Incorporating model uncertainty in detecting rare variants: the Bayesian risk index

Abstract

We are interested in investigating the involvement of multiple rare variants within a given region by conducting analyses of individual regions with two goals: (1) to determine if regional rare variation in aggregate is associated with risk; and (2) conditional upon the region being associated, to identify specific genetic variants within the region that are driving the association. In particular, we seek a formal integrated analysis that achieves both of our goals. For rare variants with low minor allele frequencies, there is very little power to statistically test the null hypothesis of equal allele or genotype counts for each variant. Thus, genetic association studies are often limited to detecting association within a subset of the common genetic markers. However, it is very likely that associations exist for the rare variants that may not be captured by the set of common markers. Our framework aims at constructing a risk index based on multiple rare variants within a region. Our analytical strategy is novel in that we use a Bayesian approach to incorporate model uncertainty in the selection of variants to include in the index as well as the direction of the associated effects. Additionally, the approach allows for inference at both the group and variant-specific levels. Using a set of simulations, we show that our methodology has added power over other popular rare variant methods to detect global associations. In addition, we apply the approach to sequence data from the WECARE Study of second primary breast cancers.

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics

“…For rare variants, there may be many rare causal variants in a region, and therefore sampling methods may be required to explore the model space. Some Bayesian-based methods have been proposed for rare variants, such as in Quintana et al (2011Quintana et al ( , 2012.…”

A sequence of methodological changes due to sequencing

“…Multiple different strategies have been employed, and these can be roughly grouped as variance-based test statistics [8,9 && ,10]; data-adaptive test statistics [11,12 & , [13][14][15][16][17][18][19]; optimal tests incorporating multiple test statistics [18][19][20]21 && , [22][23][24]; and Bayesian approaches [25][26][27][28] (Table 1) …”

“…et al[25] and Zhang et al[28] included latent variables capturing the effect direction of a variant, and used Bayesian model selection techniques to find the best models.A drawback to Bayesian analyses is that computationally intensive Markov chain Monte Carlo (MCMC) procedures are often required to estimate the posterior distributions. The Bayesian Risk Index approach of Quintana et al[25] requires MCMC when the number of variants in the model exceeds 20.…”

“…The Bayesian Risk Index approach of Quintana et al[25] requires MCMC when the number of variants in the model exceeds 20. To avoid computationally intensive MCMC, Yi et al[26] used mode-finding techniques from standard statistical analysis to estimate parameters and standard errors.…”

A Variational Bayes Discrete Mixture Test for Rare Variant Association

“…The two major differences of our method compared to the method of Quintana et al [22] are 1) we propose a computationally efficient variational Bayes approximate inference algorithm that is scalable to whole-genome analysis, and 2) we propose a likelihood ratio test that can be used to prioritize genes or regions of the genome for further investigation that has an approximately ${\chi }_1^2$ asymptotic distribution. Similar to Quintana et al [22, 23], another feature of our method is that a variant-level posterior probability of association is generated, which can be used to prioritize variants for follow-up.…”