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.

The impact of missing data on analyses of a time-dependent exposure in a longitudinal cohort: a simulation study

“…age) and categorical covariates (i.e. the demographic variables: sex, country of birth, education; and lifestyle factors: smoking status, physical activity and alcohol consumption) [28]. The means and variance-covariance matrix used for the multivariate normal distribution were obtained from the observed data of the 26,846 participants who attended both waves.…”

Application of two machine learning algorithms to genetic association studies in the presence of covariates

“…Values of the correlation between X and Z ranging from 0.2 to 0.9 are considered. In the case of a continuous covariate, the discrete approach described by Tannenbaum, S. et al (2001) [ 28 ] is applied to induce correlation between X and Z . For M ODEL 3, we simulate a mediator binary variable Z via a logistic regression on X and let Z = 1 if ψ ≥ or Z = 0 if ψ < where ψ is a uniform random number between 0 and 1 and is a predicted probability that Z = 1 conditional on X.…”

Performance of Methods for Handling Missing Categorical Covariate Data in Population Pharmacokinetic Analyses

“…A frequently used approach for handling missing data is single or multiple imputations (MI) (15), but these techniques were not evaluated in this article. MI has been applied in modeling with NONMEM, e.g., in (16), but this technique requires additional simulation steps and cannot be deployed in a single NONMEM estimation. Furthermore, since imputation requires additional computation, estimates obtained by these methods may be considered less efficient than those obtained from likelihood-based methods (15).…”