Design of pharmacokinetic studies for latent covariates

Latent covariates are covariates that are known to exist but are either observable but unavailable or unobservable at the time of the clinical study. Designs to account for latent covariates must incorporate both uncertainty in the prevalence of the covariate and the data-type of the covariate. The informativeness of the covariate will then depend on whether the covariate data is continuous, ordinal or nominal. In this work we consider designs for latent covariates that may either directly influence the parameter of interest, or indirectly via actions on an observable covariate which then influences the parameter of interest. We consider a motivating example based on the effect of a genetic polymorphism on the influence of a continuous covariate (age) on drug clearance (CL). The polymorphism could take the case of a haplotype with many variant alleles, or a copy number variation in genes with different phenotypic expressions which could be treated as continuous data, or as a bi- or tri-allelic single nucleotide polymorphism that could form either an ordinal or nominal covariate on drug CL. The aim of this study was to investigate designs for clinical studies for latent covariates that accommodate both unknown prevalence and unknown data-type. Initially, the informativeness of a covariate was explored using linear regression assuming the three data-types continuous, ordinal and nominal. The linear covariate model was then considered within a nonlinear mixed effects modelling framework. Two simulation scenarios were considered: (1) the influence of the latent covariate directly on the parameter of interest and (2) the influence of the latent covariate on an observable non-latent continuous covariate, which was assumed to follow a normal or stratified distribution, and the effect of this covariate on the parameter of interest. A power analysis for population PK modelling (1) where the latent covariate had direct influence on the parameter also showed similar behaviour to the linear regression solution. When the influence of the latent covariate was mediated via another observable non-latent continuous covariate, the power for the continuous model was highest but the power of the ordinal model was indistinguishable from that of the nominal model. Stratification of the observable non-latent continuous covariate did not appreciably change the power to identify the latent covariate from that when we assumed the observable covariate conformed to a normal distribution. It was found that parameter estimation is generally at least 1.5 to 7 fold more precise for continuous models than for categorical models.