Efficiency and Robustness Issues in Complex Statistical Designs for Two-Color Microarray Experiments

Abstract

Identifying differentially expressed genes is one of the common goals of microarray experiments. The use of an efficient design in microarray experiments can improve the power of the inferential procedure. Besides efficiency, robustness considerations should also be considered in selecting good microarray designs because missing observations often occur in the microarray experiments. In this dissertation, $E$--optimality criterion is used as the efficiency criterion and three robustness criteria are proposed to quantify the robustness of a microarray design.For a given number of available arrays and number of treatment conditions, different microarray designs can be considered. The number of possible designs could be very large and thus a complete analysis of efficiency and robustness considerations could be computationally infeasible. A genetic algorithm based method is suggested for selecting good microarray designs for a set of given research questions. This method can be used to find good designs for both the one--way and two--factor factorial experiments. The use of both the efficiency and robustness criteria in the search procedure is also proposed. As an example, efficient and robust designs for the factorial experiments are reported for different numbers of arrays.