Analyze multivariate phenotypes in genetic association studies by combining univariate association tests

Abstract

Multivariate phenotypes are frequently encountered in genome-wide association studies (GWAS). Such phenotypes contain more information than univariate phenotypes, but how to best exploit the information to increase the chance of detecting genetic variant of pleiotropic effect is not always clear. Moreover, when multivariate phenotypes contain a mixture of quantitative and qualitative measures, limited methods are applicable. In this paper, we first evaluated the approach originally proposed by O'Brien and by Wei and Johnson that combines the univariate test statistics and then we proposed two extensions to that approach. The original and proposed approaches are applicable to a multivariate phenotype containing any type of components including continuous, categorical and survival phenotypes, and applicable to samples consisting of families or unrelated samples. Simulation results suggested that all methods had valid type I error rates. Our extensions had a better power than O'Brien's method with heterogeneous means among univariate test statistics, but were less powerful than O'Brien's with homogeneous means among individual test statistics. All approaches have shown considerable increase in power compared to testing each component of a multivariate phenotype individually in some cases. We apply all the methods to GWAS of serum uric acid levels and gout with 550,000 single nucleotide polymorphisms in the Framingham Heart Study.

Figure 1. Power comparison among combining statistics methods, univariate tests of each individual phenotypes (scenarios 1–4)

Note: Color bars present the power of the combining statistics approaches: The bar with Obrien on top represents O’Brien’s method, with RS(30) presents random splitting method that uses 30% families to estimate T_W, with CV represents cross-validation method Power for each approach was calculated at alpha=0.05. White bars present power of univariate test of individual phenotypes with phenotype number on the top; * indicates the phenotype is dichotomous. The group of bars in the middle corresponds alpha=0.05 for each phenotype, not corrected for multiple testing; the group of bars on the right corresponds an alpha level with Bonferroni correction for 5 tests (alpha=0.01 for each individual phenotype)

Figure 2. Power comparisons between combining statistics methods, general multivariate methods and single phenotype analysis for all continuous traits (scenarios 5 and 6) Scenario 5

Note: Color bars present the power of the combining statistics approaches: Obrien on top represents O’Brien’s method; RS(30), random splitting method that uses 30% families to estimate T_W; CV, cross-validation method; LME, linear mixed effects model assuming the same effects across all phenotypes; SS, summary statistics (mean of the statistics); PCP first principal component of the phenotypes. Power for each approach was calculated at alpha=0.05. White bars present power of univariate test of individual phenotypes with phenotype number on the top; * indicates the phenotype is dichotomous. The group of bars in the middle right corresponds alpha=0.05 for each phenotype, not corrected for multiple testing; the group of bars on the far right corresponds an alpha level with Bonferroni correction for 5 tests (alpha=0.01 for each individual phenotype) *The power of MANOVA method was adjusted to empirical 5% level.

Figure 3

Comparison of individual GWAS of uric acid (UA) and gout with combining statistics approaches. The top two panels are GWAS of UA and gout respectively; 3rd–5th panels are results of O’Brien’s, random sample splitting and cross-validation methods respectively. The x-axis is chromosome locations, y-axis is the minus log base 10 of the p-value truncated at 10. Points highlighted in red are those exceeding the genome-wide significant threshold (1.28×10⁻⁷) and in blue are those exceeding a threshold (2.56×10⁻⁶) of suggestive association.