The Doubly Contaminated Normal Model and Its Application to Microarray Data Analysis

• Activity Number: 124
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Richard Charnigo*+ and Qian Fan and Hongying Dai
• Companies: University of Kentucky and University of Kentucky and Children's Mercy Hospital
• Keywords: mixture model ; large scale hypothesis testing ; contaminated normal model ; contaminated beta model ; multiple comparisons ; gene expression

Abstract

The contaminated beta model (Allison et al, 2002; Dai and Charnigo, 2008) or contaminated normal model (Dai and Charnigo, 2010) may be employed to describe the distribution of a large collection of P values or of the underlying Z test statistics, respectively, arising from a microarray experiment. The contaminated normal model has the advantage of explicitly accounting for the signs of the test statistics, which in a microarray experiment may correspond to gene overexpression (positive statistics) or underexpression (negative statistics). However, the contaminated beta model has the advantage of providing better fits to microarray data sets in which there are abundances of both overexpressed and underexpressed genes. Therefore, we propose a new doubly contaminated normal model to describe the distribution of a large collection of Z test statistics. The doubly contaminated normal model enjoys both of the advantages enumerated above. Point and interval estimators of parameters from the doubly contaminated normal model, along with related hypothesis testing procedures, are investigated theoretically and via simulations. We conclude with an application to a real microarray data set.