Permutation-based approaches do not adequately allow for linkage disequilibrium in gene-wide multi-locus association analysis

Additional information about risk genes or risk pathways for diseases can be extracted from genome-wide association studies through analyses of groups of markers. The most commonly employed approaches involve combining individual marker data by adding the test statistics, or summing the logarithms of their P-values, and then using permutation testing to derive empirical P-values that allow for the statistical dependence of single-marker tests arising from linkage disequilibrium (LD). In the present study, we use simulated data to show that these approaches fail to reflect the structure of the sampling error, and the effect of this is to give undue weight to correlated markers. We show that the results obtained are internally inconsistent in the presence of strong LD, and are externally inconsistent with the results derived from multi-locus analysis. We also show that the results obtained from regression and multivariate Hotelling T(2) (H-T2) testing, but not those obtained from permutations, are consistent with the theoretically expected distributions, and that the H-T2 test has greater power to detect gene-wide associations in real datasets. Finally, we show that while the results from permutation testing can be made to approximate those from regression and multivariate Hotelling T(2) testing through aggressive LD pruning of markers, this comes at the cost of loss of information. We conclude that when conducting multi-locus analyses of sets of single-nucleotide polymorphisms, regression or multivariate Hotelling T(2) testing, which give equivalent results, are preferable to the other more commonly applied approaches.