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README.Rmd
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---
title: "replicateBE"
output:
github_document:
toc: true
toc_depth: 4
fig_width: 6
fig_height: 6
dev: png
---
<!-- README.md is generated from README.Rmd. Please edit that file -->
[](https://www.gnu.org/licenses/gpl-3.0) 
    [](https://cran.r-project.org/web/checks/check_results_replicateBE.html)   [](https://r-pkg.org/pkg/replicateBE) [](https://r-pkg.org/pkg/replicateBE)    
```{r, setup, echo = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#",
fig.path = "man/figures/README-"
)
```
```{r, echo = FALSE, results = "asis"}
txt <- paste0("Version ", packageVersion("replicateBE"), " built ",
packageDate("replicateBE", date.fields = "Built"),
" with R ", substr(packageDescription("replicateBE", fields = "Built"), 3, 7))
if (grepl("900", as.character(packageVersion("replicateBE"))) |
is.na(packageDate("replicateBE", date.fields = "Date/Publication"))) {
txt <- paste(txt, "\n(development version not on CRAN).")
} else {
txt <- paste0(txt, "\n(stable release on CRAN ",
packageDate("replicateBE", date.fields = "Date/Publication"), ").")
}
cat(txt)
```
<h2>Comparative BA-calculation for the EMA’s Average Bioequivalence with Expanding Limits (ABEL)</h2>
## Introduction{#introduction}
The package provides data sets (internal `.rda` and in <abbr title="Character Separated Variables">CSV</abbr>-format in `/extdata/`) supporting users in a black-box performance qualification (PQ) of their software installations. Users can analyze own data imported from <abbr title="Character Separated Variables">CSV</abbr>- and Excel-files (in `xlsx` or the legacy `xls` format). The methods given by the <abbr title="European Medicines Agency">EMA</abbr> for reference-scaling of <abbr title="Highy Variable Drugs / Drug Products">HVD(P)s</abbr>, *i.e.*, Average Bioequivalence with Expanding Limits (ABEL)<sup id="a1">[1](#f1),</sup><sup id="a2">[2](#f2)</sup> are implemented.<br>
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 <abbr title="European Generic Medicines Association">EGA</abbr>/<abbr title="European Medicines Agency">EMA</abbr> workshop.<sup id="a3">[3](#f3)</sup><br>
Health Canada’s approach<sup id="a4">[4](#f4)</sup> requiring a mixed-effects model is approximated by intra-subject contrasts.
Direct widening of the acceptance range as recommended by the Gulf Cooperation Council<sup id="a5">[5](#f5)</sup> (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~. This was required in a pilot phase by the <abbr title="World Health Organization">WHO</abbr> but lifted in 2021; reference-scaling of _AUC_ is acceptable if the protocol is submitted to the <abbr title="Prequalification Unit – Medicines Assessment Team">PQT/MED</abbr>.<sup id="a6">[6](#f6)</sup>
<small>[TOC ↩](#replicatebe)</small>
### Methods{#methods}
#### Estimation of _CV_~wR~ (and _CV_~wT~ in full replicate designs){#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 <abbr title="Analysis of Variance">ANOVA</abbr>). Estimated by the function `lm()` of package `stats`.
```{r eval = FALSE}
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", ])
```
<small>[TOC ↩](#replicatebe)</small>
#### Method A{#method-a}
Called by function `method.A()`. A linear model of log-transformed <abbr title="pharmacokinetic">PK</abbr> responses and effects
_sequence_, _subject_(_sequence_), _period_, _treatment_\
where all effects are fixed (_e.g._, by an <abbr title="Analysis of Variance">ANOVA</abbr>). Estimated by the function `lm()` of package `stats`.
```{r eval = FALSE}
modA <- lm(log(PK) ~ sequence + subject %in% sequence + period + treatment,
data = data)
```
<small>[TOC ↩](#replicatebe)</small>
#### Method B{#method-b}
Called by function `method.B()`. A linear model of log-transformed <abbr title="pharmacokinetic">PK</abbr> 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.
```{r eval = FALSE}
modB <- lmer(log(PK) ~ sequence + period + treatment + (1|subject),
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 <abbr title="European Medicines Agency">EMA</abbr>’s <abbr title="Questions & Answers">Q&A</abbr> document and hence, the default of the function.
```{r eval = FALSE}
modB <- lme(log(PK) ~ sequence + period + treatment, random = ~1|subject,
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.
