Generalized Estimating Equations Logistic Regression

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 data are challenging as they inherently have correlation due to a subject’s repeated set of observations. 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 is the case with the independent observations and 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 on the sampling unit and demonstrates 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 the GEE model in SAS, SPSS, R, and STATA basing our work on the variance means relationship methods, Ziang and Leger (1986a, b), Liang and Zeger (1986).