Efficient block designs for 2-colour microarray experiments

Abstract

This article deals with the problem of obtaining efficient designs for 2-colour microarray experiments. If arrays are considered as blocks and varieties as treatments and the number of varieties that can be accommodated on each arrary as block size, then a classical incomplete block design can be useful for microarray experiments. Since only two varieties can be accommodated on one array in 2-colour microarray experiment, effects due to arrays may be considered as random. To deal with the problem of obtaining an efficient design when array effects are random, lower bounds to A- and D-efficiencies of the design in a given class of designs have been obtained for block designs under a mixed effects model. For obtaining efficient block designs under fixed/mixed effects model for microarray experiments, the exchange and interchange algorithm of Rathore et. al. (2006) was modified by incorporating the procedure of translated into a computer program using Microsoft Visual C++. The algorithm is general in nature and can be used for generation of efficient block design for any 2<=k<=v, where v is the number of varieties (treatments) and k is the block size. The algorithm has been exploited for computer aided search of an efficient block design in v varieties and b-arrays for two colour micro-array experiments (k=2) in the parametric range 3 <= v <= 16, v<= b<= v (v-1)/2 and 17 <= v = b <= 25. Designs obtained through the algorithm under fixed effects model have been compared with the corresponding best designs available in the literature (designs with highest lower bound to A-efficiency) and 2-associate partially balanced incomplete block (PBIB(2)) designs. 30 designs are found to be more efficient than the best available block designs. The robustness aspects of efficient designs obtained under a fixed effects model and best available block designs were investigated under mixed effects model. Strength of the algorithm for obtaining block designs for 3-colour microarray experiments has also been demonstrated with the help of examples.