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项目作者： Helmut01

项目描述 ：
Comparative BA-calculation for the EMA's Average Bioequivalence with Expanding Limits (ABEL)
高级语言： R
项目地址: git://github.com/Helmut01/replicateBE.git
创建时间： 2017-06-24T21:58:44Z
项目社区：https://github.com/Helmut01/replicateBE
开源协议：
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replicateBE

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Version 1.1.3.9000 built 2022-05-03 with R 4.2.0 (development version
not on CRAN).


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

Introduction

The package 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 (in xlsx or the legacy xls format). The methods
given by the EMA for
reference-scaling of
HVD(P)s,
i.e., Average Bioequivalence with Expanding Limits
(ABEL)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 swT/swR and the
upper confidence limit of σwT/σwR. This was
required in a pilot phase by the
WHO but lifted in 2021;
reference-scaling of AUC is acceptable if the protocol is submitted to
the
PQT/MED.6

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Methods

Estimation of CVwR (and CVwT 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., by an
ANOVA). Estimated by the
function lm() of package stats.

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

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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 package stats.

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

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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:

  • Estimation by the function lmer() of package 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.
  1. modB <- lmer(log(PK) ~ sequence + period + treatment + (1|subject),
  2.                        data = data)
  • Estimation by the function lme() of package 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.
  1. modB <- lme(log(PK) ~ sequence +  period + treatment, random = ~1|subject,
  2.                       data = data)
  • Estimation by the function lmer() of package 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.
  1. modB <- lmer(log(PK) ~ sequence + period + treatment + (1|subject),
  2.                        data = data)

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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 Cmax according to the
guideline of South Africa7 can be specified.

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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)

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Cross-validation

Details about the reference datasets:

  1. help("data", package = "replicateBE")
  2. ?replicateBE::data

Results of the 30 reference datasets agree with ones obtained in SAS
(v9.4), Phoenix WinNonlin (v6.4 – v8.3.4.295), STATISTICA (v13), SPSS
(v22.0), Stata (v15.0), and JMP (v10.0.2).8

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Examples

  • Evaluation of the internal reference dataset
    019 by Method A.
  1. library(replicateBE) # attach the package
  2. res <- method.A(verbose = TRUE, details = TRUE,
  3.                 print = FALSE, data = rds01)
  4. # 
  5. # Data set DS01: Method A by lm() 
  6. # ─────────────────────────────────── 
  7. # Type III Analysis of Variance Table
  8. # 
  9. # Response: log(PK)
  10. #                   Df   Sum Sq  Mean Sq  F value     Pr(>F)
  11. # sequence           1   0.0077 0.007652  0.00268  0.9588496
  12. # period             3   0.6984 0.232784  1.45494  0.2278285
  13. # treatment          1   1.7681 1.768098 11.05095  0.0010405
  14. # sequence:subject  75 214.1296 2.855061 17.84467 < 2.22e-16
  15. # Residuals        217  34.7190 0.159995                    
  16. # 
  17. # treatment T – R:
  18. #   Estimate Std. Error    t value   Pr(>|t|) 
  19. # 0.14547400 0.04650870 3.12788000 0.00200215 
  20. # 217 Degrees of Freedom
  21. cols <- c(12, 17:21)           # extract relevant columns
  22. # cosmetics: 2 decimal places acc. to the GL
  23. tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
  24. names(tmp) <- names(res)[cols]
  25. tmp  <- cbind(tmp, res[22:24]) # pass|fail
  26. print(tmp, row.names = FALSE)
  27. #  CVwR(%)  L(%)   U(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
  28. #    46.96 71.23 140.40   107.11   124.89 115.66 pass pass pass

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  • The same dataset evaluated by Method B, Satterthwaite approximation
    of degrees of freedom.
  1. res  <- method.B(option = 1, verbose = TRUE, details = TRUE,
  2.                  print = FALSE, data = rds01)
  3. # 
  4. # Data set DS01: Method B (option = 1) by lmer() 
  5. # ────────────────────────────────────────────── 
  6. # Response: log(PK)
  7. # Type III Analysis of Variance Table with Satterthwaite's method
  8. #             Sum Sq  Mean Sq NumDF    DenDF F value    Pr(>F)
  9. # sequence  0.001917 0.001917     1  74.7208 0.01198 0.9131536
  10. # period    0.398078 0.132693     3 217.1188 0.82881 0.4792840
  11. # treatment 1.579332 1.579332     1 216.9386 9.86464 0.0019197
  12. # 
  13. # treatment T – R:
  14. #   Estimate Std. Error    t value   Pr(>|t|) 
  15. #  0.1460900  0.0465130  3.1408000  0.0019197 
  16. # 216.939 Degrees of Freedom (equivalent to SAS’ DDFM=SATTERTHWAITE)
  17. cols <- c(12, 17:21)
  18. tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
  19. names(tmp) <- names(res)[cols]
  20. tmp  <- cbind(tmp, res[22:24])
  21. print(tmp, row.names = FALSE)
  22. #  CVwR(%)  L(%)   U(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
  23. #    46.96 71.23 140.40   107.17   124.97 115.73 pass pass pass

