Multilevel growth curve models with covariate effects: application to recovery after stroke

Abstract

In measuring the progression of, or recovery from, a disease an individual's outcome may be assessed on a number of occasions. A model of the relationship between outcome and time since disease occurred which accounts for patient characteristics could be used to describe patterns of recovery, to predict outcome for a patient, or to evaluate health interventions. We use multilevel models to analyse such data, focusing on the choice of powers of time both for mean outcome and covariate effects. We give equations for predicted outcome and corresponding standard errors (i) based only on baseline characteristics, and (ii) by conditioning on previous outcomes for an individual. In a study of 331 stroke patients, outcome was measured approximately 0, 2,4,6 and 12 months after stroke. Patient characteristics included age, sex, and pre-stroke handicap, together with stroke-severity indicators (presence of limb deficit, dysphasia, dysarthria or incontinence). Of these, only the effects of age, dysphasia and presence of deficit varied with time. Conditioning on previous observations improved the accuracy of predictions. The outcome variable clearly had a skewed distribution, and the model residuals showed evidence of non-Normality. We discuss alternative models for non-Normal data, and show that, here, the standard (Normal errors) multilevel model gives equivalent parameter estimates and predictions to those obtained from alternative models.