```{r eval = FALSE}
modB <- lmer(log(PK) ~ sequence + period + treatment + (1|subject),
data = data)
```
<small>[TOC ↩](#replicatebe)</small>
#### Average Bioequivalence{#average-bioequivalence}
Called by function `ABE()`. The model is identical to [Method A](#method-a). Conventional BE limits (80.00 – 125.00\%) are employed by default. Tighter limits (90.00 – 111.11\%) for narrow therapeutic index drugs (<abbr title="European Medicines Agency">EMA</abbr> and others) or wider limits (75.00 – 133.33\%) for *C*~max~ according to the guideline of South Africa<sup id="a7">[7](#f7)</sup> can be specified.
<small>[TOC ↩](#replicatebe)</small>
### Tested designs{#tested-designs}
#### Four period (full) replicates{#four-period-full-replicates}
`TRTR | RTRT`
`TRRT | RTTR`
`TTRR | RRTT`
`TRTR | RTRT | TRRT | RTTR`
`TRRT | RTTR | TTRR | RRTT`
#### Three period (full) replicates{#three-period-full-replicates}
`TRT | RTR`
`TRR | RTT`
#### Two period (full) replicate{#two-period-full-replicate}
`TR | RT | TT | RR` <small>(Balaam’s design; *not recommended* due to poor power characteristics)</small>
#### Three period (partial) replicates{#three-period-partial-replicates}
`TRR | RTR | RRT`
`TRR | RTR` <small>(Extra-reference design; biased in the presence of period effects, *not recommended*)</small>
<small>[TOC ↩](#replicatebe)</small>
### Cross-validation{#cross-validation}
Details about the reference datasets:
```{r eval = FALSE}
help("data", package = "replicateBE")
?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).<sup id="a8">[8](#f8)</sup>
<small>[TOC ↩](#replicatebe)</small>
## Examples{#examples}
- Evaluation of the internal reference dataset 01<sup id="a9">[9](#f9)</sup> by Method A.
```{r example1}
library(replicateBE) # attach the package
res <- method.A(verbose = TRUE, details = TRUE,
print = FALSE, data = rds01)
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)
```
<small>[TOC ↩](#replicatebe)</small>
- The same dataset evaluated by Method B, Satterthwaite approximation of degrees of freedom.
```{r example2}
res <- method.B(option = 1, verbose = TRUE, 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)
```
<small>[TOC ↩](#replicatebe)</small>
- 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.
```{r example3}
res <- method.B(option = 3, ola = TRUE, verbose = TRUE,
details = TRUE, print = FALSE, data = rds01)
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)
```
<small>[TOC ↩](#replicatebe)</small>
- The same dataset evaluated according to the conditions of the <abbr title="Gulf Cooperation Council">GCC</abbr> (if _CV_~wR~ > 30\% widened limits 75.00 – 133.33\%, GMR-constraint 80.00 – 125.00\%).
```{r example4}
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)
```
<small>[TOC ↩](#replicatebe)</small>
- The same dataset evaluated according to the conditions of South Africa (if _CV_~wR~ > 30\% fixed limits 75.00 – 133.33\%).
```{r example5}
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)
```
<small>[TOC ↩](#replicatebe)</small>
- Evaluation of the internal reference dataset 05.<sup id="a10">[10](#f10)</sup> Tighter limits for the <abbr title="Narrow Therapeutic Index Drug">NTID</abbr> phenytoin.
```{r example6}
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)
```
<small>[TOC ↩](#replicatebe)</small>
## Installation{#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 <abbr title="The Comprehensive R Archive Network">CRAN</abbr>:
```{r eval = FALSE}
install.packages("replicateBE", repos = "https://cloud.r-project.org/")
```
* To use the development version, please install the released version from [CRAN](https://cran.r-project.org/package=replicateBE) first to get its dependencies right ([readxl](https://cran.r-project.org/package=readxl) ≥1.0.0, [PowerTOST](https://cran.r-project.org/package=PowerTOST) ≥1.5.3, [lmerTest](https://cran.r-project.org/package=lmerTest), [nlme](https://cran.r-project.org/package=nlme), [pbkrtest](https://cran.r-project.org/package=pbkrtest)).
You need tools for building R packages from sources on your machine. For Windows users:\
- Download [Rtools](https://cran.r-project.org/bin/windows/Rtools/) from <abbr title="The Comprehensive R Archive Network">CRAN</abbr> and follow the suggestions of the installer.
