Simultaneous Generation of Binary and Normal Data with Specified Marginal and Association Structures

Situations in which multiple outcomes and predictors of different distributional types are collected are becoming increasingly common in biopharmaceutical practice, and joint modeling of mixed types has been gaining popularity in recent years. Evaluation of various statistical techniques that have been developed for mixed data in simulated environments necessarily requires joint generation of multiple variables. This article is concerned with building a unified framework for simulating multiple binary and normal variables simultaneously given marginal characteristics and association structure via combining well-established results from the random number generation literature. We illustrate the proposed approach in two simulation settings where we use artificial data as well as real depression score data from psychiatric research, demonstrating a very close resemblance between the specified and empirically computed statistical quantities of interest through descriptive and model-based tools.