Exploiting SNP correlations within random forest for genome-wide association studies

Abstract

The primary goal of genome-wide association studies (GWAS) is to discover variants that could lead, in isolation or in combination, to a particular trait or disease. Standard approaches to GWAS, however, are usually based on univariate hypothesis tests and therefore can account neither for correlations due to linkage disequilibrium nor for combinations of several markers. To discover and leverage such potential multivariate interactions, we propose in this work an extension of the Random Forest algorithm tailored for structured GWAS data. In terms of risk prediction, we show empirically on several GWAS datasets that the proposed T-Trees method significantly outperforms both the original Random Forest algorithm and standard linear models, thereby suggesting the actual existence of multivariate non-linear effects due to the combinations of several SNPs. We also demonstrate that variable importances as derived from our method can help identify relevant loci. Finally, we highlight the strong impact that quality control procedures may have, both in terms of predictive power and loci identification. Variable importance results and T-Trees source code are all available at www.montefiore.ulg.ac.be/~botta/ttrees/ and github.com/0asa/TTree-source respectively.

Figure 1. A closer look into a T-Tree test-node.

The group 1 is tested. Out of this group, three SNPs are exploited by the weak learner. In red (resp. green), probability of being a case (resp. control) estimated by the weak-learner.

Figure 2. Group and variable importances for the two novel candidate regions for Crohn's disease.

Regions 2p12 (top) and 7q31 (bottom), as found by T-Trees on . First row: SNP and block importances. Second row: univariate (Fisher) p-values and haplotype p-values as derived from the case/control omnibus test with degrees of freedom where corresponds to the number of common haplotypes (a haplotype is said to be common if its frequency is greater than in the population under study). Third row: number of haplotypes in each block. Bottom plot: ld pattern () in the regions.