Generalized mean p -values for combining dependent tests: comparison of generalized central limit theorem and robust risk analysis

Wellcome Open Research

article

Daniel J. Wilson¹ 

[1] Big Data Institute, Nuffield Department of Population Health, University of Oxford

关键词: Combined tests;    p-values;    generalized means;    generalized central limit theorem;    robust risk analysis;    harmonic mean p-value;    dependent tests;   

DOI  :  10.12688/wellcomeopenres.15761.1

学科分类：内科医学

来源: Wellcome

【 摘 要 】

The test statistics underpinning several methods for combiningp-values are special cases of generalized meanp-value (GMP), including the minimum (Bonferroni procedure), harmonic mean and geometric mean. A key assumption influencing the practical performance of such methods concerns the dependence betweenp-values. Approaches that do not require specific knowledge of the dependence structure are practically convenient. Vovk and Wang derived significance thresholds for GMPs under the worst-case scenario of arbitrary dependence using results from Robust Risk Analysis (RRA). Here I calculate significance thresholds and closed testing procedures using Generalized Central Limit Theorem (GCLT). GCLT formally assumes independence, but enjoys a degree of robustness to dependence. The GCLT thresholds are less stringent than RRA thresholds, with the disparity increasing as the exponent of the GMP (r) increases. I motivate a model ofp-value dependence based on a Wishart-Multivariate-Gamma distribution for the underlying log-likelihood ratios. In simulations under this model, the RRA thresholds produced tests that were usually less powerful than Bonferroni, while the GCLT thresholds produced tests more powerful than Bonferroni, for allr − ∞. Abover − 1, the GCLT thresholds suffered pronounced false positive rates. Abover − 1/2, standard central limit theorem applied and the GCLT thresholds no longer possessed any useful robustness to dependence. I consider the implications of these results in the context of various interpretations of GMPs, and conclude that the GCLT-based harmonic meanp-value procedure and Simes' (1986) test represent good compromises in power-robustness trade-off for combining dependent tests.

【 授权许可】

CC BY