Matt Bryan
Comparing rates of change across groups is a natural use of longitudinal data as a common purpose for collecting such data is to understand how the outcome changes over time. A standard approach to comparing rates across groups is to use a linear mixed effects model with a group by time interaction. However, in the presence of a non-linear trend in the outcome, this approach may not be sufficient. Other existing approaches are typically designed for specific applications and are not easily generalizable. Thus, we propose methodology for longitudinal outcomes that allow for comparing rates of change across groups under the presence of a non-linear trend over time. Our rate regression method assumes a proportional change in the rate at every point in time across groups defined by a covariate of interest. Simulation results have demonstrated gains in power of the rate regression model in comparison to a linear mixed effects model under the presence of a non-linear trend in time. Possible areas of application for the proposed method include research in child and adolescent development and treatment trials. Numerous possible extensions to the rate regression method also exist such as in methods for multivariate longitudinal data and semiparametric methods for estimating a generalized time trend.
