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An autoregressive linear mixed effects model for the analysis of longitudinal data which include dropouts and show profiles approaching asymptotes
Author(s) -
Funatogawa Takashi,
Funatogawa Ikuko,
Takeuchi Masahiro
Publication year - 2008
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.3417
Subject(s) - asymptote , covariance , autoregressive model , estimator , statistics , mathematics , mixed model , econometrics , mathematical analysis
We are interested in longitudinal data of a continuous response that show profiles with an initial sharp change and approaching asymptotes for each patient, and many patients drop out with a reason related to the response. In this paper, we focus on a model that assumes a dropout process is missing at random (MAR). In this dropout process, we can obtain consistent maximum likelihood estimators as long as both the mean and covariance structures are correctly specified. However, parsimonious covariance structures for the profiles approaching asymptotes are unclear. An autoregressive linear mixed effects model can express the profile with random individual asymptotes. We show that this model provides a new parsimonious covariance structure. The covariance structure at steady state is compound symmetry and the other elements of the covariance depend on the measurement points. In simulation studies, the estimate of the asymptote is unbiased in MAR dropouts, but biased in non‐ignorable dropouts. We also applied this model to actual schizophrenia trial data. Copyright © 2008 John Wiley & Sons, Ltd.