
  6. World Health Organization. Application of reference-scaled criteria for AUC in bioequivalence studies conducted for submission to PQTm. 22 November 2018. ↩
  7. Medicines Control Council. Registration of Medicines. Biostudies. June 2015. ↩
  8. Schütz H, Tomashevskiy M, Labes D, Shitova A, González-de la Parra M, Fuglsang A. Reference Datasets for Studies in a Replicate Design Intended for Average Bioequivalence with Expanding Limits. AAPS J. 2020; 22(2): Article 44. doi:10.1208/s12248-020-0427-6. ↩
  9. European Medices Agency. EMA/582648/2016. Annex II. 21 September 2016. ↩
10. Shumaker RC, Metzler CM. The Phenytoin Trial is a Case Study of ‘Individual’ Bioequivalence. Drug Inf J. 1998; 32(4): 1063–1072. doi:10.1177/009286159803200426. ↩

About

Comparative BA-calculation for the EMA's Average Bioequivalence with Expanding Limits (ABEL)

Report repository

Releases

Packages

No packages published

Languages

R 100.0%