Tutorial in Biostatistics: Evaluating the impact of 'critical periods' in longitudinal studies of growth using piecewise mixed effects models.

Recent developments in modern multivariate methods provide applied researchers with the means to address many important research questions that arise in studies with repeated measures data collected on individuals over time. One such area of applied research is focused on studying change associated with some event or critical period in human development. This tutorial deals with the use of the general linear mixed model for regression analysis of correlated data with a two-piece linear function of time corresponding to the pre- and post-event trends. The model assumes a continuous outcome is linearly related to a set of explanatory variables, but allows for the trend after the event to be different from the trend before it. This task can be accomplished using a piecewise linear random effects model for longitudinal data where the response depends upon time of the event. A detailed example that examines the influence of menarche on changes in body fat accretion will be presented using data from a prospective study of 162 girls measured annually from approximately age 10 until 4 years post menarche.