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Speeding up Monte Carlo simulations for the adaptive sum of powered score test with importance sampling
Author(s) -
Deng Yangqing,
He Yinqiu,
Xu Gongjun,
Pan Wei
Publication year - 2022
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13407
Subject(s) - monte carlo method , computer science , range (aeronautics) , sampling (signal processing) , sample size determination , statistical hypothesis testing , algorithm , mathematical optimization , statistics , mathematics , materials science , filter (signal processing) , composite material , computer vision
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.