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The first‐order Markov conditional linear expectation approach for analysis of longitudinal data
Author(s) -
Bender Shaun,
Gamerman Victoria,
Reese Peter P.,
Gray Daniel Lloyd,
Li Yimei,
Shults Justine
Publication year - 2021
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8883
Subject(s) - generalized estimating equation , overdispersion , conditional probability distribution , mathematics , statistics , conditional variance , generalized linear model , conditional independence , econometrics , exponential family , marginal model , markov chain , conditional expectation , outcome (game theory) , estimating equations , gee , count data , regression analysis , poisson distribution , maximum likelihood , volatility (finance) , mathematical economics , autoregressive conditional heteroskedasticity
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.