Efficient computation of significance levels for multiple associations in large studies of correlated data, including genomewide association studies

Abstract

Large exploratory studies, including candidate-gene-association testing, genomewide linkage-disequilibrium scans, and array-expression experiments, are becoming increasingly common. A serious problem for such studies is that statistical power is compromised by the need to control the false-positive rate for a large family of tests. Because multiple true associations are anticipated, methods have been proposed that combine evidence from the most significant tests, as a more powerful alternative to individually adjusted tests. The practical application of these methods is currently limited by a reliance on permutation testing to account for the correlated nature of single-nucleotide polymorphism (SNP)-association data. On a genomewide scale, this is both very time-consuming and impractical for repeated explorations with standard marker panels. Here, we alleviate these problems by fitting analytic distributions to the empirical distribution of combined evidence. We fit extreme-value distributions for fixed lengths of combined evidence and a beta distribution for the most significant length. An initial phase of permutation sampling is required to fit these distributions, but it can be completed more quickly than a simple permutation test and need be done only once for each panel of tests, after which the fitted parameters give a reusable calibration of the panel. Our approach is also a more efficient alternative to a standard permutation test. We demonstrate the accuracy of our approach and compare its efficiency with that of permutation tests on genomewide SNP data released by the International HapMap Consortium. The estimation of analytic distributions for combined evidence will allow these powerful methods to be applied more widely in large exploratory studies.

Figure 1

Parameters of the extreme-value distribution for S_k as function of length k. A, Location, chromosome 18. B, Location, chromosome 21. C, Scale, chromosome 18. D, Scale, chromosome 21. E, Shape, chromosome 18. F, Shape, chromosome 21.

Figure 2

Quantile-quantile plot of extreme-value distribution for S_k. A, Length 10, chromosome 18. B, Length 10, chromosome 21. C, Length 100, chromosome 18. D, Length 100, chromosome 21.

Figure 3

Quantile-quantile plot of beta distribution for the minimum P value for S_k. A, Chromosome 18, parameters (.8032,1.3766). B, Chromosome 21, parameters (.7932,1.3423).

Figure 4

Effect of assumption of independence in correlated tests. Solid line shows the P value of the 95th percentile of the empirical distribution, under assumption of independent tests. Dotted line shows the P value according to the fitted extreme-value distribution.

Figure 5

Power of fixed-length sum compared with variable-length sum, for 10,000 tests. A, Five true associations with χ² NCP 15. B, Ten associations with NCP 11. C, Fifty associations with NCP 5. D, One hundred associations with NCP 3.