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Some consequences of assuming simple patterns for the treatment effect over time in a linear mixed model
Author(s) -
Bamia Christina,
White Ian R.,
Kenward Michael G.
Publication year - 2012
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.5707
Subject(s) - covariate , random effects model , covariance , statistics , mathematics , mixed model , estimator , linear model , constant (computer programming) , generalized linear mixed model , analysis of covariance , variance (accounting) , computer science , medicine , business , programming language , meta analysis , accounting
Linear mixed models are often used for the analysis of data from clinical trials with repeated quantitative outcomes. This paper considers linear mixed models where a particular form is assumed for the treatment effect, in particular constant over time or proportional to time. For simplicity, we assume no baseline covariates and complete post‐baseline measures, and we model arbitrary mean responses for the control group at each time. For the variance–covariance matrix, we consider an unstructured model, a random intercepts model and a random intercepts and slopes model. We show that the treatment effect estimator can be expressed as a weighted average of the observed time‐specific treatment effects, with weights depending on the covariance structure and the magnitude of the estimated variance components. For an assumed constant treatment effect, under the random intercepts model, all weights are equal, but in the random intercepts and slopes and the unstructured models, we show that some weights can be negative: thus, the estimated treatment effect can be negative, even if all time‐specific treatment effects are positive. Our results suggest that particular models for the treatment effect combined with particular covariance structures may result in estimated treatment effects of unexpected magnitude and/or direction. Methods are illustrated using a Parkinson's disease trial. Copyright © 2012 John Wiley & Sons, Ltd.