Topics in multiple hypotheses testing
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It is common to test many hypotheses simultaneously in the application of statistics. The probability of making a false discovery grows with the number of statistical tests performed. When all the null hypotheses are true, and the test statistics are indepen- dent and continuous, the error rates from the family wise error rate (FWER)- and the false discovery rate (FDR)-controlling procedures are equal to the nominal level. When some of the null hypotheses are not true, both procedures are conservative. In the first part of this study, we review the background of the problem and propose methods to estimate the number of true null hypotheses. The estimates can be used in FWER- and FDR-controlling procedures with a consequent increase in power. We conduct simulation studies and apply the estimation methods to data sets with bio- logical or clinical significance. In the second part of the study, we propose a mixture model approach for the analysis of ChIP-chip high density oligonucleotide array data to study the interac- tions between proteins and DNA. If we could identify the specific locations where proteins interact with DNA, we could increase our understanding of many important cellular events. Most experiments to date are performed in culture on cell lines, bac- teria, or yeast, and future experiments will include those in developing tissues, organs, or cancer biopsies, and they are critical in understanding the function of genes and proteins. Here we investigate the ChIP-chip data structure and use a beta-mixture model to help identify the binding sites. To determine the appropriate number of components in the mixture model, we suggest the Anderson-Darling testing. Our study indicates that it is a reasonable means of choosing the number of components in a beta-mixture model. The mixture model procedure has broad applications in biology and is illustrated with several data sets from bioinformatics experiments.
Qian, Yi (2005). Topics in multiple hypotheses testing. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from