Supplementary Material for: Using Both Cases and Controls for Testing Hardy-Weinberg Proportions in a Genetic Association Study

<i>Objectives:</i> Assessment of the Hardy-Weinberg proportion (HWP) in controls has been widely used as a quality control measure in case-control association studies. However, when the disease being studied is common, controls might not represent the general population, which could result in inaccurate HWP test results. Such results could lead investigators to discard important single-nucleotide polymorphisms (SNPs) that could potentially be causal. In this paper, we showed the inappropriateness of the HWP test in controls and proposed a mixture HWP (mHWP) exact test using a mixture sample that mimics the general population. <i>Methods:</i> The mHWP exact test estimates HWP in a mixture sample that is a combination of both cases and controls proportional to the prevalence of disease. We implemented a re-sampling procedure to construct mixture samples and then obtained the empirical p value of HWP in the general population. Simulation studies were performed to investigate the performance of the proposed mHWP exact test. The method was also applied to a genetic association study of obesity. <i>Results:</i> The results showed that the mHWP exact test is more likely than either the traditional HWP method in controls or the likelihood-based approach to keep causal SNPs for further analysis when the disease is more common. <i>Conclusion:</i> The mHWP exact test using a mixture sample is a better HWP test for case-control genetic association studies than the traditional HWP in controls or the likelihood-based approach, and it will improve our ability to keep causal SNPs in the case-control genetic association studies.

<i>研究目标：</i> 在病例对照关联研究中，以对照组群体的哈迪-温伯格比例（Hardy-Weinberg proportion, HWP）检验作为质量控制手段的应用已颇为广泛。然而，当所研究的疾病为常见病时，对照组群体可能无法代表总体人群，这会导致HWP检验结果出现偏差。此类偏差可能会使研究者误将潜在具有因果效应的单核苷酸多态性（single-nucleotide polymorphisms, SNPs）排除。本研究阐明了以对照组进行HWP检验的不合理性，并提出了一种基于模拟总体人群的混合哈迪-温伯格比例（mHWP）精确检验方法。
<i>研究方法：</i> mHWP精确检验以结合病例与对照的混合样本为基础，其样本比例与疾病患病率保持一致。本研究通过重抽样流程构建混合样本，并据此得到总体人群中HWP检验的经验p值。通过模拟实验评估了所提mHWP精确检验的性能，并将该方法应用于一项肥胖症的遗传关联研究中。
<i>研究结果：</i> 结果显示，当疾病患病率较高时，相较于传统的对照组HWP检验方法或基于似然的检验方法，mHWP精确检验更易保留具有因果效应的SNPs以供后续分析。
<i>研究结论：</i> 相较于传统的对照组HWP检验或基于似然的检验方法，基于混合样本的mHWP精确检验更适用于病例对照遗传关联研究中的HWP检验，可提升研究中保留因果SNPs的能力。