Generalized Estimating Equations Logistic Regression

Abstract

Many fields of study use longitudinal datasets, which usually consist of repeated measurements of a response variable, often accompanied by a set of covariates for each of the subjects/units. However, longitudinal datasets are problematic because they inherently show correlation due to a subject’s repeated set of measurements. For example, one might expect a correlation to exist when looking at a patient’s health status over time or a student’s performance over time. But in those cases, when the responses are correlated, we cannot readily obtain the underlying joint distribution; hence, there is no closed-form joint likelihood function to present, as with the standard logistic regression model. One remedy is to fit a generalized estimating equations (GEE) logistic regression model for the data, which is explored in this chapter. This chapter addresses repeated measures of the sampling unit, showing how the GEE method allows missing values within a subject without losing all the data from the subject, and time-varying predictors that can appear in the model. The method requires a large number of subjects and provides estimates of the marginal model parameters. We fit this model in SAS, SPSS, and R, basing our work on the variance means relationship methods, Ziang and Leger (Biometrics 42:121–130, 1986a, Biometrics 73:13–22, 1986b), and Liang and Zeger (Biometrika 73:13–22, 1986).