Bivariate logistic Bayesian LASSO for detecting rare haplotype association with two correlated phenotypes

In genetic association studies, joint modeling of related traits/phenotypes can utilize the correlation between them and thereby provide more power and uncover additional information about genetic etiology. Moreover, detecting rare genetic variants are of current scientific interest as a key to missing heritability. Logistic Bayesian LASSO (LBL) has been proposed recently to detect rare haplotype variants using case-control data, that is, a single binary phenotype. As there is currently no haplotype association method that can handle multiple binary phenotypes, we extend LBL to fill this gap. We develop a bivariate model by using a latent variable to induce correlation between the two outcomes. We carry out extensive simulations to investigate the bivariate LBL and compare with the univariate LBL. The bivariate LBL performs better or similar to the univariate LBL in most settings. It has the highest gain in power when a haplotype is associated with both traits and it affects at least one trait in a direction opposite to the direction of the correlation between the traits. We analyze two data sets-Genetic Analysis Workshop 19 sequence data on systolic and diastolic blood pressures and a genome-wide association data set on lung cancer and smoking and detect several associated rare haplotypes.