The first‐order Markov conditional linear expectation approach for analysis of longitudinal data

• Published in: Statistics in medicine Vol. 40; no. 8; pp. 1972 - 1988
• Main Authors: Bender, Shaun, Gamerman, Victoria, Reese, Peter P., Gray, Daniel Lloyd, Li, Yimei, Shults, Justine
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 15.04.2021
• Subjects: binary random variables; discrete data; first‐order antedependence; first‐order Markov; generalized estimating equations; Generalized linear models; Performance evaluation; first-order antedependence; first-order Markov; discrete data; generalized estimating equations; binary random variables
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.8883

We consider longitudinal discrete data that may be unequally spaced in time and may exhibit overdispersion, so that the variance of the outcome variable is inflated relative to its assumed distribution. We implement an approach that extends generalized linear models for analysis of longitudinal data and is likelihood based, in contrast to generalized estimating equations (GEE) that are semiparametric. The method assumes independence between subjects; first‐order antedependence within subjects; exponential family distributions for the first outcome on each subject and for the subsequent conditional distributions; and linearity of the expectations of the conditional distributions. We demonstrate application of the method in an analysis of seizure counts and in a study to evaluate the performance of transplant centers. Simulations for both studies demonstrate the benefits of the proposed likelihood based approach; however, they also demonstrate better than anticipated performance for GEE.