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

Yangqing Deng, Yinqiu He, Gongjun Xu, Wei Pan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)261-273
Number of pages13
Issue number1
StatePublished - Mar 2022

Bibliographical note

Funding Information:
In our opinion, the first two authors should be treated as the co–first authors. We thank the editors and reviewers for many insightful and helpful comments. This research was supported by NIH grants R01GM113250, R01GM126002, R01HL105397, R01HL116720, R21AG057038 and R01AG065636; by NSF grants DMS 1711226, DMS 1712717, SES 1659328 and SES‐1846747; and by the MSI at the University of Minnesota. This study makes use of data generated by the WTCCC; a full list of the investigators who contributed to the generation of the data is available from www.wtccc.org.uk; funding for the project was provided by the Wellcome Trust under award 076113 and 085475.

Publisher Copyright:
© 2020 The International Biometric Society


  • GWAS
  • SNPs
  • aSPU
  • adaptive test
  • genome-wide association studies


Dive into the research topics of 'Speeding up Monte Carlo simulations for the adaptive sum of powered score test with importance sampling'. Together they form a unique fingerprint.

Cite this