  The LIPGENE-SU.VI.MAX study, like many others, recorded high dimensional
continuous phenotypic data and categorical genotypic data. LIPGENE-SU.VI.MAX
focuses on the need to account for both phenotypic and genetic factors when
studying the metabolic syndrome (MetS), a complex disorder that can lead to
higher risk of type 2 diabetes and cardiovascular disease. Interest lies in
clustering the LIPGENE-SU.VI.MAX participants into homogeneous groups or
sub-phenotypes, by jointly considering their phenotypic and genotypic data, and
in determining which variables are discriminatory.
  A novel latent variable model which elegantly accommodates high dimensional,
mixed data is developed to cluster LIPGENE-SU.VI.MAX participants using a
Bayesian finite mixture model. A computationally efficient variable selection
algorithm is incorporated, estimation is via a Gibbs sampling algorithm and an
approximate BIC-MCMC criterion is developed to select the optimal model.
  Two clusters or sub-phenotypes (`healthy' and `at risk') are uncovered. A
small subset of variables is deemed discriminatory which notably includes
phenotypic and genotypic variables, highlighting the need to jointly consider
both factors. Further, seven years after the LIPGENE-SU.VI.MAX data were
collected, participants underwent further analysis to diagnose presence or
absence of the MetS. The two uncovered sub-phenotypes strongly correspond to
the seven year follow up disease classification, highlighting the role of
phenotypic and genotypic factors in the MetS, and emphasising the potential
utility of the clustering approach in early screening. Additionally, the
ability of the proposed approach to define the uncertainty in sub-phenotype
membership at the participant level is synonymous with the concepts of
precision medicine and nutrition.
