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Speeding up Monte Carlo simulations for the adaptive sum of powered score test with importance sampling

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  • Yangqing Deng
  • Yinqiu He
  • Gongjun Xu
  • Wei Pan

Abstract

A central but challenging problem in genetic studies is to test for (usually weak) associations between a complex trait (e.g., a disease status) and sets of multiple genetic variants. Due to the lack of a uniformly most powerful test, data‐adaptive tests, such as the adaptive sum of powered score (aSPU) test, are advantageous in maintaining high power against a wide range of alternatives. However, there is often no closed‐form to accurately and analytically calculate the p‐values of many adaptive tests like aSPU, thus Monte Carlo (MC) simulations are often used, which can be time consuming to achieve a stringent significance level (e.g., 5e‐8) used in genome‐wide association studies (GWAS). To estimate such a small p‐value, we need a huge number of MC simulations (e.g., 1e+10). As an alternative, we propose using importance sampling to speed up such calculations. We develop some theory to motivate a proposed algorithm for the aSPU test, and show that the proposed method is computationally more efficient than the standard MC simulations. Using both simulated and real data, we demonstrate the superior performance of the new method over the standard MC simulations.

Suggested Citation

  • Yangqing Deng & Yinqiu He & Gongjun Xu & Wei Pan, 2022. "Speeding up Monte Carlo simulations for the adaptive sum of powered score test with importance sampling," Biometrics, The International Biometric Society, vol. 78(1), pages 261-273, March.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:1:p:261-273
    DOI: 10.1111/biom.13407
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    References listed on IDEAS

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    1. Yiding Ma & Peng Wei, 2019. "FunSPU: A versatile and adaptive multiple functional annotation-based association test of whole-genome sequencing data," PLOS Genetics, Public Library of Science, vol. 15(4), pages 1-21, April.
    2. Liang, Faming & Liu, Chuanhai & Carroll, Raymond J., 2007. "Stochastic Approximation in Monte Carlo Computation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 305-320, March.
    3. Shi, Jianxin & Siegmund, David & Yakir, Benny, 2007. "Importance Sampling for Estimating p Values in Linkage Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 929-937, September.
    4. He, Yinqiu & Xu, Gongjun, 2018. "Estimating tail probabilities of the ratio of the largest eigenvalue to the trace of a Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 320-334.
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