Longitudinal Data Analysis for Discrete and Continuous Outcomes

TLDR

Longitudinal data consist of repeated outcome and covariate measurements per subject, and analysis aims to model the marginal expectation of the outcome as a function of covariates while accounting for within‑subject correlation, extending quasi‑likelihood methods. This paper proposes a unified approach using generalized estimating equations to analyze a wide range of discrete and continuous longitudinal outcomes. The authors develop a class of GEEs for regression parameters and illustrate its use with data on mothers' stress and children's morbidity. The GEEs produce consistent, asymptotically Gaussian solutions and a consistent variance estimator even when time dependence is misspecified.

Abstract

Longitudinal data sets are comprised of repeated observations of an outcome and a set of covariates for each of many subjects. One objective of statistical analysis is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlation among the repeated observations for a given subject. This paper proposes a unifying approach to such analysis for a variety of discrete and continuous outcomes. A class of generalized estimating equations (GEEs) for the regression parameters is proposed. The equations are extensions of those used in quasi-likelihood (Wedderburn, 1974, Biometrika 61, 439-447) methods. The GEEs have solutions which are consistent and asymptotically Gaussian even when the time dependence is misspecified as we often expect. A consistent variance estimate is presented. We illustrate the use of the GEE approach with longitudinal data from a study of the effect of mothers' stress on children's morbidity.