Fang, Yusi
(2023)
Methods for Combining Frequent or Sparse Signals in Omics Applications.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Combining p-values to aggregate effects has been of long-standing interest. We discuss three types of p-value combination scenarios for omics studies in Chapters 2-4 of this dissertation.
Chapter 2 considers combining independent and non-sparse signals in a small group of pvalues, where the number of true signals in p-values and their strengths can vary with heterogeneity.We propose the Fisher ensemble (FE) to aggregate the existing Fisher and AFp methods. The FE
achieves asymptotic Bahadur optimality and integrates the strengths of Fisher and AFp. We extend FE to a variant with emphasized power for concordant effect size directions. A transcriptomic meta-analysis of the AGEMAP dataset shows the advantages of the proposed methods.
Chapter 3 proposes a simple yet truly adaptive modified Fisher’s method for combining independent, weak and sparse signals in a large group of p-values. It achieves the optimal separating rate in a large-scale setup with sparse and heterogeneous signals. Our method is robust when the p-values are not exact and can maintain the optimal separating rate under mild conditions. The proposed method is applied to a neuroticism GWAS application for the pathway-based association study.
Chapter 4 considers combining dependent, weak and sparse signals in a large group of p-values. We study a family of p-value combination tests by heavy-tailed distribution transformations. We derive the conditions for a method of the family to enjoy robustness against the unknown dependency structure and to attain the optimal detection boundary for detecting weak and sparse signals. Only an equivalent class of the Cauchy test can possess robustness property. By applying our theoretical findings, we suggest a truncated Cauchy test that belongs to the class to improve the Cauchy test. A neuroticism GWAS application demonstrates the theoretical findings and advantages of the truncated Cauchy method.
Contribution to Public Health: Omics data integration is critical for contemporary biomedical research. P-value combination approaches are widely utilized in omics studies for aggregating information from multiple sources. This dissertation establishes a robust theoretical foundation of p-value combination and offers practical, data-driven methodologies for omics data integration.
Keywords: p-value combination; global hypothesis testing; large-scale inference; meta-analysis.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
9 May 2023 |
| Date Type: |
Publication |
| Defense Date: |
4 April 2023 |
| Approval Date: |
9 May 2023 |
| Submission Date: |
11 April 2023 |
| Access Restriction: |
2 year -- Restrict access to University of Pittsburgh for a period of 2 years. |
| Number of Pages: |
220 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
School of Public Health > Biostatistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
p-value combination; global hypothesis testing; large-scale inference; meta-analysis. |
| Date Deposited: |
10 May 2023 01:46 |
| Last Modified: |
10 May 2023 01:46 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/44526 |
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