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Finite mixture model is an important branch of clustering methods and can beapplied on data sets with mixed types of variables. However, challenges existin its applications. First, it typically relies on the EM algorithm which couldbe sensitive to the choice of initial values. Second, biomarkers subject tolimits of detection (LOD) are common to encounter in clinical data, whichbrings censored variables into finite mixture model. Additionally, researchersare recently getting more interest in variable importance due to the increasingnumber of variables that become available for clustering.  To address these challenges, we propose a Bayesian finite mixture model tosimultaneously conduct variable selection, account for biomarker LOD and obtainclustering results. We took a Bayesian approach to obtain parameter estimatesand the cluster membership to bypass the limitation of the EM algorithm. Toaccount for LOD, we added one more step in Gibbs sampling to iteratively fillin biomarker values below or above LODs. In addition, we put a spike-and-slabtype of prior on each variable to obtain variable importance. Simulationsacross various scenarios were conducted to examine the performance of thismethod. Real data application on electronic health records was also conducted.

A Bayesian Finite Mixture Model with Variable Selection for Data with Mixed-type Variables