Mixture Modeling and Outlier Detection in Microarray Data Analysis

Microarray technology has become a dynamic tool in gene expression analysis because it allows for the simultaneous measurement of thousands of gene expressions. Uniqueness in experimental units and microarray data platforms, coupled with how gene expressions are obtained, make the field open for interesting research questions. In this dissertation, we present our investigations of two independent studies related to microarray data analysis. First, we study a recent platform in biology and bioinformatics that compares the quality of genetic information from exfoliated colonocytes in fecal matter with genetic material from mucosa cells within the colon. Using the intraclass correlation coe?cient (ICC) as a measure of reproducibility, we assess the reliability of density estimation obtained from preliminary analysis of fecal and mucosa data sets. Numerical findings clearly show that the distribution is comprised of two components. For measurements between 0 and 1, it is natural to assume that the data points are from a beta-mixture distribution. We explore whether ICC values should be modeled with a beta mixture or transformed first and fit with a normal mixture. We find that the use of mixture of normals in the inverse-probit transformed scale is less sensitive toward model mis-specification; otherwise a biased conclusion could be reached. By using the normal mixture approach to compare the ICC distributions of fecal and mucosa samples, we observe the quality of reproducible genes in fecal array data to be comparable with that in mucosa arrays. For microarray data, within-gene variance estimation is often challenging due to the high frequency of low replication studies. Several methodologies have been developed to strengthen variance terms by borrowing information across genes. However, even with such accommodations, variance may be initiated by the presence of outliers. For our second study, we propose a robust modification of optimal shrinkage variance estimation to improve outlier detection. In order to increase power, we suggest grouping standardized data so that information shared across genes is similar in distribution. Simulation studies and analysis of real colon cancer microarray data reveal that our methodology provides a technique which is insensitive to outliers, free of distributional assumptions, effective for small sample size, and data adaptive.