Supplementary Material for: Integrating Multiple Correlated Phenotypes for Genetic Association Analysis by Maximizing Heritability

Many correlated disease variables are analyzed jointly in genetic studies in the hope of increasing power to detect causal genetic variants. One approach involves assessing the relationship between each phenotype and each SNP individually and using a Bonferroni correction for the effective number of tests conducted. Alternatively, one can apply a multivariate regression or a dimension reduction technique, such as principal component analysis, and test for the association with the principal components of the phenotypes rather than the individual phenotypes. Inspired by the previous approaches of combining phenotypes to maximize heritability at individual SNPs, in this paper, we propose to construct a maximally heritable (MaxH) phenotype by taking advantage of the estimated total heritability and co-heritability. The heritability and co-heritability only need to be estimated once; therefore, our method is applicable to genome-wide scans. The MaxH phenotype is a linear combination of the individual phenotypes with increased heritability and power over the phenotypes being combined. Simulations show that the heritability and power achieved agree well with the theory for large samples and two phenotypes. We compare our approach with commonly used methods and assess both the heritability and the power of the MaxH phenotype. Moreover, we provide suggestions for how to choose the phenotypes for combination. An application of our approach to a GWAS on chronic obstructive pulmonary disease shows its practical relevance.