Can We Allow the Geneticists to Use the Same Data Set to Find the Most Differentially Expressed Genes and Do the Statistical Analysis in Microarray Analysis?

Abstract

The answer to the question of the title is no since there will be a selection bias. The bias can be huge since the number of genes is large. However this seems to be the usual practice in microarry. How do statisticians cope with this problem? Simultaneous inference such as those derived using Bonferroni inequality is one answer. It is however too conservative. There are other approaches such as using the one-dimensional p-values and then do the Westfall and Young's correction. Other criteria such as controlling FDR in Benjamini and Hochberg and pFDR in Storey were proposed. These latter two approaches however may be too liberal. In this informal talk, I will discuss some of my work with my graduate student Jing Qiu at Cornell. We focus on say 100 selected genes (genes with most up or down regulated expression levels) and construct simultaneous confidence intervals. A random effect ANOVA model is assumed. This leads to shrinkage estimators which actually correct the selection bias. The confidence intervals constructed are much sharper than the simultaneous intervals constructed using Bonferroni inequlity. The saving could range between 20% to 80% . Normal prior is assumed. Prior mixing with zero will be discussed too. The talk should be understandable to statisticians with little knowledge of genetics.