Mitigation of the convergence issues associated with semi-replicated bioequivalence data

Semi-replicated designs for investigation of bioequivalence constitute a challenge when mixed models are applied. With the commonly available packages and regardless of choice of covariance structure the software may force variance components into the covariance matrix that render it over-specified. This may give rise to arbitrary estimates of certain variance components, lack of convergence or warnings. Classically the covariance matrix is decomposed as V = ZGZ^t  + R, with G containing the between-subject variance components, Z being the design matrix for the random effects and R containing the within-subject variance components. By abandoning the definitions of G and R, and instead working directly in V, it is possible to specify a correct model with only the variance components of interest. Proof-of-concept for this idea is delivered with a script in the statistical language R. The script is available as supplementary material (Data S1).