Analysis of longitudinal data using weighted least squares and generalized estimating equations

In longitudinal studies, correlated binary data arise when repeated measurements of a dichotomous response variable are taken over time. Two general approaches that can be used to analyze such data are weighted least squares (WLS) and generalized estimating equations (GEE). In this research, issues related to the analysis of longitudinal binary data using the GEE and WLS approaches are studied.;In order to evaluate the finite-sample properties of the modified GEE methods studied in this thesis and to compare the GEE and WLS approaches, it is necessary to generate correlated binary response data with specified correlation structures. Since existing methods are not applicable to the situations considered in this research, a new simulation model for generating correlated binary responses is developed.;In certain situations, the GEE and WLS approaches produce the same estimates of the parameters and their variances and covariances. In settings where this is not the case, the relative performances of the two methods are compared in an extensive simulation study. This study indicates that there is very little difference between the WLS and GEE results, regardless of how well the assumed GEE working correlation structure approximated the true correlation structure. Thus, when the covariates are categorical, the easy-to-use WLS method is recommended.;As originally proposed, the GEE approach uses standardized Pearson residuals to consistently estimate the working covariance matrix. When the response at each time point is binary, the Pearson residual may not be the best choice. Alternative estimation procedures based on the Anscombe and deviance residuals appropriate for binary responses are studied. The goal is to determine if the use of residuals particularly suited to binary responses improves the efficiency of the resulting parameter estimates and the power of the hypothesis test. The results indicated that the procedure using the Anscombe residual has the highest Wald test power and the same efficiency as the other two procedures.