Correlated bivariate continuous and binary outcomes: Issues and applications

Abstract

Increasingly multiple outcomes are collected in order to characterize treatment effectiveness or to evaluate the impact of large policy initiatives. Often the multiple outcomes are non-commensurate, e.g. measured on different scales. The common approach to inference is to model each outcome separately ignoring the potential correlation among the responses. We describe and contrast several full likelihood and quasi-likelihood multivariate methods for non-commensurate outcomes. We present a new multivariate model to analyze binary and continuous correlated outcomes using a latent variable. We study the efficiency gains of the multivariate methods relative to the univariate approach. For complete data, all approaches yield consistent parameter estimates. When the mean structure of all outcomes depends on the same set of covariates, efficiency gains by adopting a multivariate approach are negligible. In contrast, when the mean outcomes depend on different covariate sets, large efficiency gains are realized. Three real examples illustrate the different approaches.