Statistical Evaluation of Clinical Trial Design for a Population Pharmacokinetic Study —A Case Study—

Evaluation of Approaches to Deal with Low-Frequency Nuisance Covariates in Population Pharmacokinetic Analyses

Clinical studies include occurrences of rare variables, like genotypes, which due to their frequency and strength render their effects difficult to estimate from a dataset. Variables that influence the estimated value of a model-based parameter are termed covariates. It is often difficult to determine if such an effect is significant, since type I error can be inflated when the covariate is rare. Their presence may have either an insubstantial effect on the parameters of interest, hence are ignorable, or conversely they may be influential and therefore non-ignorable. In the case that these covariate effects cannot be estimated due to power and are non-ignorable, then these are considered nuisance, in that they have to be considered but due to type 1 error are of limited interest. This study assesses methods of handling nuisance covariate effects. The specific objectives include (1) calibrating the frequency of a covariate that is associated with type 1 error inflation, (2) calibrating its strength that renders it non-ignorable and (3) evaluating methods for handling these non-ignorable covariates in a nonlinear mixed effects model setting. Type 1 error was determined for the Wald test. Methods considered for handling the nuisance covariate effects were case deletion, Box-Cox transformation and inclusion of a specific fixed effects parameter. Non-ignorable nuisance covariates were found to be effectively handled through addition of a fixed effect parameter.

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.

Relevance of assessing drug concentration exposure in pharmacogenetic and imaging studies

Pharmacodynamic differences are difficult to interpret without drug concentration data. In particular, variability in drug exposure may confound the interpretation of pharmacogenetic, therapeutic outcome, and neuroimaging studies. Inter-individual variability in concentrations can be quite high due to variable adherence and pharmacokinetics. For example, clearance may be influenced by genetics, drug interactions, age and illness. We review findings that acute responses to selective serotonin reuptake inhibitors can have a concentration-response relationship using positron emission tomography and neuroendocrine measures. We also present preliminary evidence that the concentration-response relationship for paroxetine is influenced by genotypic differences at the serotonin transporter promoter. In large clinical studies, the accurate assessment of drug exposure can be challenging, with several techniques used to assess exposure. Population pharmacokinetics (Pop PK) is a method that is ideally suited for analysing concentration data from large trials because both patient-specific and population parameters can be determined with only a small number of plasma samples per patient. As opposed to relying on prescribed doses or a single trough level, the ability to determine more accurately exposure with Pop PK reduces the heterogeneity introduced by exposure variability. Pop PK hierarchic Bayesian approaches have been effective for characterizing anticonvulsants, antibiotics, antineoplastics and antiarrhythmics. We have recently successfully incorporated these pop PK analyses into routine assessments of elderly patients in clinical trials of selective serotonin reuptake inhibitors (SSRIs) and second generation antipsychotics. For the design and interpretation of neuroimaging, pharmacogenetic, and behavioural studies, the assessment of drug concentration exposure is therefore feasible and has potentially important ramifications.