Using linkage genome scans to improve power of association in genome scans

Abstract

Scanning the genome for association between markers and complex diseases typically requires testing hundreds of thousands of genetic polymorphisms. Testing such a large number of hypotheses exacerbates the trade-off between power to detect meaningful associations and the chance of making false discoveries. Even before the full genome is scanned, investigators often favor certain regions on the basis of the results of prior investigations, such as previous linkage scans. The remaining regions of the genome are investigated simultaneously because genotyping is relatively inexpensive compared with the cost of recruiting participants for a genetic study and because prior evidence is rarely sufficient to rule out these regions as harboring genes with variation of conferring liability (liability genes). However, the multiple testing inherent in broad genomic searches diminishes power to detect association, even for genes falling in regions of the genome favored a priori. Multiple testing problems of this nature are well suited for application of the false-discovery rate (FDR) principle, which can improve power. To enhance power further, a new FDR approach is proposed that involves weighting the hypotheses on the basis of prior data. We present a method for using linkage data to weight the association P values. Our investigations reveal that if the linkage study is informative, the procedure improves power considerably. Remarkably, the loss in power is small, even when the linkage study is uninformative. For a class of genetic models, we calculate the sample size required to obtain useful prior information from a linkage study. This inquiry reveals that, among genetic models that are seemingly equal in genetic information, some are much more promising than others for this mode of analysis.

Figure 1

Achieved power of a single test for a variety of binary weighting schemes. Within each bar plot, the left (right) bar reveals the power if the value is up-weighted (down-weighted). The plot displays the deviation in power of the weighted test from the marginal unweighted power (0.5). Rows, from top to bottom, are B=2, 6, and 50; columns. from left to right, are ε=0.001, 0.01, and 0.1.

Figure 2

Extra discoveries as a function of the quality of the bets. The scenario investigated has m=10,000 tests, and a fraction (a=0.1) of them are nonnull. The quality of the bets, measured in terms of η, varies between 0 and 20. We consider four choices of ε: 0.01 (short-dashed line), 0.1 (dotted line), 0.2 (dot-dashed line), and 0.4 (long-dashed line).

Figure 3

Plot of linkage traces for three chromosomes with weights. The green and red traces are weights with exponential (B=1) and cumulative (B=2) weights, respectively, that are based on the linkage trace (blue). The bottom panel has no signal.

Figure 4

Power as a function of μ_a. Power is defined as the number of true discoveries of L=10 causal variants. Distinct lines correspond to different methods and/or linkage signals, coded as follows (from lowest to highest power): dotted is the Bonferroni method; dot-dashed is wBH through use of linkage data with no signal (μ_l=0); solid is the BH method (Storey’s version); dashed are wBH through use of linkage data with a weak (μ_l=1), moderate (μ_l=2.5), and strong (μ_l=3.5) signal.