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Stat Med. 2019 Mar 15;38(6):903-916. doi: 10.1002/sim.8014. Epub 2018 Nov 8.

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

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Department of Mathematical Sciences, Clemson University, Clemson, South Carolina.
Division of Cancer Epidemiology and Genetics, Biostatistics Branch, National Cancer Institute, Bethesda, Maryland.
Health Behavior Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Rockville, Maryland.


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.


binary Markov model; misspecification; random effects; transition model; working correlation


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