Quality Control and Robust Estimation for cDNA Microarrays with Replicates

We consider robust estimation of gene intensities from cDNA microarray data with replicates. Several statistical methods for estimating gene intensities from microarrays have been proposed, but there has been little work on robust estimation. This is particularly relevant for experiments with replicates, because even one outlying replicate can have a disastrous effect on the estimated intensity for the gene concerned. Because of the many steps involved in the experimental process from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outlying data value could occur because of scratches or dust on the surface, imperfections in the glass, or imperfections in the array production. We develop a Bayesian hierarchical model for robust estimation of cDNA microarray intensities. Outliers are modeled explicitly using a t-distribution, and our model also addresses classical issues such as design effects, normalization, transformation, and non-constant variance. Parameter estimation is carried out using Markov chain Monte Carlo. By identifying potential outliers, the method provides automatic quality control of replicate, array and gene measurements. ∗Raphael Gottardo is Assistant Professor, Department of Statistics, University of BritishColumbia, 333-6356 Agricultural Road, Vancouver, BC V6T 1Z2 (E-mail: [email protected]; Web: www.hajek.stat.ubc.ca/ raph). Adrian E. Raftery is Professor of Statistics and Sociology, University of Washington, Department of Statistics Box 354322, Seattle, WA 98195-4322 (E-mail: [email protected]; Web: www.stat.washington.edu/raftery). Ka Yee Yeung is Research Assistant Professor, Department of Microbiology, University of Washington, Box 358070, Seattle, WA 98195. (E-mail: [email protected]). Roger Bumgarner is Associate Professor, Department of Microbiology, University of Washington, Box 358070, Seattle, WA 98195. (E-mail: [email protected]). The authors thank Julian Besag for helpful discussion and Angelique van’t Wout for providing us with some of the data. This research was supported by NIH Grant 8 R01 EB002137-02, and Raftery’s research was also partially supported by ONR Grant N00014-01-10745. Yeung and Bumgarner were supported by NIH-NIDDK grant 5U24DK058813-02.