Approximating probabilities of correlated events  

作　　者：LI QiZhai1,2, ZHENG Gang3, LIU AiYi4, LI ZhaoHai2,5 & YU Kai2 1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 2Biostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD 20892, USA 3Office of Biostatistics Research, National Heart, Lung and Blood Institute, Bethesda, MD 20892, USA 4Biostatistics and Bioinformatics Branch, National Institute of Child Health and Human Development, Bethesda, MD 20892, USA 5Department of Statistics, George Washington University, Washington, DC 20052, USA 

出　　处：《Science China Mathematics》2010年第11期2937-2948,共12页中国科学：数学（英文版）

基　　金：supported by the Intramural Program of NIH;supported in part by National Natural Science Foundation of China (Grant No.10901155);supportedin part by NIH (Grant No. EY014478).

摘　　要：Efron (1997) considered several approximations of p-values for simultaneous hypothesis testing. An extension of his approaches is considered here to approximate various probabilities of correlated events. Compared with multiple-integrations, our proposed method, the parallelogram formulas, based on a one-dimensional integral, not only substantially reduces the computational complexity but also maintains good accuracy. Applications of the proposed method to genetic association studies and group sequential analysis are investigated in detail. Numerical results including real data analysis and simulation studies demonstrate that the proposed method performs well.Efron (1997) considered several approximations of p-values for simultaneous hypothesis testing. An extension of his approaches is considered here to approximate various probabilities of correlated events. Compared with multiple-integrations, our proposed method, the parallelogram formulas, based on a one-dimensional integral, not only substantially reduces the computational complexity but also maintains good accuracy. Applications of the proposed method to genetic association studies and group sequential analysis are investigated in detail. Numerical results including real data analysis and simulation studies demonstrate that the proposed method performs well.

关 键 词：CASE-CONTROL group SEQUENTIAL test GENETIC association studies MAX PARALLELOGRAM 

分 类 号：O212.1[理学—概率论与数理统计]