Performance of alternative statistical models for bivariate binary data in samples of small and moderate siz

Bivariate binary data often arise in medical studies of bilateral organs or in studies of twins or spouses. This work is motivated by the Boston Partners Study, which examines risk factors for HIV among male homosexual couples. Different types of logistic regression models have been designed to emphasize different aspects of modeling bivariate binary outcomes. These models can be grouped into three major classes: marginal (population-averaged), response-conditional and cluster-specific. Accuracy of inferences on both regression and clustering parameters depends upon various factors including study design, sample size, distributional assumptions regarding the prevalence of the outcome and the form and strength of clustering among outcomes.;In this dissertation we address three problems in the use of bivariate binary logistic regression models: (1) how are inferences on regression and clustering parameters affected by design features, particularly covariate distributions in small samples; (2) what actors influence the accuracy of approximation formulas relating regression parameters from these logistic regression models; and (3) how is the performance of these logistic regression models affected by misspecification of the distribution of the underlying risk of events? The performance of these models in small samples is evaluated through simulation studies by comparing coverage properties of 95% confidence intervals and mean percent error.;We found that the marginal and response-conditional models, implemented through the Alternating Logistic Regressions (ALR) of Carey and the Polychotomous Logistic Regression (PCH) model of Rosner respectively, generally performed well. Estimates for both regression and clustering effects obtained from the cluster-specific model through the pseudo-likelihood approach (MIX) of Wolfinger were attenuated across all conditions examined. Analytical evaluation revealed that approximation formulas, proposed by Neuhaus and Zeger, relating regression parameters from these three models had rather small but consistent bias across all conditions examined. The PCH model was robust and both ALR and MIX models were somewhat sensitive to the specific data generating mechanism. We characterized the relationship between two measures of clustering effect: logarithm of the pairwise odds ratio and the degree of heterogeneity in underlying risk across clusters.