Locating disease genes using Bayesian variable selection with the Haseman-Elston method

Abstract

Background: We applied stochastic search variable selection (SSVS), a Bayesian model selection method, to the simulated data of Genetic Analysis Workshop 13. We used SSVS with the revisited Haseman-Elston method to find the markers linked to the loci determining change in cholesterol over time. To study gene-gene interaction (epistasis) and gene-environment interaction, we adopted prior structures, which incorporate the relationship among the predictors. This allows SSVS to search in the model space more efficiently and avoid the less likely models.

Results: In applying SSVS, instead of looking at the posterior distribution of each of the candidate models, which is sensitive to the setting of the prior, we ranked the candidate variables (markers) according to their marginal posterior probability, which was shown to be more robust to the prior. Compared with traditional methods that consider one marker at a time, our method considers all markers simultaneously and obtains more favorable results.

Conclusions: We showed that SSVS is a powerful method for identifying linked markers using the Haseman-Elston method, even for weak effects. SSVS is very effective because it does a smart search over the entire model space.

Figure 1

Top ranked markers based upon SSVS The markers are ranked according to their marginal posterior obtained using 10,000 cycles of Gibbs algorithm. Disease loci are located on chromosomes 7, 15, and 21, and gender effect is ranked at the 15^th (Replicate 1 of the simulated data).

Figure 2

Rankings of markers with p = 0.02 and p = 0.002 Ranking of the markers for two different prior settings (p = 0.02 and p = 0.002) is plotted, which shows its robustness to the choice of p.

Figure 3

Gene × gene and gene × gender interaction effects The top ranked 30 markers selected from the first stage and their interactions are considered in the second stage. The interaction between chromosome 21 and gender are observed.

Figure 4

Type I error of Haseman-Elston methods with D² and CP as responses False positives when squared-difference is used do not overlap with ones of cross-product. This suggests that complementary information are contained in each responses.