How Many Genes Are Needed for a Discriminant Microarray Data Analysis ?

The analysis of the leukemia data from Whitehead/MIT group is a discriminant analysis (also called a supervised learning). Among thousands of genes whose expression levels are measured, not all are needed for discriminant analysis: a gene may either not contribute to the separation of two types of tissues/cancers, or it may be redundant because it is highly correlated with other genes. There are two theoretical frameworks in which variable selection (or gene selection in our case) can be addressed. The first is model selection, and the second is model averaging. We have carried out model selection using Akaike information criterion and Bayesian information criterion with logistic regression (discrimination, prediction, or classification) to determine the number of genes that provide the best model. These model selection criteria set upper limits of 22-25 and 12-13 genes for this data set with 38 samples, and the best model consists of only one (no.4847, zyxin) or two genes. We have also carried out model averaging over the best single-gene logistic predictors using three different weights: maximized likelihood, prediction rate on training set, and equal weight. We have observed that the performance of most of these weighted predictors on the testing set is gradually reduced as more genes are included, but a clear cutoff that separates good and bad prediction performance is not found.