The Latent Class Stochastic Process Model for Evaluation of Hidden Heterogeneity in Longitudinal Data

Abstract

Various approaches to statistical model building and data analysis that incorporate unobserved heterogeneity are ubiquitous in different scientific disciplines. Frailty models introduce the concept of unobserved or hidden heterogeneity in survival analysis for time-to-event data. Longitudinal data provide an additional source of heterogeneity that can contribute to differences in risks of time-to-event outcomes. Individual age trajectories of biomarkers can differ due to various observed as well as unobserved factors and such individual differences propagate to differences in risks of related time-to-event outcomes such as the onset of a disease or death. In this chapter, we briefly review recent biostatistical approaches to deal with heterogeneity, focusing on approaches that model both time-to-event and longitudinal data such as joint models (see Chap. 11). One of the approaches to deal with hidden heterogeneity assumes that a population under study may consist of “latent” subpopulations or classes with distinct patterns of longitudinal trajectories of biomarkers that can also have different effects on the time-to-event outcome in each subpopulation. Within the joint modeling framework, a special class of models, joint latent class models, was developed to account for such heterogeneity in a population. In this chapter, we also present a version of the stochastic process model (see Chap. 12), which we call the “latent class stochastic process model” that deals with a similar approach in the context of such models.