Some properties of the Liang-Zeger method for the analysis of correlated binary data

Abstract

In this work, we investigate the properties of estimates produced using generalised estimating equations (GEEs), applied to the analysis of correlated binary data. Chapter One is a review of the different formulations and techniques used in dealing with correlated binary responses. In order to see how GEEs perform we need models that can describe and produce correlated binary responses. These are discussed in Chapter Two. In Chapter Three we derive general asymptotic expressions for both the estimates and the 'sandwich' estimates. These can be used to give insight on the properties of these estimates and frees us from the burden of simulation. We then apply these general results to specific formulations given in Chapters Four and Five. In Chapter Four, we study the bias and efficiency of Liang-Zeger (LZ) estimates and the 'sandwich' estimate of variance. Here we are only interested in estimating β and so higher-order association terms are nuisance parameters. Chapter Five compares the properties of different modelling scenarios in the GEE estimation framework. We wish to ascertain the benefits (if any) of elaborate modelling upon the estimates and their variances. We conclude that the extra demands of more complex modelling of the 'working' covariance does not result in greater precision in parameter estimates.