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  • The same dataset evaluated by Method B, Kenward-Roger approximation
    of degrees of freedom. Outlier assessment, recalculation of
    CVwR after exclusion of outliers, new expanded limits.
  1. res  <- method.B(option = 3, ola = TRUE, verbose = TRUE,
  2.                  details = TRUE, print = FALSE, data = rds01)

  1. # 
  2. # Outlier analysis
  3. #  (externally) studentized residuals
  4. #  Limits (2×IQR whiskers): -1.717435, 1.877877
  5. #  Outliers:
  6. #  subject sequence  stud.res
  7. #       45     RTRT -6.656940
  8. #       52     RTRT  3.453122
  9. # 
  10. #  standarized (internally studentized) residuals
  11. #  Limits (2×IQR whiskers): -1.69433, 1.845333
  12. #  Outliers:
  13. #  subject sequence stand.res
  14. #       45     RTRT -5.246293
  15. #       52     RTRT  3.214663
  16. # 
  17. # Data set DS01: Method B (option = 3) by lmer() 
  18. # ────────────────────────────────────────────── 
  19. # Response: log(PK)
  20. # Type III Analysis of Variance Table with Kenward-Roger's method
  21. #             Sum Sq  Mean Sq NumDF    DenDF F value    Pr(>F)
  22. # sequence  0.001917 0.001917     1  74.9899 0.01198 0.9131528
  23. # period    0.398065 0.132688     3 217.3875 0.82878 0.4792976
  24. # treatment 1.579280 1.579280     1 217.2079 9.86432 0.0019197
  25. # 
  26. # treatment T – R:
  27. #   Estimate Std. Error    t value   Pr(>|t|) 
  28. #  0.1460900  0.0465140  3.1408000  0.0019197 
  29. # 217.208 Degrees of Freedom (equivalent to Stata’s dfm=Kenward Roger EIM)
  30. cols <- c(27, 31:32, 19:21)
  31. tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
  32. names(tmp) <- names(res)[cols]
  33. tmp  <- cbind(tmp, res[22:24])
  34. print(tmp, row.names = FALSE)
  35. #  CVwR.rec(%) L.rec(%) U.rec(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
  36. #        32.16    78.79   126.93   107.17   124.97 115.73 pass pass pass

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  • The same dataset evaluated according to the conditions of the
    GCC (if
    CVwR > 30% widened limits 75.00 – 133.33%,
    GMR-constraint 80.00 – 125.00%).
  1. res <- method.A(regulator = "GCC", details = TRUE,
  2.                 print = FALSE, data = rds01)
  3. cols <- c(12, 17:21)
  4. tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
  5. names(tmp) <- names(res)[cols]
  6. tmp  <- cbind(tmp, res[22:24])
  7. print(tmp, row.names = FALSE)
  8. #  CVwR(%)  L(%)   U(%) CL.lo(%) CL.hi(%)  PE(%)   CI  GMR   BE
  9. #    46.96 75.00 133.33   107.11   124.89 115.66 pass pass pass

TOC ↩

  • The same dataset evaluated according to the conditions of South
    Africa (if CVwR > 30% fixed limits 75.00 – 133.33%).
  1. res <- ABE(theta1 = 0.75, details = TRUE,
  2.            print = FALSE, data = rds01)
  3. tmp <- data.frame(as.list(sprintf("%.2f", res[12:17])))
  4. names(tmp) <- names(res)[12:17]
  5. tmp <- cbind(tmp, res[18])
  6. print(tmp, row.names = FALSE)
  7. #  CVwR(%) BE.lo(%) BE.hi(%) CL.lo(%) CL.hi(%)  PE(%)   BE
  8. #    46.96    75.00   133.33   107.11   124.89 115.66 pass

TOC ↩

  • Evaluation of the internal reference dataset
    05.10 Tighter limits for the
    NTID phenytoin.
  1. res <- ABE(theta1 = 0.90, details = TRUE,
  2.            print = FALSE, data = rds05)
  3. cols <- c(13:17)
  4. tmp  <- data.frame(as.list(sprintf("%.2f", res[cols])))
  5. names(tmp) <- names(res)[cols]
  6. tmp  <- cbind(tmp, res[18])
  7. print(tmp, row.names = FALSE)
  8. #  BE.lo(%) BE.hi(%) CL.lo(%) CL.hi(%)  PE(%)   BE
  9. #     90.00   111.11   103.82   112.04 107.85 fail

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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:
  1. 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:
  1. install.packages("devtools", repos = "https://cloud.r-project.org/")
  2. devtools::install_github("Helmut01/replicateBE")

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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.

