Joint association analysis of a binary and a quantitative trait in family samples

In recent years, improved genotyping and sequencing technologies have enabled the discovery of new loci associated with various diseases or traits. For instance, by testing the association with each single-nucleotide variant (SNV) separately, genome-wide association studies (GWAS) have achieved tremendous success in identifying SNVs associated with specific traits. However, little is known about the common genetic basis of multiple traits owing to lack of efficient methods. With the use of extended quasi-likelihood, a Wald test has been proposed to perform a bivariate analysis of a continuous and a binary trait in unrelated samples. However, owing to its low computational efficiency, it has not been implemented in real applications to large-scale genetic studies. In this paper, we propose an efficient bivariate robust score test for two traits, one continuous and one binary, based on extended generalized estimating equations. Our approach is applicable to both family-based and unrelated study designs and can be extended to test the association of multiple traits. Our simulation studies demonstrate the type-I error rate of our approach is well controlled in all minor allele frequency (MAF) scenarios, with MAF ranging from 1 to 30%, and the method is more powerful in certain MAF scenarios than univariate testing with correction for multiple testing. Because of the computational advantage of score tests, our approach is readily applicable to GWAS or sequencing studies. Finally, we present a real application to uncover genetic variants associated with body mass index and type-2 diabetes in the Framingham Heart Study.