Bayesian mixture models for assessment of gene differential behaviour and prediction of pCR through the integration of copy number and gene expression data.

We consider modeling jointly microarray RNA expression and DNA copy number data. We propose Bayesian mixture models that define latent Gaussian probit scores for the DNA and RNA, and integrate between the two platforms via a regression of the RNA probit scores on the DNA probit scores. Such a regression conveniently allows us to include additional sample specific covariates such as biological conditions and clinical outcomes. The two developed methods are aimed respectively to make inference on differential behaviour of genes in patients showing different subtypes of breast cancer and to predict the pathological complete response (pCR) of patients borrowing strength across the genomic platforms. Posterior inference is carried out via MCMC simulations. We demonstrate the proposed methodology using a published data set consisting of 121 breast cancer patients.