In Helmut01/replicateBE: Average Bioequivalence with Expanding Limits (ABEL)

knitr::opts_chunk$set(
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  fig.path = "man/figures/README-"
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Comparative BA-calculation for the EMA’s Average Bioequivalence with Expanding Limits (ABEL)

Introduction{#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 s~wT~/s~wR~ and the upper confidence limit of σ~wT~/σ~wR~. 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{#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 ANOVA). Estimated by the function lm() of package 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", ])

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Method A{#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.

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

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Method B{#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.

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 EMA’s Q&A document and hence, the default of the function.

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.

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

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Average Bioequivalence{#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.

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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 (Balaam’s design; not recommended due to poor power characteristics)

Three period (partial) replicates{#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{#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 (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{#examples}

• Evaluation of the internal reference dataset 01⁹ by Method A.

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)

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• 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)
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)

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• 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)
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)

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• 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)

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• 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)

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• 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)

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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 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")

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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.

options(width = 66)
print(sessionInfo(), locale = FALSE)

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Contributors{#contributors}

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

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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.

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---

  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. ↩

Helmut01/replicateBE documentation built on May 9, 2022, 12:15 a.m.