A graphical method to assess distribution assumption in group-based trajectory models

Group-based trajectory models had a rapid development in the analysis of longitudinal data in clinical research. In these models, the assumption of homoscedasticity of the residuals is frequently made but this assumption is not always met. We developed here an easy-to-perform graphical method to assess the assumption of homoscedasticity of the residuals to apply especially in group-based trajectory models. The method is based on drawing an envelope to visualize the local dispersion of the residuals around each typical trajectory. Its efficiency is demonstrated using data on CD4 lymphocyte counts in patients with human immunodeficiency virus put on antiretroviral therapy. Four distinct distributions that take into account increasing parts of the variability of the observed data are presented. Significant differences in group structures and trajectory patterns were found according to the chosen distribution. These differences might have large impacts on the final trajectories and their characteristics; thus on potential medical decisions. With a single glance, the graphical criteria allow the choice of the distribution that best capture data variability and help dealing with a potential heteroscedasticity problem.