Information Sets and Excess Zeros in Random Effects Modeling of Longitudinal Data

Marginal regression via generalized estimating equations is widely used in biostatistics to model longitudinal data from subjects whose outcomes and covariates are observed at several time points. In this paper we consider two issues that have been raised in the literature concerning the marginal regression approach. The first is that even though the past history may be predictive of outcome, the marginal approach does not use this history. Although marginal regression has the flexibility of allowing between-subject variations in the observation times, it may lose substantial prediction power in comparison with the transitional modeling approach that relates the responses to the covariate and outcome histories. We address this issue by using the concept of “information sets” for prediction to generalize the “partly conditional mean” approach of Pepe and Couper (J. Am. Stat. Assoc. 92:991–998, 1997). This modeling approach strikes a balance between the flexibility of the marginal approach and the predictive power of transitional modeling. Another issue is the problem of excess zeros in the outcomes over what the underlying model for marginal regression implies. We show how our predictive modeling approach based on information sets can be readily modified to handle the excess zeros in the longitudinal time series. By synthesizing the marginal, transitional, and mixed effects modeling approaches in a predictive framework, we also discuss how their respective advantages can be retained while their limitations can be circumvented for modeling longitudinal data.