Bayesian variable selection using partially observed categorical prior information in fine‐mapping association studies

Abstract

Several methods have been proposed to allow functional genomic information to inform prior distributions in Bayesian fine-mapping case-control association studies. None of these methods allow the inclusion of partially observed functional genomic information. We use functional significance (FS) scores that combine information across multiple bioinformatics sources to inform our effect size prior distributions. These scores are not available for all singlenucleotide polymorphisms (SNPs) but by partitioning SNPs into naturally occurring FS score groups, we show how missing FS scores can easily be accommodated via finite mixtures of elicited priors. Most current approaches adopt a formal Bayesian variable selection approach and either limit the number of causal SNPs allowed or use approximations to avoid the need to explore the vast parameter space. We focus instead on achieving differential shrinkage of the effect sizes through prior scale mixtures of normals and use marginal posterior probability intervals to select candidate causal SNPs. We show via a simulation study how this approach can improve localisation of the causal SNPs compared to existing mutli-SNP fine-mapping methods. We also apply our approach to fine-mapping a region around the CASP8 gene using the iCOGS consortium breast cancer SNP data. K E Y W O R D SBayesian, fine mapping, missing data, prior information, variable selection

The utility of the Laplace effect size prior distribution in Bayesian fine‐mapping studies

“…To allow comparison with the Laplace prior we equate the prior variances giving , which gives . This final pair of prior hyperparameter values are calculated on a different basis to the preceding two hyperparameter pairs (which were based on maximum‐likelihood estimates obtained using the breast cancer GWAS top hits) but fixing the prior variance or assigning it distribution is a standard approach in Bayesian variable selection problems (Alenazi et al, 2019).…”

“…Abbreviation: SNP, single-nucleotide polymorphism. Spencer et al (2015); NG is the normal-gamma prior of Alenazi et al (2019); NGFS is the normal-gamma prior of Alenazi et al ( 2019) that incorporates functional genomic scores into the effect size prior.…”

“…Other priors have been utilized in fine‐mapping studies including the t ‐distribution (Marchini & Howie, 2010), the normal‐gamma prior (Alenazi et al, 2019; Boggis et al, 2016), and the Laplace prior (Hoggart et al, 2008). There are also methods starting to become available that implement methods based on binned empirical effect sizes that do not assume specific parametric distributions (Vsevolozhskaya & Zaykin, 2019).…”

“…The Laplace prior shares many of the advantages of the Gaussian distribution as a prior on the effect size when used in conjunction with an asymptotic Gaussian‐likelihood: there is a closed‐form expression for the posterior distribution which does not require @@MCMC as does the normal‐gamma prior (Alenazi et al, 2019; Boggis et al, 2016); and calculating the Bayes factor does not require a Laplace approximation, as does the t ‐distribution prior implemented in SNPTEST (Marchini & Howie, 2010). The zero‐mean Laplace prior has more mass close to zero than the Gaussian and also has heavier tails.…”

Quantifying posterior effect size distribution of susceptibility loci by common summary statistics

“…On the one hand, it allows FAB to be flexible and not to be restricted to a parametric prior distributions for the effect size. For instance, FAB is not restricted to the typical default choice of the normal distribution for the causal SNP effect size prior (Wakefield, 2007), Laplace (Walters, Cox, & Yaacob, 2019) or normal‐gamma (Alenazi, Cox, Juarez, Lin, & Walters, 2019) prior. On the other hand, FAB includes the parametric scenario as a special case.…”