Science China Mathematics

, Volume 53, Issue 11, pp 2937–2948

Approximating probabilities of correlated events

  • QiZhai Li
  • Gang Zheng
  • AiYi Liu
  • ZhaoHai Li
  • Kai Yu
Articles

DOI: 10.1007/s11425-010-4053-0

Cite this article as:
Li, Q., Zheng, G., Liu, A. et al. Sci. China Math. (2010) 53: 2937. doi:10.1007/s11425-010-4053-0

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-controlgroup sequential testgenetic association studiesMAXparallelogram

MSC(2000)

62F03

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • QiZhai Li
    • 1
    • 2
  • Gang Zheng
    • 3
  • AiYi Liu
    • 4
  • ZhaoHai Li
    • 2
    • 5
  • Kai Yu
    • 2
  1. 1.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.Biostatistics Branch, Division of Cancer Epidemiology and GeneticsNational Cancer InstituteBethesdaUSA
  3. 3.Office of Biostatistics Research, National HeartLung and Blood InstituteBethesdaUSA
  4. 4.Biostatistics and Bioinformatics BranchNational Institute of Child Health and Human DevelopmentBethesdaUSA
  5. 5.Department of StatisticsGeorge Washington UniversityWashington, DCUSA