Thanks to the recent advances in microarray technologies where the expression levels of thousands of mRNA transcripts are measured simultaneously, researchers now can attempt to identify many features of the genetic basis of variations in these gene expressions. Such information can be used to narrow down a list of candidate genes, to elucidate causal relationships between modulator and modulated genes, and to identify key drivers of diseases. Although successful in many ways, the so called expression quantitative trait loci (eQTL) mapping studies to date have been carried out using traditional QTL mapping
methods repeatedly applied to each gene expression level in isolation. This approach is not efficient since information common across transcripts is not utilized. Furthermore, false discovery rates (FDRs) are inflated since multiplicities across transcripts are not considered.
Kendziorski, Chen {\it et al.} (2006) proposed an empirical Bayes approach that combines data across both markers and transcripts, facilitating simultaneous localization of eQTL while controlling an overall expected posterior FDR. Their approach relies on a mixture model, with the number of components directly related to the number of genetic markers genotyped. When there are too few or too many markers, the approach is not sufficient. In this talk, we will specifically address these cases. We first address the sparse map case to enable eQTL interval mapping between markers. The model extends that proposed in Kendziorski, Chen {\it et al.} (2006) by allowing for mixing over pseudomarkers (markers that have not been genotyped). A Dirichlet process mixture model is proposed to address the dense map case. Results are demonstrated using simulations and case study data. This is joint work with my advisor Christina Kendziorski.
