So many correlated tests, so little time! Rapid adjustment of P values for multiple correlated tests

Abstract

Contemporary genetic association studies may test hundreds of thousands of genetic variants for association, often with multiple binary and continuous traits or under more than one model of inheritance. Many of these association tests may be correlated with one another because of linkage disequilibrium between nearby markers and correlation between traits and models. Permutation tests and simulation-based methods are often employed to adjust groups of correlated tests for multiple testing, since conventional methods such as Bonferroni correction are overly conservative when tests are correlated. We present here a method of computing P values adjusted for correlated tests (P(ACT)) that attains the accuracy of permutation or simulation-based tests in much less computation time, and we show that our method applies to many common association tests that are based on multiple traits, markers, and genetic models. Simulation demonstrates that P(ACT) attains the power of permutation testing and provides a valid adjustment for hundreds of correlated association tests. In data analyzed as part of the Finland-United States Investigation of NIDDM Genetics (FUSION) study, we observe a near one-to-one relationship (r(2)>.999) between P(ACT) and the corresponding permutation-based P values, achieving the same precision as permutation testing but thousands of times faster.

Figure 1.

Bivariate normal probability represented by P_ACT when L=2 for one-sided tests (A) and two-sided tests (B). Elliptical lines represent the contours of a bivariate normal density function with positive correlation. Shaded area represents the space (extending to infinity) over which the probability P_ACT is measured.

Figure 2.

LD (r²) between 20 SNPs from HNF1A

Figure 3.

Correlation structures used in simulations of 10 correlated traits. A, Uncorrelated traits. B, Equal correlation between traits. C, Autocorrelated traits. D, Independent blocks of correlated traits. E, Negatively correlated blocks of correlated traits.

Figure 4.

A, Estimates of P_ACT and P_perm for 3,007 SNPs tested for disease association under three genetic models. B, Estimates of P_ACT and P_perm for 3,584 SNPs tested for association with 18 quantitative traits. Unblackened circles represent 3,575 SNPs genotyped for the candidate-gene study. Blackened circles represent nine simulated SNPs.