Bayesian approaches to clustering for longitudinal data analysis and its applications in personalized medicine

Precision medicine or personalized medicine is an emerging area of interest that aims to improve clinical outcomes by tailoring individualized treatment plans. This is driven by the large amount of data that is being routinely collected in modern clinical settings (for example DNA sequences, continuously monitored biomarkers, extensive medical imaging etc). The biomarkers measured over time provide important information on both disease progression and potential treatment efficacy. In the context of personalized medicine, the population is not homogeneous, and it is important to capture and model the heterogeneity to recommend individual treatment regimens. Heterogeneity in populations is typically dealt with using mixture models or heuristic clustering methods. A standard frequentist method makes use of latent class linear mixed models, where the longitudinal responses are modeled using a linear mixed model with a mixture distribution for the random effects. Alternatively, one can use profile regression, which is a Bayesian approach. Profile regression tries to divide the whole population into homogeneous subgroups using covariates and fits a regression model for the outcomes on each of the groups. Our aim in this dissertation will be to study potential extensions and practical applications of Bayesian profile regression with particular emphasis on personalized medicine.