  1. options(width = 66)
  2. print(sessionInfo(), locale = FALSE)
  3. # R version 4.2.0 (2022-04-22 ucrt)
  4. # Platform: x86_64-w64-mingw32/x64 (64-bit)
  5. # Running under: Windows 10 x64 (build 22000)
  6. # 
  7. # Matrix products: default
  8. # 
  9. # attached base packages:
  10. # [1] stats     graphics  grDevices utils     datasets  methods  
  11. # [7] base     
  12. # 
  13. # other attached packages:
  14. # [1] replicateBE_1.1.3.9000
  15. # 
  16. # loaded via a namespace (and not attached):
  17. #  [1] tidyselect_1.1.2    xfun_0.30           purrr_0.3.4        
  18. #  [4] splines_4.2.0       lmerTest_3.1-3      lattice_0.20-45    
  19. #  [7] colorspace_2.0-3    vctrs_0.4.1         generics_0.1.2     
  20. # [10] htmltools_0.5.2     yaml_2.3.5          utf8_1.2.2         
  21. # [13] rlang_1.0.2         pillar_1.7.0        nloptr_2.0.0       
  22. # [16] glue_1.6.2          PowerTOST_1.5-4     readxl_1.4.0       
  23. # [19] lifecycle_1.0.1     stringr_1.4.0       munsell_0.5.0      
  24. # [22] gtable_0.3.0        cellranger_1.1.0    mvtnorm_1.1-3      
  25. # [25] evaluate_0.15       knitr_1.39          fastmap_1.1.0      
  26. # [28] parallel_4.2.0      pbkrtest_0.5.1      fansi_1.0.3        
  27. # [31] highr_0.9           broom_0.8.0         Rcpp_1.0.8.3       
  28. # [34] backports_1.4.1     scales_1.2.0        lme4_1.1-29        
  29. # [37] TeachingDemos_2.12  ggplot2_3.3.5       digest_0.6.29      
  30. # [40] stringi_1.7.6       dplyr_1.0.8         numDeriv_2016.8-1.1
  31. # [43] grid_4.2.0          cli_3.3.0           tools_4.2.0        
  32. # [46] magrittr_2.0.3      tibble_3.1.6        tidyr_1.2.0        
  33. # [49] crayon_1.5.1        pkgconfig_2.0.3     MASS_7.3-57        
  34. # [52] ellipsis_0.3.2      Matrix_1.4-1        minqa_1.2.4        
  35. # [55] rmarkdown_2.14      rstudioapi_0.13     cubature_2.0.4.4   
  36. # [58] R6_2.5.1            boot_1.3-28         nlme_3.1-157       
  37. # [61] compiler_4.2.0

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Contributors

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

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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.

TOC ↩

1.
EMA. EMA/582648/2016.
Annex I. London. 21 September 2016.
Online
↩
2.
EMA,
CHMP.
CPMP/EWP/QWP/1401/98 Rev. 1/ Corr **. London. 20 January 2010.
Online.
↩
3.
EGA.
Revised EMA Bioequivalence Guideline. Questions & Answers. London.
June 2010.
Online
↩
4. Health Canada. Guidance
Document. Conduct and Analysis of Comparative Bioavailability Studies.
Ottawa. 2018/06/08.
Online.
↩
5. Executive Board of the
Health Ministers’ Council for
GCC States. The GCC
Guidelines for Bioequivalence. Version 3.0. May 2021.
Online.
↩
6.
WHO. Application of
reference-scaled criteria for AUC in bioequivalence studies conducted
for submission to
PQT/MED.
Geneva. 02 July 2021.
Online.
↩
7.
MCC. Registration of
Medicines. Biostudies. Pretoria. June 2015.
Online.
↩
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.
EMA. EMA/582648/2016.
Annex II. London. 21 September 2016.
Online.
↩
10. Shumaker RC, Metzler CM.
The Phenytoin Trial is a Case Study of ‘Individual’ Bioequivalence.
Drug Inf J. 1998; 32(4): 1063–72.
doi:10.1177/009286159803200426.
↩