Detecting rare haplotype association with two correlated phenotypes of binary and continuous types

Abstract

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.

Bivariate quantitative Bayesian LASSO for detecting association of rare haplotypes with two correlated continuous phenotypes

“…The amounts of penalty for the slope coefficients are controlled by the hyper-parameters and . We let them follow gamma ( a , b ) distribution with a = b = 20, following the original LBL method and its extensions ( Biswas and Lin, 2012 ; Yuan and Biswas, 2019 ; Yuan and Biswas, 2021 ).…”

“…In particular, must be greater than for all k values. Thus, the prior for d , given f , is set to be We use a weakly informative half-Cauchy prior for with a fixed hyper-parameter A given by , where , and set ( Yuan and Biswas, 2019 ; Yuan and Biswas, 2021 ). A non-informative uniform prior is used for and , whose probability density function is given by , where .…”

“…We use the posterior distributions of regression coefficients for testing the association of haplotypes with the two phenotypes jointly. In particular, to test the association of the haplotype with the two continuous phenotypes jointly, the hypotheses are where we set to be 0.1 ( Biswas and Lin, 2012 ; Yuan and Biswas, 2019 ; Yuan and Biswas, 2021 ). Notably, the alternate hypothesis corresponds to the association with at least one phenotype.…”

“…If this maximum BF exceeds a certain threshold, we conclude that the haplotype block is associated with at least one of the two phenotypes. We calculated the appropriate threshold following Yuan and Biswas (2019) and Yuan and Biswas (2021) —to be described in detail in the Simulation study and Application sections.…”

“…LBL was extended to incorporate gene–environment interactions ( Zhang et al, 2017a ; Zhang et al, 2017b ; Papachristou and Biswas, 2020 ), data generated using complex sampling designs ( Zhang et al, 2017a ), and family data ( Wang and Lin, 2014 ; Datta et al, 2018 ). LBL was also adapted to accommodate two phenotypes, namely, bivariate LBL-2B for binary phenotypes and bivariate LBL-BC for binary and continuous phenotypes ( Yuan and Biswas, 2019 ; Yuan and Biswas, 2021 ). LBL and its extensions utilize regularization to decrease the unassociated effects close to zero, which, in turn, helps the effect of an associated haplotype, especially if it is a rare one, to stand out.…”