Practical issues in using generalized estimating equations for inference on transitions in longitudinal data: What is being estimated?

• Published in: Statistics in medicine Vol. 38; no. 6; pp. 903 - 916
• Main Authors: Bible, Joe, Albert, Paul S., Simons‐Morton, Bruce G., Liu, Danping
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 15.03.2019
• Subjects: Adolescent; binary Markov model; Data Interpretation, Statistical; Humans; Longitudinal Studies; Markov analysis; misspecification; Models, Statistical; Population; Probability; random effects; Statistics as Topic; Time Factors; transition model; Underage Drinking - statistics & numerical data; working correlation; random effects; transition model; misspecification; working correlation; binary Markov model
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.8014

Generalized estimating equations (GEEs) are commonly used to estimate transition models. When the Markov assumption does not hold but first‐order transition probabilities are still of interest, the transition inference is sensitive to the choice of working correlation. In this paper, we consider a random process transition model as the true underlying data generating mechanism, which characterizes subject heterogeneity and complex dependence structure of the outcome process in a very flexible way. We formally define two types of transition probabilities at the population level: “naive transition probabilities” that average across all the transitions and “population‐average transition probabilities” that average the subject‐specific transition probabilities. Through asymptotic bias calculations and finite‐sample simulations, we demonstrate that the unstructured working correlation provides unbiased estimators of the population‐average transition probabilities while the independence working correlation provides unbiased estimators of the naive transition probabilities. For population‐average transition estimation, we demonstrate that the sandwich estimator fails for unstructured GEE and recommend the use of either jackknife or bootstrap variance estimates. The proposed method is motivated by and applied to the NEXT Generation Health Study, where the interest is in estimating the population‐average transition probabilities of alcohol use in adolescents.