High Dimensional Statistical Testing With Applications to Gene Significance Detection

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  • March 20, 2019
Creator
  • Cao, Hongyuan
    • Affiliation: College of Arts and Sciences, Department of Statistics and Operations Research
Abstract
  • High-throughput screening has become an important mainstay for contemporary biomedical research. A standard approach is to use a large number of t-tests simultaneously and then select p-values in a manner that controls false discovery rate (FDR). Existing methods require very strong assumptions on the distribution of the data and the distribution of the p-values. We propose an asymptotically valid, data-driven procedure to find critical values for the t-statistics which requires minimal assumptions. A new asymptotically consistent estimate for the proportion of alternatives has been developed along the way. We demonstrate that our approach has improved computational efficiency and power over existing approaches while requiring fewer assumptions. The method controls the k-family wise error rate (k-FWER), the tail probability of false discovery proportion (FDTP) and false discovery rate (FDR). Simulation studies support our theoretical results and demonstrate the favorable performance of our new multiple testing procedure. We also apply our method to analyze cancer microarray studies. One feature of our approach is that it takes the alternative into account. Existing approaches take the alternative into account as well. However, we found that a standard concavity assumption on the p-value distribution for the alternative is violated under certain circumstances. A more general concept is the monotone likelihood ratio condition (MLRC) introduced in Sun and Cai (2007). We show that the concavity assumption can be violated for (i) a simple heteroscedastic normal mixture model and (ii) dependent tests. Some interesting implications, including the choice of test statistics, existing FDR control procedures (step-up and step-down) and the power definition, are discussed.
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Rights statement
  • In Copyright
Advisor
  • Zeng, Donglin
  • Budhiraja, Amarjit
  • Kosorok, Michael
  • Nobel, Andrew
  • Liu, Yufeng
Degree
  • Doctor of Philosophy
Degree granting institution
  • University of North Carolina at Chapel Hill Graduate School
Graduation year
  • 2010
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  • This item is restricted from public view for 1 year after publication.
Date uploaded
  • April 26, 2017

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