Quantifying treatment effects when flexibly modeling individual change in a nonlinear mixed effects model

A core task in analyzing randomized clinical trials based on longitudinal data is to find the best way to describe the change over time for each treatment arm. We review the implementation and estimation of a flexible piecewise Hierarchical Linear Model (HLM) to model change over time. The flexible piecewise HLM consists of two phases with differing rates of change. The breakpoints between these two phases, as well as the rates of change per phase are allowed to vary between treatment groups as well as individuals. While this approach may provide better model fit, how to quantify treatment diff erences over the longitudinal period is not clear. In this paper, we develop a procedure for summarizing the longitudinal data for the flexible piecewise HLM on the lines of Cook et al. (2004). We focus on quantifying the overall treatment efficacy using the area under the curve (AUC) of the individual flexible piecewise HLM models. Methods are illustrated through data from a placebo-controlled trial in the treatment of depression comparing psychotherapy and pharmacotherapy.