Ranks of genuine associations in whole-genome scans

Abstract

With the recent advances in high-throughput genotyping techniques, it is now possible to perform whole-genome association studies to fine map causal polymorphisms underlying important traits that influence susceptibility to human diseases and efficacy of drugs. Once a genome scan is completed the results can be sorted by the association statistic value. What is the probability that true positives will be encountered among the first most associated markers? When a particular polymorphism is found associated with the trait, there is a chance that it represents either a "true" or a "false" association (TA vs. FA). Setting appropriate significance thresholds has been considered to provide assurance of sufficient odds that the associations found to be significant are genuine. However, the problem with genome scans involving thousands of markers is that the statistic values of FAs can reach quite extreme magnitudes. In such situations, the distributions corresponding to TAs and the most extreme FAs become comparable and significance thresholds tend to penalize TAs and FAs in a similar fashion. When sorting between true and false associations, the "typical" place (i.e., rank) of TAs among the most significant outcomes becomes important, ordered by the association statistic value. The distribution of ranks that we study here allows calculation of several useful quantities. In particular, it gives the number of most significant markers needed for a follow-up study to guarantee that a true association is included with certain probability. This can be calculated conditionally on having applied a multiple-testing correction. Effects of multilocus (e.g., haplotype association) tests and impact of linkage disequilibrium on the distribution of ranks associated with TAs are evaluated and can be taken into account.

Figure 1.

Diffusion-generated P-value correlation decay. The distance between two neighboring markers (1 unit on the x-axis) is 15 kb.

Figure 2.

P-value correlation decay within (left) and between (right) LD blocks. The distance between two neighboring markers (1 unit on the x-axis) is 15 kb.

Figure 3.

Expected power associated with individual effects (bottom line) given overall power for three effects (m = 3) (top line).

Figure 4.

Plot of degrees of freedom vs. significance level (α) for 80% power tests at the 70% quantile.

Figure 5.

Plot of degrees of freedom vs. significance level (α) for 80% power tests at the 5% quantile.