- Install `devtools` and build the development version by:
```{r eval = FALSE}
install.packages("devtools", repos = "https://cloud.r-project.org/")
devtools::install_github("Helmut01/replicateBE")
```
<small>[TOC ↩](#replicatebe)</small>
## Session Information{#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.
```{r, sessioninfo}
options(width = 66)
print(sessionInfo(), locale = FALSE)
```
<small>[TOC ↩](#replicatebe)</small>
## Contributors{#contributors}
Helmut Schütz (author) <span style="font-size:smaller">[ORCID iD](https://orcid.org/0000-0002-1167-7880)</span><br>
Michael Tomashevskiy (contributor)<br>
Detlew Labes (contributor) <span style="font-size:smaller">[ORCID iD](https://orcid.org/0000-0003-2169-426X)</span>
<small>[TOC ↩](#replicatebe)</small>
## Disclaimer{#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.
<small>[TOC ↩](#replicatebe)</small>
***
<span id="f1" style="font-size:smaller"> 1. <abbr title="European Medicines Agency">EMA</abbr>. EMA/582648/2016. Annex I. London. 21 September 2016. [Online](https://www.ema.europa.eu/en/documents/other/31-annex-i-statistical-analysis-methods-compatible-ema-bioequivalence-guideline_en.pdf)</span> [↩](#a1)\
<span id="f2" style="font-size:smaller"> 2. <abbr title="European Medicines Agency">EMA</abbr>, <abbr title="Committee for Medicinal Products for Human Use">CHMP</abbr>. CPMP/EWP/QWP/1401/98 Rev. 1/ Corr \*\*. London. 20 January 2010. [Online](https://www.ema.europa.eu/en/documents/scientific-guideline/guideline-investigation-bioequivalence-rev1_en.pdf).</span> [↩](#a2)\
<span id="f3" style="font-size:smaller"> 3. <abbr title="European Generic Medicines Association">EGA</abbr>. *Revised EMA Bioequivalence Guideline. Questions & Answers.* London. June 2010. [Online](https://www.medicinesforeurope.com/wp-content/uploads/2016/03/EGA_BEQ_QA_WEB_QA_1_32.pdf#page=21)</span> [↩](#a3)\
<span id="f4" style="font-size:smaller"> 4. Health Canada. *Guidance Document. Conduct and Analysis of Comparative Bioavailability Studies.* Ottawa. 2018/06/08. [Online](https://www.canada.ca/content/dam/hc-sc/documents/services/drugs-health-products/drug-products/applications-submissions/guidance-documents/bioavailability-bioequivalence/conduct-analysis-comparative.pdf).</span> [↩](#a4)\
<span id="f5" style="font-size:smaller"> 5. Executive Board of the Health Ministers’ Council for <abbr title="Gulf Cooperation Council">GCC</abbr> States. *The GCC Guidelines for Bioequivalence. Version 3.0.* May 2021. [Online](https://www.sfda.gov.sa/sites/default/files/2021-10/GCC_Guidelines_Bioequivalence.pdf).</span> [↩](#a5)\
<span id="f6" style="font-size:smaller"> 6. <abbr title="World Health Organization">WHO</abbr>. *Application of reference-scaled criteria for AUC in bioequivalence studies conducted for submission to <abbr title="Prequalification Unit – Medicines Assessment Team">PQT/MED</abbr>.* Geneva. 02 July 2021. [Online](https://extranet.who.int/pqweb/sites/default/files/documents/AUC_criteria_July2021.pdf).</span> [↩](#a6)\
<span id="f7" style="font-size:smaller"> 7. <abbr title="Medicines Control Council">MCC</abbr>. *Registration of Medicines. Biostudies.* Pretoria. June 2015. [Online](https://www.sahpra.org.za/wp-content/uploads/2020/01/61de452d2.06_Biostudies_Jun15_v6.pdf).</span> [↩](#a7)\
<span id="f8" style="font-size:smaller"> 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](https://doi.org/10.1208/s12248-020-0427-6).</span> [↩](#a8)\
<span id="f9" style="font-size:smaller"> 9. <abbr title="European Medicines Agency">EMA</abbr>. EMA/582648/2016. Annex II. London. 21 September 2016. [Online](https://www.ema.europa.eu/en/documents/other/31-annex-ii-statistical-analysis-bioequivalence-study-example-data-set_en.pdf).</span> [↩](#a9)\
<span id="f10" style="font-size:smaller">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](https://doi.org/10.1177/009286159803200426).</span> [↩](#a10)