This talk discusses analysis of DNA microarray data in connection with predictive discrimination between cancer states or other defined clinical or physiological outcomes. Our main application is in breast cancer, where interest lies in identifying characteristics of genetic expression, involving possibly very many genes, that relate to state or outcome. The problem is usefully framed as one of predictive discrimination. With two outcome groups, solution involves a binary regression modeling framework. The formal statistical problem is ill-posed, since tumour sample sizes are substantially smaller than the number of available and potentially interesting precictors -- the measured expression levels of many genes (or just sequences) on a microarray. We can address this in a Bayesian framework using singular factor regression with smoothness priors. Singular factor methods are also, of course, valuable in exploratory analysis of large-scale expression array data sets. The talk will discuss some aspects of model specification and analysis, and results of studies of breast cancer data in connection with oestrogen receptor status and axilliary nodal status as defined outcomes of interest, among other topics.
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