Retrospective Binary-Trait Association Test Elucidates Genetic Architecture of Crohn Disease

Abstract

In genetic association testing, failure to properly control for population structure can lead to severely inflated type 1 error and power loss. Meanwhile, adjustment for relevant covariates is often desirable and sometimes necessary to protect against spurious association and to improve power. Many recent methods to account for population structure and covariates are based on linear mixed models (LMMs), which are primarily designed for quantitative traits. For binary traits, however, LMM is a misspecified model and can lead to deteriorated performance. We propose CARAT, a binary-trait association testing approach based on a mixed-effects quasi-likelihood framework, which exploits the dichotomous nature of the trait and achieves computational efficiency through estimating equations. We show in simulation studies that CARAT consistently outperforms existing methods and maintains high power in a wide range of population structure settings and trait models. Furthermore, CARAT is based on a retrospective approach, which is robust to misspecification of the phenotype model. We apply our approach to a genome-wide analysis of Crohn disease, in which we replicate association with 17 previously identified regions. Moreover, our analysis on 5p13.1, an extensively reported region of association, shows evidence for the presence of multiple independent association signals in the region. This example shows how CARAT can leverage known disease risk factors to shed light on the genetic architecture of complex traits.

Figure 1

Empirical Power of CARAT, CARATd, and LMM Empirical power is based on 5,000 replicates. An upper bound for the standard error of the empirical power is 0.007. For a difference between two empirical power values, the upper bound on the standard error is 0.01. (A and B) Power results in the “2 Subpopulations” setting, in which the leftmost value on the horizontal axis (50%/50%) corresponds to no population stratification and the rightmost value (80%/20%) corresponds to profound stratification. Power results when the phenotype is generated according to a liability threshold model with two subpopulations (A) or to a logistic regression model with two subpopulations (B). (C and D) Power results in the “Admixture and Cryptic Relatedness” setting, for which the percentages on the horizontal axis are defined so that the numerator is the variance, on the liability or logistic scale, explained by the ancestry and cryptic relatedness effects (the first number) or by the covariate effects (the second number), and the denominator is the total variance explained by the two types of effects. The horizontal scale indicates the relative impact of ancestry versus covariates on the phenotype, with the far left corresponding to no effect of ancestry and strong effects of covariates and the far right corresponding to no effect of covariates and a strong effect of ancestry. The dotted lines denote settings with cryptic relatedness, and the solid lines denote settings without cryptic relatedness. Power results when the phenotype is generated according to a liability threshold model (C) or according to a logistic regression model (D) in the “Admixture and Cryptic Relatedness” setting.