A Semiparametric Bayesian Model for Repeatedly Repeated Binary Outcomes.

We discuss the analysis of data from single nucleotide polymorphism (SNP) arrays comparing tumor and normal tissues. The data consist of sequences of indicators for loss of heterozygosity (LOH) and involve three nested levels of repetition: chromosomes for a given patient, regions within chromosomes, and SNPs nested within regions. We propose to analyze these data using a semiparametric model for multi-level repeated binary data. At the top level of the hierarchy we assume a sampling model for the observed binary LOH sequences that arises from a partial exchangeability argument. This implies a mixture of Markov chains model. The mixture is defined with respect to the Markov transition probabilities. We assume a nonparametric prior for the random mixing measure. The resulting model takes the form of a semiparametric random effects model with the matrix of transition probabilities being the random effects. The model includes appropriate dependence assumptions for the two remaining levels of the hierarchy, i.e., for regions within chromosomes and for chromosomes within patient. We use the model to identify regions of increased LOH in a dataset coming from a study of treatment-related leukemia in children with an initial cancer diagnostic. The model successfully identifies the desired regions and performs well compared to other available alternatives.