Analysis of Partially Observed Clustered Data using Generalized Estimating Equations and Multiple Imputation

Abstract

Clustered data arise in many settings, particularly within the social and biomedical sciences. For example, multiple-source reports are commonly collected in child and adolescent psychiatric epidemiologic studies where researchers use various informants (for instance, parents and adolescents) to provide a holistic view of a subject's symptoms. Fitzmaurice et al. (1995, American Journal of Epidemiology 142: 1194–1203) have described estimation of multiple-source models using a standard generalized estimating equation (GEE) framework. However, these studies often have missing data because additional stages of consent and assent are required. The usual GEE is unbiased when data are missing completely at random in the context of Little and Rubin (2002, Statistical Analysis with Missing Data [Wiley]). This is a strong assumption that may not be tenable. Other options, such as the weighted GEE, are computationally challenging when missingness is nonmonotone. Multiple imputation is an attractive method to fit incomplete data models while requiring only the less restrictive missing-at-random assumption. Previously, estimation of partially observed clustered data was computationally challenging. However, recent developments in Stata have facilitated using them in practice. We demonstrate how to use multiple imputation in conjunction with a GEE to investigate the prevalence of eating disorder symptoms in adolescents as reported by parents and adolescents and to determine the factors associated with concordance and prevalence. The methods are motivated by the Avon Longitudinal Study of Parents and their Children, a cohort study that enrolled more than 14,000 pregnant mothers in 1991–92 and has followed the health and development of their children at regular intervals. While point estimates for the missing-at-random model were fairly similar to those for the GEE under missing completely at random, the missing-at-random model had smaller standard errors and required less stringent assumptions regarding missingness.