Multiple correlated traits/phenotypes are often collected in genetic association studies and they may share a common genetic mechanism. Joint analysis of correlated phenotypes has well‐known advantages over one‐at‐a‐time analysis including gain in power and better understanding of genetic etiology. However, when the phenotypes are of discordant types such as binary and continuous, the joint modeling is more challenging. Another research area of current interest is discovery of rare genetic variants. Currently there is no method available for detecting association of rare (or common) haplotypes with multiple discordant phenotypes jointly. Our goal is to fill this gap specifically for two discordant phenotypes. We consider a rare haplotype association method for a binary phenotype, logistic Bayesian LASSO (univariate LBL) and its extension for two correlated binary phenotypes (bivariate LBL‐2B). Under this framework, we propose a haplotype association test with binary and continuous phenotypes jointly (bivariate LBL‐BC). Specifically, we use a latent variable to induce correlation between the two phenotypes. We carry out extensive simulations to investigate bivariate LBL‐BC and compare it with univariate LBL and bivariate LBL‐2B. In most settings, bivariate LBL‐BC performs the best. In only two situations, bivariate LBL‐BC has similar performance—when the two phenotypes are (1) weakly or not correlated and the target haplotype affects the binary phenotype only and (2) strongly positively correlated and the target haplotype affects both phenotypes in positive direction. Finally, we apply the method to a data set on lung cancer and nicotine dependence and detect several haplotypes including a rare one.

中文翻译：

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检测具有二元和连续类型的两个相关表型的罕见单倍型关联

在遗传关联研究中经常收集到多种相关的性状/表型，它们可能具有共同的遗传机制。与一次性分析相比，相关表型的联合分析具有众所周知的优势，包括功能增强和对遗传病因学的更好理解。但是，当表型是不连续的类型（例如二进制和连续）时，联合建模更具挑战性。当前关注的另一个研究领域是稀有遗传变异的发现。当前，尚无方法可用于同时检测稀有（或常见）单倍型与多个不一致表型的关联。我们的目标是专门针对两种不一致的表型填补这一空白。我们考虑了一种针对二进制表型的罕见单倍型关联方法，Logistic贝叶斯LASSO（单变量LBL）及其对两个相关二进制表型（双变量LBL-2B）的扩展。在此框架下，我们提出了具有二元和连续表型（双变量LBL-BC）的单倍型关联测试。具体来说，我们使用潜在变量来诱导两个表型之间的相关性。我们进行了广泛的模拟来研究双变量LBL-BC，并将其与单变量LBL和双变量LBL-2B进行比较。在大多数情况下，双变量LBL-BC表现最佳。在仅两种情况下，双变量LBL-BC具有相似的性能-当两种表型（1）弱相关或不相关且目标单倍型仅影响二元表型且（2）强正相关且目标单倍型以正型影响两种表型时方向。最后，