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Genomewide association (GWA) studies assay hundreds of thousands of single nucleotide polymorphisms (SNPs) simultaneously across the entire genome and associate them with diseases, other biological or clinical traits. The association analysis usually tests each SNP as an independent entity and ignores the biological information such as linkage disequilibrium. Although the Bonferroni correction and other approaches have been proposed to address the issue of multiple comparisons as a result of testing many SNPs, there is a lack of understanding of the distribution of an association test statistic when an entire genome is considered together. In other words, there are extensive efforts in hypothesis testing, and almost no attempt in estimating the density under the null hypothesis. By estimating the true null distribution, we can apply the result directly to hypothesis testing; better assess the existing approaches of multiple comparisons; and evaluate the impact of linkage disequilibrium on the GWA studies. To this end, we estimate the empirical null distribution of an association test statistic in GWA studies using simulated population data. We further propose a convenient and accurate method based on adaptive spline to estimate the empirical value in GWA studies and validate our findings using a real data set. Our method enables us to fully characterize the null distribution of an association test that not only can be used to test the null hypothesis of no association, but also provide important information about the impact of density of the genetic markers on the significance of the tests. Our method does not require users to perform computationally intensive permutations, and hence provides a timely solution to an important and difficult problem in GWA studies.

The Null Distributions of Test Statistics in Genomewide Association Studies