Growth Mixture Models (GMMs) are used to model heterogeneity in longitudinal trajectories. GMMs assume that each subject's growth curve, characterized by random coefficients in mixed effects models, belongs to an underlying latent cluster with a cluster- specific mean profile. Within-subject variability is typically treated as a nuisance and assumed to be non-differential. Elliott (2007) extended the idea of modeling random effects as finite mixtures as in GMMs into the variance structure setting, where underlying "clusters" of within-subject variabilities were related to the health outcome of interest while the subject-specific trajectories were treated entirely as nuisance and modeled by penalized smoothing splines. More generally, we can consider joint models that link information from mean trajectories and residual variance to health outcomes of interest. This can be done via models that use either shared random-effects or shared latent classes to model continuous longitudinal data to predict a binary disease outcome in the primary model. Extensions of these approaches can be develop that use functional data analysis for the longitudinal data to distinguish long-term trends of the mean trajectory, cumulative change captured by the derivative of mean trajectory, and short-term residual variability, thus allowing the potential effects of longitudinal trajectories on the health risks to vary and accumulate over time. We consider applications to predict onset of senility in a population sample of older adults using memory test scores, and to predict severe hot flashes using the hormone levels collected over time for women in menopausal transition.
Dept of Biostatistics
biostats [at] columbia [dot] edu