Articles

Science China Mathematics

, Volume 53, Issue 11, pp 2937-2948

Approximating probabilities of correlated events

  • QiZhai LiAffiliated withAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBiostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute Email author 
  • , Gang ZhengAffiliated withOffice of Biostatistics Research, National Heart, Lung and Blood Institute
  • , AiYi LiuAffiliated withBiostatistics and Bioinformatics Branch, National Institute of Child Health and Human Development
  • , ZhaoHai LiAffiliated withBiostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer InstituteDepartment of Statistics, George Washington University
  • , Kai YuAffiliated withBiostatistics Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute

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Abstract

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.

Keywords

case-control group sequential test genetic association studies MAX parallelogram

MSC(2000)

62F03