Discovering subpopulation structure with latent class mixed models

Abstract

The linear mixed model is a well-known method for incorporating heterogeneity (for example, subject-to-subject variation) into a statistical analysis for continuous responses. However heterogeneity cannot always be fully captured by the usual assumptions of normally distributed random effects. Latent class mixed models offer a way of incorporating additional heterogeneity which can be used to uncover distinct subpopulations, to incorporate correlated non-normally distributed outcomes and to classify individuals. The methodology is motivated with examples in health care studies and a detailed illustration is drawn from the Nutritional Prevention of Cancer trials. Latent class models are used with longitudinal data on prostate specific antigen (PSA) as well as incidence of prostate cancer. The models are extended to accommodate prostate cancer as a survival endpoint; this is compared to treating it as a binary endpoint. Four subpopulations are identified which differ both with regard to their PSA trajectories and their incidence rates of prostate cancer.