To assess bioequivalence, the 90% confidence interval for the difference in the means of the log-transformed data should be calculated using appropriate methods to the study design. The antilogs (exponents) of the confidence limits obtained constitute the 90% confidence interval for the ratio of the geometric means between the T and R products. [@fda;@chow;@hauschke] To establish bioequivalence, the calculated confidence interval should fall within a bioequivalence limit, usually 80-125% for the ratio of the product averages. For nonreplicated crossover designs, general linear model procedures available in PROC GLM in SAS are preferred, although linear mixed-effects model procedures can also be indicated for analysis. [@fda]
BE R package [@R-BE] can analyze bioequivalence study data with
industrial strength. The current version of BE performs bioequivalency
tests for several pharmacokinetic parameters of the conventional
two-treatment, two-period, two-sequence (2x2) randomized crossover
design. The statistical model includes factors accounting for the
following sources of variation: sequence (SEQ), subjects nested in
sequences (SUBJ(SEQ)), period (PRD), and treatment (TRT).
In this document, the author performed validation of bioequivalence
tests performed by BE R package as compared to bioequivalence tests
performed by PROC GLM or PROC MIXED in SAS.
## $AUClast
## $AUClast$`Analysis of Variance (log scale)`
## SS DF MS F p
## SUBJECT 2.875497e+00 32 8.985928e-02 3.183942248 0.0008742828
## GROUP 1.024607e-01 1 1.024607e-01 1.145416548 0.2927731856
## SUBJECT(GROUP) 2.773036e+00 31 8.945279e-02 3.169539016 0.0009544080
## PERIOD 3.027399e-05 1 3.027399e-05 0.001072684 0.9740824428
## DRUG 3.643467e-02 1 3.643467e-02 1.290972690 0.2645764201
## ERROR 8.749021e-01 31 2.822265e-02 NA NA
## TOTAL 3.786834e+00 65 NA NA NA
##
## $AUClast$`Between and Within Subject Variability`
## Between Subject Within Subject
## Variance Estimate 0.03061507 0.02822265
## Coefficient of Variation, CV(%) 17.63193968 16.91883011
##
## $AUClast$`Least Square Means (geometric mean)`
## Reference Drug Test Drug
## Geometric Means 5092.098 4858.245
##
## $AUClast$`90% Confidence Interval of Geometric Mean Ratio (T/R)`
## Lower Limit Point Estimate Upper Limit
## 90% CI for Ratio 0.889436 0.9540753 1.023412
##
## $AUClast$`Sample Size`
## True Ratio=1 True Ratio=Point Estimate
## 80% Power Sample Size 6 7
##
##
## $Cmax
## $Cmax$`Analysis of Variance (log scale)`
## SS DF MS F p
## SUBJECT 2.861492e+00 32 8.942162e-02 2.237604579 0.01367095
## GROUP 9.735789e-05 1 9.735789e-05 0.001054764 0.97429977
## SUBJECT(GROUP) 2.861394e+00 31 9.230304e-02 2.309706785 0.01131826
## PERIOD 4.717497e-03 1 4.717497e-03 0.118046317 0.73348258
## DRUG 6.837756e-03 1 6.837756e-03 0.171101730 0.68198228
## ERROR 1.238856e+00 31 3.996310e-02 NA NA
## TOTAL 4.112258e+00 65 NA NA NA
##
## $Cmax$`Between and Within Subject Variability`
## Between Subject Within Subject
## Variance Estimate 0.02616997 0.0399631
## Coefficient of Variation, CV(%) 16.28355371 20.1921690
##
## $Cmax$`Least Square Means (geometric mean)`
## Reference Drug Test Drug
## Geometric Means 825.5206 808.8778
##
## $Cmax$`90% Confidence Interval of Geometric Mean Ratio (T/R)`
## Lower Limit Point Estimate Upper Limit
## 90% CI for Ratio 0.9013625 0.9798396 1.065149
##
## $Cmax$`Sample Size`
## True Ratio=1 True Ratio=Point Estimate
## 80% Power Sample Size 8 8
##
##
## $Tmax
## $Tmax$`Wilcoxon Signed-Rank Test`
## p-value
## 0.2326894
##
## $Tmax$`Hodges-Lehmann Estimate`
## Lower Limit Point Estimate Upper Limit
## 90% Confidence Interval -0.33000 -0.03500 0.1050
## 90% Confidence Interval(%) 74.37661 97.28237 108.1529
sessionInfo()## R version 3.6.3 (2020-02-29)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17763)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=Korean_Korea.949 LC_CTYPE=Korean_Korea.949
## [3] LC_MONETARY=Korean_Korea.949 LC_NUMERIC=C
## [5] LC_TIME=Korean_Korea.949
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] knitr_1.28
##
## loaded via a namespace (and not attached):
## [1] compiler_3.6.3 magrittr_1.5 tools_3.6.3 htmltools_0.4.0
## [5] Rcpp_1.0.4.6 stringi_1.4.6 rmarkdown_2.1 stringr_1.4.0
## [9] xfun_0.12 digest_0.6.25 rlang_0.4.5 evaluate_0.14