title: Some consequences of assuming simple patterns for the treatment effect over time in a linear mixed model.
abstract: 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.
authors.affiliation: Department of Hygiene, Epidemiology and Medical Statistics, University of Athens, Medical School, Athens, Greece. cbamia@nut.uoa.gr
authors.forename: Christina
authors.initials: C
authors.lastname: Bamia
authors.forename: Ian R
authors.initials: IR
authors.lastname: White
authors.forename: Michael G
authors.initials: MG
authors.lastname: Kenward
mesh_terms: D000203:Activities of Daily Living; D000978:Antiparkinson Agents / Q000627:therapeutic use; D056808:Biostatistics / Q000379:methods*; D001971:Bromocriptine / Q000627:therapeutic use; D002986:Clinical Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D006801:Humans; D007211:Indoles / Q000627:therapeutic use; D016014:Linear Models; D015233:Models, Statistical; D010300:Parkinson Disease / Q000188:drug therapy / Q000503:physiopathology; D016032:Randomized Controlled Trials as Topic / Q000379:methods / Q000706:statistics & numerical data
chemical_list: D000978:Antiparkinson Agents; D007211:Indoles; C046649:ropinirole; D001971:Bromocriptine