Optimal Tests for Combining <i>p</i>-Values
Combining information (<i>p</i>-values) obtained from individual studies to test whether there is an overall effect is an important task in statistical data analysis. Many classical statistical tests, such as chi-square tests, can be viewed as being a <i>p</i>-value combinati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/1/322 |
| _version_ | 1797499589129928704 |
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| author | Zhongxue Chen |
| author_facet | Zhongxue Chen |
| author_sort | Zhongxue Chen |
| collection | DOAJ |
| description | Combining information (<i>p</i>-values) obtained from individual studies to test whether there is an overall effect is an important task in statistical data analysis. Many classical statistical tests, such as chi-square tests, can be viewed as being a <i>p</i>-value combination approach. It remains challenging to find powerful methods to combine <i>p</i>-values obtained from various sources. In this paper, we study a class of <i>p</i>-value combination methods based on gamma distribution. We show that this class of tests is optimal under certain conditions and several existing popular methods are equivalent to its special cases. An asymptotically and uniformly most powerful <i>p</i>-value combination test based on constrained likelihood ratio test is then studied. Numeric results from simulation study and real data examples demonstrate that the proposed tests are robust and powerful under many conditions. They have potential broad applications in statistical inference. |
| first_indexed | 2024-03-10T03:49:34Z |
| format | Article |
| id | doaj.art-b155314f52e54a088e8a7bc7b8a4bced |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T03:49:34Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-b155314f52e54a088e8a7bc7b8a4bced2023-11-23T11:11:13ZengMDPI AGApplied Sciences2076-34172021-12-0112132210.3390/app12010322Optimal Tests for Combining <i>p</i>-ValuesZhongxue Chen0Department of Epidemiology and Biostatistics, School of Public Health, Indiana University Bloomington, 1025 E. 7th Street, Bloomington, IN 47405, USACombining information (<i>p</i>-values) obtained from individual studies to test whether there is an overall effect is an important task in statistical data analysis. Many classical statistical tests, such as chi-square tests, can be viewed as being a <i>p</i>-value combination approach. It remains challenging to find powerful methods to combine <i>p</i>-values obtained from various sources. In this paper, we study a class of <i>p</i>-value combination methods based on gamma distribution. We show that this class of tests is optimal under certain conditions and several existing popular methods are equivalent to its special cases. An asymptotically and uniformly most powerful <i>p</i>-value combination test based on constrained likelihood ratio test is then studied. Numeric results from simulation study and real data examples demonstrate that the proposed tests are robust and powerful under many conditions. They have potential broad applications in statistical inference.https://www.mdpi.com/2076-3417/12/1/322chi-square testconstrained likelihood ratio testFisher testgamma distributionuniformly most powerful test |
| spellingShingle | Zhongxue Chen Optimal Tests for Combining <i>p</i>-Values Applied Sciences chi-square test constrained likelihood ratio test Fisher test gamma distribution uniformly most powerful test |
| title | Optimal Tests for Combining <i>p</i>-Values |
| title_full | Optimal Tests for Combining <i>p</i>-Values |
| title_fullStr | Optimal Tests for Combining <i>p</i>-Values |
| title_full_unstemmed | Optimal Tests for Combining <i>p</i>-Values |
| title_short | Optimal Tests for Combining <i>p</i>-Values |
| title_sort | optimal tests for combining i p i values |
| topic | chi-square test constrained likelihood ratio test Fisher test gamma distribution uniformly most powerful test |
| url | https://www.mdpi.com/2076-3417/12/1/322 |
| work_keys_str_mv | AT zhongxuechen optimaltestsforcombiningipivalues |