Data Analytic Methods for Correlated Binary Responses

There has been increasing use of longitudinal studies in medicine and elsewhere, yielding data that tend to be correlated with one another. While methodology for the analysis of repeated continuous outcome data has been well developed, not much has been done for their discrete counterparts. The generalized estimating equations (GEE) approach has, however, become popular for the analysis for correlated binary responses since their introduction in 1986. There are usually a large number of potentially useful covariates related to the response and yet no methodology has been suggested for variable selection in correlated binary outcome models. The motivation for this research arose from the need to develop a strategy appropriate for the selection of covariates in these situations. In this thesis, we have proposed and studied a stepwise selection procedure for correlated binary regression based on the GEE model and contrast it with the widely used stepwise logistic regression. We developed a score test for forward selection and a modified Wald's test for backward elimination. We showed that under certain regularity conditions, these test statistics have asymptotic chi-square distributions. We developed a generalized score to test for model adequacy once a model is selected. This methodology is illustrate d with a real data set from a study on functional decline in the activities of daily living in a group of elderly patients. Seventeen covariates known or suspected to affect functional decline were used in the stepwise regression model. Three correlation structures (a) independence, (b) equal and (c) one-step dependence were assumed. Using an extensive Monte Carlo simulation, the proposed stepwise procedure was evaluated under different degrees of association among the binary responses. This was achieved by generating correlated binary data and five covariates, under some specified distributions. We found that for responses with a substantial degree of association e.g. odds ratio greater than two, the selection procedure using an assumed correlation structure produced superior results. For odds ratios close to unity, the three structures produced similar results. These were run using a computer program written in the Interactive Matrix Language (IML) in SAS. Advisors/Committee Members: Amini, Saeid B.