Optimal Designs for Microarray Experiments with Biological and Technical Replicates

Microarrays are powerful tools for global monitoring of gene expressions in many areas of biomedical research (Brown and Botstein (1999)). Since the first publication on the statistical analysis of data from microarray experiments (Chen et al. (1997)), considerable amount of research has been carried out regarding such analysis. However, little work has been done on designing microarray experiments despite the fact that designing is the key for optimization of resources and efficient estimation of the parameters of interest. Microarray experiments consist of large number of steps, as a result various sources of errors and variability crop-in during the experiment which then affect the final outcome. However, the sources of variation in the microarray experiment are yet to be completely understood. The extent to which these sources of variations are known should be considered while designing the experiment so as to obtain quality data and precise results. The main purpose of this article is to describe approaches for designing microarray experiments considering both technical and biological replicates. Our approach is similar to the ones taken by Churchill (2002); Wit and McClure (2004). The method for searching optimal designs has been implemented in Matlab. In Section 2, we describe the various sources of variations in the microarray experiment. Section 3 describes the model, optimality criteria, and the implementation. In Section 4, we illustrate our approach with examples. The paper concludes with a discussion section.