Simulation of Correlated Continuous and Categorical Variables using a Single Multivariate Distribution

Abstract

Clinical trial simulations make use of input/output models with covariate effects; the virtual patient population generated for the simulation should therefore display physiologically reasonable covariate distributions. Covariate distribution modeling is one method used to create sets of covariate values (vectors) that characterize individual virtual patients, which should be representative of real subjects participating in clinical trials. Covariates can be continuous (e.g., body weight, age) or categorical (e.g., sex, race). A modeling method commonly used for incorporating both continuous and categorical covariates, the Discrete method, requires the patient population to be divided into subgroups for each unique combination of categorical covariates, with separate multivariate functions for the continuous covariates in each subset. However, when there are multiple categorical covariates this approach can result in subgroups with very few representative patients, and thus, insufficient data to build a model that characterizes these patient groups. To resolve this limitation, an application of a statistical methodology (Continuous method) was conceived to enable sampling of complete covariate vectors, including both continuous and categorical covariates, from a single multivariate function. The Discrete and Continuous methods were compared using both simulated and real data with respect to their ability to generate virtual patient distributions that match a target population. The simulated data sets consisted of one categorical and two correlated continuous covariates. The proportion of patients in each subgroup, correlation between the continuous covariates, and ratio of the means of the continuous covariates in the subgroups were varied. During evaluation, both methods accurately generated the summary statistics and proper proportions of the target population. In general, the Continuous method performed as well as the Discrete method, except when the subgroups, defined by categorical value, had markedly different continuous covariate means, for which, in the authors' experience, there are few clinically relevant examples. The Continuous method allows analysis of the full population instead of multiple subgroups, reducing the number of analyses that must be performed, and thereby increasing efficiency. More importantly, analyzing a larger pool of data increases the precision of the covariance estimates of the covariates, thus improving the accuracy of the description of the covariate distribution in the simulated population.