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.

中文翻译：

---

加速蒙特卡洛模拟以进行重要性抽样的动力分数测试的自适应总和

遗传研究中的一个核心但具有挑战性的问题是测试复杂性状（例如，疾病状态）与多个遗传变异集之间的（通常是微弱的）关联。由于缺乏统一的最强大的测试，数据自适应测试（例如幂分数的自适应总和（aSPU）测试）在针对各种替代方案保持高功率方面是有利的。然而，通常没有封闭形式来准确和分析地计算许多自适应测试（如 aSPU）的p值，因此经常使用蒙特卡洛 (MC) 模拟，这可能很耗时才能达到严格的显着性水平（例如， 5e-8) 用于全基因组关联研究 (GWAS)。估计这么小的p-value，我们需要大量的 MC 模拟（例如，1e+10）。作为替代方案，我们建议使用重要性采样来加速此类计算。我们开发了一些理论来激发 aSPU 测试的拟议算法，并表明所提出的方法在计算上比标准 MC 模拟更有效。通过使用模拟数据和真实数据，我们证明了新方法优于标准 MC 模拟的性能。