In genome-wide association studies (GWAS) for thousands of phenotypes in biobanks, most binary phenotypes have substantially fewer cases than controls. Many widely used approaches for joint analysis of multiple phenotypes produce inflated type I error rates for such extremely unbalanced case-control phenotypes. In this research, we develop a method to jointly analyze multiple unbalanced case-control phenotypes to circumvent this issue. We first group multiple phenotypes into different clusters based on a hierarchical clustering method, then we merge phenotypes in each cluster into a single phenotype. In each cluster, we use the saddlepoint approximation to estimate the p value of an association test between the merged phenotype and a single nucleotide polymorphism (SNP) which eliminates the issue of inflated type I error rate of the test for extremely unbalanced case-control phenotypes. Finally, we use the Cauchy combination method to obtain an integrated p value for all clusters to test the association between multiple phenotypes and a SNP. We use extensive simulation studies to evaluate the performance of the proposed approach. The results show that the proposed approach can control type I error rate very well and is more powerful than other available methods. We also apply the proposed approach to phenotypes in category IX (diseases of the circulatory system) in the UK Biobank. We find that the proposed approach can identify more significant SNPs than the other viable methods we compared with.

中文翻译：

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极度不平衡病例对照关联研究的多种表型联合分析

在对生物库中数千种表型进行的全基因组关联研究 (GWAS) 中，大多数二元表型的病例数明显少于对照组。许多广泛使用的多种表型联合分析方法对于这种极其不平衡的病例对照表型产生了夸大的 I 型错误率。在本研究中，我们开发了一种联合分析多个不平衡病例对照表型的方法来规避这个问题。我们首先基于层次聚类方法将多个表型分组为不同的簇，然后将每个簇中的表型合并为单个表型。在每个簇中，我们使用鞍点近似来估计 合并表型和单核苷酸多态性 (SNP) 之间关联测试的 p 值，这消除了极端不平衡病例对照表型测试的 I 型错误率夸大的问题。最后，我们使用柯西组合方法获得所有簇的积分p 值，以测试多个表型与 SNP 之间的关联。我们使用广泛的模拟研究来评估所提出方法的性能。结果表明，所提出的方法可以很好地控制 I 类错误率，并且比其他可用方法更强大。我们还将所提出的方法应用于英国生物银行的 IX 类（循环系统疾病）表型。我们发现，与我们比较的其他可行方法相比，所提出的方法可以识别更重要的 SNP。