A latent class mixed model for analysing biomarker trajectories with irregularly scheduled observations

This paper considers a latent class model to uncover subpopulation structure for both biomarker trajectories and the probability of disease outcome in highly unbalanced longitudinal data. A specific pattern of trajectories can be viewed as a latent class in a finite mixture where membership in latent classes is modelled with a polychotomous logistic regression. The biomarker trajectories within a latent class are described by a linear mixed model with possibly time-dependent covariates and the probabilities of disease outcome are estimated via a class specific model. Thus the method characterizes biomarker trajectory patterns to unveil the relationship between trajectories and outcomes of disease. The coefficients for the model are estimated via a generalized EM (GEM) algorithm, a natural tool to use when latent classes and random coefficients are present. Standard errors of the coefficients are calculated using a parametric bootstrap. The model fitting procedure is illustrated with data from the Nutritional Prevention of Cancer trials; we use prostate specific antigen (PSA) as the biomarker for prostate cancer and the goal is to examine trajectories of PSA serial readings in individual subjects in connection with incidence of prostate cancer.