A Novel Method for Simulation of Correlated Continuous and Categorical Variables Using A Single Multivariate Distribution
S. Tannenbaum (1,2), Nick Holford (2,4), H. Lee (2,3), C. Peck (2), D. Mould (5)
(1) Pharmacology Modeling and Simulation, Novartis Pharmaceuticals Corp., East Hanover, NJ, USA, (2) Center for Drug Development Science, University of California Washington Center, Washington, DC, USA, (3) School of Medicine, University of Pittsburgh, Pittsburgh, PA, USA, (4) Dept of Pharmacology & Clinical Pharmacology, University of Auckland, Auckland, NZ, (5) Projections Research, Inc., Phoenixville, PA, USA
Introduction: Covariate distribution modeling (CDM) is used to generate virtual patients (covariate vectors), based on data from an existing patient population. Covariates may be continuous (weight) or categorical (sex); mixed covariate types present a challenge when creating a CDM.
In the standard (Discrete) method (DM), the population is subdivided by each unique combination of categorical covariates, each with a separate multivariate normal distribution (MVND) for the continuous covariates. However, when there are many categories, some subgroups have insufficient data to build a representative model. Therefore, a novel (Continuous) method (CM) was conceived in which complete covariate vectors, including both continuous and categorical covariates, could be sampled from a single MVND.
Methods: A MVND is comprised of a mean vector and a variance-covariance matrix (VCVM). In the DM, categorical covariates are sampled from their individual distributions; continuous covariates are then generated from the proper subgroup’s MVND. In the CM, all covariates are treated as continuous; the resultant single MVND is used to generate complete patient covariate vectors. Since categorical covariates (e.g., X) will have continuous values, cutoff values to assign the categorical levels are defined as the inverse of the LN cumulative distribution with mean(lnX), sd(lnX), and cumulative probability r. The CM and DM were applied to real and simulated data sets to compare their abilities to generate matching virtual patient distributions.
Results: For the real data, both methods accurately generated the summary statistics (continuous) and proportions (categorical) of the covariates, with high precision and negligible bias. The DM results, however, were based on incomplete data. Because there were Conclusions: Compared to the DM, the CM’s benefits result from analyzing the whole population instead of subsets. Including a large amount of data in the creation of the MVND enhances its stability and, as a consequence, the reliability of the generated covariate combinations. In addition, by allowing all covariates to be described by a single MVND, the number of analyses that must be performed is reduced, increasing efficiency. The CM appears to generate unbiased, precise covariates for the purposes of simulating covariate vectors in a clinical trial simulation.