Objective of this work is: to provide instrument to make bioequivalence analysis with type C model and a development of a demonstrative code for step-by-step clarification of mixed model computation procedure for any interested developers. ReplicateBE based on REML minimization with direct variance-covariance matrix inversion and forward differentiation of REML function.
The replicate designed bioequivalence is a powerful approach to get more information about variation. In some cases the number of subjects required to demonstrate bioequivalence can be reduced by up to about 50% (Van Peer, A., 2010). For a high variability product, replication can really improve the precision and provide more complete intra-individual variation estimate. Also replicate design could be used for reference-scaled average bioequivalence (RSABE) to demonstrate bioequivalence for highly variable drugs (HVDs).
With accordance to US FDA guideline linear mixed-effects model procedures, available in PROC MIXED in SAS or equivalent software, should be used for the analysis of replicated crossover studies for average BE (US FDA).
At this moment linear mixed model effect analysis can be done with proprietary (SPSS, SAS, Stata) and open source (R:nlme, R:lme4, Julia:MixedModels) software. But not all statistical mixed models packages support flexible covariance structure fitting with structures like “heterogeneous compound symmetry” (CSH), FA0(2). This doesn’t means that lme4 or MixedModels can’t be used for bioequivalence estimation, but CSH structure not available in this packages and comparison of results performed in SAS/SPSS with lme4 can be problematically.
Objective of this work is: to provide instrument to make bioequivalence analysis with type C model and a development of a demonstrative code for step-by-step clarification of mixed model computation procedure for any interested developers.
ReplicateBE was validated with 6 reference public datasets, 22 generated datasets and simulation study. ReplicateBE version 0.1.4 and 0.2.0 is compliant to SAS/SPSS, values checked: REML estimate, variance components estimate, fixed effect estimate, standard error of fixed effect estimate. Validation procedures included in package test procedure and perform each time when new version released or can be done at any time on user machine. Confidence interval (95%) for type I error (alpha) is 0.048047 – 0.050733 (10000 iterations). No statistically significant difference found with acceptable rate (0.05) found (version 0.1.4).
ReplicateBE not designed for modeling in a general purpose, but can be used in situation with similar structure. Also ReplicateBE based on direct inversing of variance-covarance matrix V, so computation of may be time expensive if size of matrix is big. This does not happen in bioequivalence study where size of V is no more 4 (4 periods). But in general this can be serious disadvantage. This situation can be avoided using sweep based transformations (Wolfinger et al., 1994). In ReplicateBE variance structure strictly denoted and can’t be changed, but it can be a target in package developing path. In ReplicateBE Satterthwaite degree of freedom (DF) not equal with SAS/SPSS DF estimate in all datasets, the reason and need for adjustments remains to be clarified.