Design of pharmacokinetic studies for latent covariates

Background: Latent covariates are covariates that are either not available or unobservable at the time of the clinical study. Single nucleotide polymorphisms (SNPs) are of interest in pharmacokinetic studies and are often latent at the time the patient is enrolled. The amount of information provided by latent covariates depends on whether the covariate distribution is continuous, ordinal or nominal. In this work we consider the effect of a SNP on the influence of age on drug clearance.

Aims: To explore designs for clinical studies for latent covariates that accommodates the unknown covariate distribution, i.e. continuous, ordinal or nominal

Methods: Initially, the informativeness of a covariate explored using linear regression assuming continuous, ordinal and nominal models (here clearance (CL) was considered to be the dependent variable). The standard error (SE) for each parameter for each model was derived from the Fisher Information Matrix (FIM). Secondly, the linear covariate model was considered within a nonlinear mixed effects modelling framework. The population pharmacokinetics (PK) model was a two compartment zero order input. Three simulation scenarios were considered: (1) the influence of the SNP directly on CL (2) the influence of SNP on age and then the effect of age on CL and (3) the same scenario as in (2) but with age arising from a stratified rather than normal distribution. In all scenarios the SNP was assumed to conform to either a continuous, ordinal or nominal distribution. A power analysis for each scenario was conducted by simulation in MATLAB and estimation was performed in NONMEM according to predefined criteria.

Results: For the linear regression model, the calculated SEs for the different models were lowest for the continuous model and highest for the nominal model with the ordinal model falling between. The power analysis from the population PK model (1) where the SNP had direct influence on CL showed a power of 0.999 with the continuous model, followed by the power of 0.352 with the ordinal model with the nominal model having the least power of 0.197. For (2) when age and SNP were considered together, it was found that the power for the continuous model was highest with 1 while for the ordinal it is 0.75 and for the nominal it was 0.77 following a normal distribution of age. The stratification of age resulted in higher power compared to age following a normal distribution with power for the continuous 1 while for ordinal and nominal it was 0.86.

Conclusion: It was found that parameter estimation is easiest for continuous models and generally poorest for nominal models. Further work is required to provide an estimate as to the likely sample size differences required for each of the covariate distributions.