Variant selection from Chromosome 13 for the EOMI data: The dashed curve shows the fitted density function for the marginal inclusion scores of non-associated variants, and the vertical bar shows the classification rules at the FDR level 0.25.

<p>Variant selection from Chromosome 13 for the EOMI data: The dashed curve shows the fitted density function for the marginal inclusion scores of non-associated variants, and the vertical bar shows the classification rules at the FDR level 0.25.</p

BRVD results for the EOMI data.

<p>Size: the number of variants included in each chromosome; : the selected value of ; mean: , i.e., the average value of over five independent runs at the selected value of ; SD: standard deviation of .</p

CPU time cost by the BRVD on an Intel Xeon E5-2690 processor (2.9 GHz) for running iterations.

<p>: sample size; : number of variants.</p

The CPU time of BRVD versus the number of variants for the EOMI data (with ).

<p>The CPU time of BRVD versus the number of variants for the EOMI data (with ).</p

Bayesian Detection of Causal Rare Variants under Posterior Consistency

<div><p>Identification of causal rare variants that are associated with complex traits poses a central challenge on genome-wide association studies. However, most current research focuses only on testing the global association whether the rare variants in a given genomic region are collectively associated with the trait. Although some recent work, e.g., the Bayesian risk index method, have tried to address this problem, it is unclear whether the causal rare variants can be consistently identified by them in the small--large- situation. We develop a new Bayesian method, the so-called Bayesian Rare Variant Detector (BRVD), to tackle this problem. The new method simultaneously addresses two issues: (i) (Global association test) Are there any of the variants associated with the disease, and (ii) (Causal variant detection) Which variants, if any, are driving the association. The BRVD ensures the causal rare variants to be consistently identified in the small--large- situation by imposing some appropriate prior distributions on the model and model specific parameters. The numerical results indicate that the BRVD is more powerful for testing the global association than the existing methods, such as the combined multivariate and collapsing test, weighted sum statistic test, RARECOVER, sequence kernel association test, and Bayesian risk index, and also more powerful for identification of causal rare variants than the Bayesian risk index method. The BRVD has also been successfully applied to the Early-Onset Myocardial Infarction (EOMI) Exome Sequence Data. It identified a few causal rare variants that have been verified in the literature.</p></div

Type-I errors of BRVD for the simulated examples.

<p>Type-I errors of BRVD for the simulated examples.</p

Marginal ROC curves for BRVD and BRI: Left panel: ROC curves with covariates adjusted; right panel: ROC curves with covariates omitted.

<p>Marginal ROC curves for BRVD and BRI: Left panel: ROC curves with covariates adjusted; right panel: ROC curves with covariates omitted.</p

Jeffrey's grades of evidence (Jeffreys, 1961).

<p>The posterior probability is calculated with the prior probabilities .</p

Illustrative plot for causal rare variants detection.

<p>The dashed curve shows the fitted density function for the marginal inclusion scores of non-associated variants, and the vertical bar shows the classification rules at the FDR level 0.05 (solid line) and the FDR level 0.01 (dashed line). The left panel is for and the right panel is for .</p

Global ROC curves for BRVD versus BRI and SKAT for the simulated example (with covariate adjustment).

<p>Each plot represents a ROC curve as we vary the global BF threshold for BRVD and BRI, and vary the -value threshold for SKAT.</p