Finite mixture model analysis of microarray expression data on samples of uncertain biological type with application to reproductive efficiency

Common goals of microarray experiments are the detection of genes that are differentially expressed between several biological types and the construction of classifiers that predict biological type of samples. Here we consider a situation where there is no training data. There is considerable interest in comparing expression profiles associated with successful pregnancies (SP) and unsuccessful pregnancies (UP) in model and farm animals. Successful pregnancy rate is known to be much higher in embryos generated by in vitro fertilization (IVF) than in nuclear transfer (NT) embryos, and higher under induced ovulation for large follicles (LF) than for small follicles (SF). The tasks of identifying genes differentially expressed between SP and UP, and predicting SP for future samples are not well accomplished by comparing IVF and NT, or LF and SF. A suitable method is finite mixture model analysis (FMMA), which models each observed class (IVF and NT, or LF and SF) as a mixture of two distributions, one for SP and one for UP, with different known or unknown proportions (here known to be 0.50 SP for IVF and 0.02 SP for NT). The means of the two distributions differ for the differentially expressed genes, which we identify via a likelihood ratio test. We confirm by simulation that FMMA strongly outperforms hierarchical clustering and linear discriminant analysis using the known class labels (NT, IVF). We apply FMMA to a real data set on IVF and NT embryos, and compute their posterior probabilities of SP, which confirm our prior knowledge of the SP proportions for IVF and NT.