The Analysis of Correlated Binary Outcomes Using Multivariate Logistic Regression

A method for analyzing correlated binary outcomes when the responses are distinct measurements made simultaneously on a single individual is presented. This extension of univariate logistic regression allows us to model the dependence of the responses on a set of covariates while estimating the degree of association among them. For the case of two dichotomous outcomes, a form of the cumulative bivariate logistic distribution proposed by Gumbel is used to characterize their joint probabilities in terms of logistic marginal probabilities and the correlation coefficient of the responses. The model is then extended to accommodate three or more dichotomous outcomes. A two-step approximation to fitting the multivariate logistic model is also described.