Bayesian approaches to variable selection in mixture models with application to disease clustering

In biomedical research, cluster analysis is often performed to identify patient subgroups based on patients' characteristics or traits. In the model-based clustering for identifying patient subgroups, mixture models have played a fundamental role in modeling. While there is an increasing interest in using mixture modeling for identifying patient subgroups, little work has been done in selecting the predictors that are associated with the class assignment. In this study, we develop and compare two approaches to perform variable selection in the context of a mixture model to identify important predictors that are associated with the class assignment. These two approaches are the one-step approach and the stepwise approach. The former refers to an approach in which clustering and variable selection are performed simultaneously in one overall model, whereas the latter refers to an approach in which clustering and variable selection are performed in two sequential steps. We considered both shrinkage prior and spike-and-slab prior to select the importance of variables. Markov chain Monte Carlo algorithms are developed to estimate the posterior distribution of the model parameters. Practical applications and simulation studies are carried out to evaluate the clustering and variable selection performance of the proposed models.