Detecting weak signals by combining small P-values in observational studies with multiple testing
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Human health is affected by multiple risk factors. Studies may focus on a hypothesis that a particular exposure is a risk factor for disease, but complex outcomes are typically influenced by spectra of weak genetic and environmental factors. A plethora of weak associations makes it difficult to detect a real signal because some portion of these associations is expected to be spurious. However, the combined effect of many individually weak signals has proven to be a more powerful approach to study the underpinnings of health conditions. Based on ideas from meta-analysis, statistical methods have been developed for combining top-ranked weak associations. For example, Truncated Product Method (TPM) and Rank Truncated Product (RTP) have gained substantial popularity in applications for linking combined contribution of multiple weak risk factors to disease. Both TRM and RTP aggregate only top ranking signals, while adjusting for the total number of predictors to assure Type-I error protection. Unlike TPM, the RTP distribution is comparatively unwieldy and involves repeated integration, which obscures its probabilistic interpretation and makes it difficult to implement. In this article, we developed new ways of evaluating the distribution of RTP and related statistics that not only are mathematically simple, but further lead to powerful extensions for combining top-ranked and correlated weak associations.
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