Introduction

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. (CDER, FDA 2001; Chow and Liu 2008; Hauschke, Steinijans, and Pigeot 2007) 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. (CDER, FDA 2001)

BE R package (Bae 2018) 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.

Methods

library(BE)         # install.packages("BE", repos="http://r.acr.kr")
library(dplyr)      # install.packages("dplyr")
library(readxl)      # install.packages("readxl")

tab_r_be_results <- function(parameter){
  BE::test2x2(BE::NCAResult4BE, parameter)[[4]] %>% 
  as.data.frame() %>% 
  mutate(Analysis = 'R: BE package') %>% 
  select(Analysis, `Lower Limit`, `Point Estimate`, `Upper Limit`)
}

PROC GLM DATA=BE OUTSTAT=STATRES; /* GLM use only complete subjects. */
CLASS SEQ PRD TRT SUBJ;
MODEL LNAUCL = SEQ SUBJ(SEQ) PRD TRT;
RANDOM SUBJ(SEQ)/TEST;
LSMEANS TRT /PDIFF=CONTROL('R') CL ALPHA=0.1 COV OUT=LSOUT;

PROC MIXED DATA=BE; /* MIXED uses all data. */
CLASS SEQ TRT SUBJ PRD;
MODEL LNAUCL = SEQ PRD TRT;
RANDOM SUBJ(SEQ);
ESTIMATE 'T VS R' TRT -1 1 /CL ALPHA=0.1;
ODS OUTPUT ESTIMATES=ESTIM COVPARMS=COVPAR;

tab_sas_proc_results <- function(analysis_name, skip_no){
  read_excel('sas/sas-be-macro-results.xlsx', skip = skip_no, n_max = 2) %>% 
  mutate(Analysis = analysis_name) %>% 
    select(Analysis, `Lower Limit` = LL, `Point Estimate` = PE, `Upper Limit` = UL)
}

Results

AUClast_R_BE <- tab_r_be_results("AUClast")

AUClast_proc_glm <- tab_sas_proc_results('SAS: PROC GLM', skip = 108)
AUClast_proc_mixed <- tab_sas_proc_results('SAS: PROC MIXED', skip = 180)

# Combine all analyses of AUClast
AUClast_all_analyses <- bind_rows(AUClast_R_BE, AUClast_proc_glm, AUClast_proc_mixed)

Cmax_R_BE <- tab_r_be_results("Cmax")

Cmax_proc_glm <- tab_sas_proc_results('SAS: PROC GLM', skip = 294)
Cmax_proc_mixed <- tab_sas_proc_results('SAS: PROC MIXED', skip = 366)

# Combine all analyses of Cmax
Cmax_all_analyses <- bind_rows(Cmax_R_BE, Cmax_proc_glm, Cmax_proc_mixed)

Conclusion

There is no discrepancy between bioequivalence tests performed by BE R package and those performed by PROC GLM or PROC MIXED in SAS. We also performed multiple analyses with the actual clinical trial datasets and have found no differences (data not shown: confidential).

Bioequivalence tests performed by the open-source BE R package for the conventional two-treatment, two-period, two-sequence (2x2) randomized crossover design can be qualified and validated enough to acquire the identical results of the commercial statistical software, SAS.

Please report issues regarding validation of the R package to https://github.com/asancpt/BE-validation/issues.

Affiliation:
Sungpil Han M.D/Ph.D
Resident,
Department of Clinical Pharmacology and Therapeutics,
Asan Medical Center, University of Ulsan,
Seoul 05505, Republic of Korea
E-mail: shan@acp.kr
URL: www.github.com/shanmdphd

Raw data

The concentration-time curves are ploted in Figure 1 and the result of noncomparmental analysis is presented in Table 3.

Figure 1: Concentration-time curves of raw data (N=33)

Table 3: The raw pharmacokinetic data used for analysis in R and SAS (N=33)

SAS Scripts and results

To run these scripts, the dataset BE::NCAResult4BE should be exported from R by write.csv().

%MACRO BETEST(DSNAME, VARNAME);
/* PROC GLM use only complete subjects. */
PROC GLM DATA=&DSNAME OUTSTAT=STATRES; 
  CLASS SEQ PRD TRT SUBJ;
  MODEL &VARNAME = SEQ SUBJ(SEQ) PRD TRT;
  RANDOM SUBJ(SEQ)/TEST;
  LSMEANS TRT /PDIFF=CONTROL('R') CL ALPHA=0.1 COV OUT=LSOUT;

DATA STATRES;
  SET STATRES;
  IF _TYPE_='ERROR' THEN CALL SYMPUT('DF', DF);

DATA LSOUT;
  SET LSOUT;
  IF TRT='R' THEN CALL SYMPUT('GMR_R', LSMEAN);
  IF TRT='T' THEN CALL SYMPUT('GMR_T', LSMEAN);
  IF TRT='R' THEN CALL SYMPUT('V_R', COV1);
  IF TRT='T' THEN CALL SYMPUT('V_T', COV2);
  IF TRT='T' THEN CALL SYMPUT('COV', COV1);

DATA LSOUT2;
  LNPE = &GMR_T - &GMR_R;
  DF = &DF;
  SE = SQRT(&V_R + &V_T - 2*&COV);
  LNLM = TINV(0.95, DF)*SE;
  LNLL = LNPE - LNLM ;
  LNUL = LNPE + LNLM;
  PE = EXP(LNPE);
  LL = EXP(LNLL);
  UL = EXP(LNUL);
  WD = UL - LL;
PROC PRINT DATA=LSOUT2; RUN;

/* PROC MIXED  uses all data. */
PROC MIXED DATA=&DSNAME; 
  CLASS SEQ TRT SUBJ PRD;
  MODEL &VARNAME = SEQ PRD TRT;
  RANDOM SUBJ(SEQ);
  ESTIMATE 'T VS R' TRT -1 1 /CL ALPHA=0.1; 
  ODS OUTPUT ESTIMATES=ESTIM COVPARMS=COVPAR;

DATA COVPAR;
  SET COVPAR;
  IF CovParm = 'Residual' THEN CALL SYMPUT('MSE', Estimate);

DATA ESTIM;
  SET ESTIM;
  MSE = &MSE;
  LNLM = (Upper - Lower)/2;
  PE = EXP(Estimate);
  LL = EXP(Lower);
  UL = EXP(Upper);
  WD = UL - LL;
PROC PRINT Data=ESTIM; RUN;

%MEND BETEST;

DATA PKDATA; 
  INFILE 'c:\Users\mdlhs\asancpt\BE-validation\sas\NCAResult4BE.csv' FIRSTOBS=2 DLM=",";
  INPUT SUBJ $ SEQ $ PRD $ TRT $ AUClast Cmax Tmax;
  IF CMAX =< 0 THEN DELETE;
  LNAUCL = LOG(AUClast);
  LNCMAX = LOG(Cmax);

*BE Test ;

%BETEST(PKDATA, LNAUCL);
%BETEST(PKDATA, LNCMAX);

Session Information

devtools::session_info()

## - Session info ----------------------------------------------------------
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##  os       Windows 7 x64 SP 1          
##  system   x86_64, mingw32             
##  ui       RTerm                       
##  language (EN)                        
##  collate  Korean_Korea.949            
##  ctype    Korean_Korea.949            
##  tz       Asia/Seoul                  
##  date     2018-10-29                  
## 
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