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

Bayesian Disease Mapping to Identify High-Risk Population for Oral Cancer: A Retrospective Spatiotemporal Analysis

Objectives

Bayesian mapping is an effective spatiotemporal approach to identify high-risk geographic areas for diseases and has not been used to identify oral cancer hotspots in Australia previously. This retrospective disease mapping study was undertaken to identify the oral cancer trends and patterns within the Queensland state in Australia.

Methods

This study included data obtained from Queensland state Cancer Registry from 1982 to 2018. Domains mapped included the oral cancer incidence and mortality in Queensland (QLD). Local government areas (LGAs) and suburbs were utilized as geographical units for the estimation using Bayesian mapping approach.

Results

Of the 78 LGAs, 21 showed high-oral cancer incidence as measured using higher median smoothed incidence risk (SIR), above the state average. Specifically, nine LGAs within predominantly rural areas had SIR above 100% of the state average. Of these, only one LGA (Mount Isa City) had a median smoothed SIR and 95% CI of 2.61 (2.14-3.15) which was constantly above 100% of the state average. Furthermore, mortality risk estimated using smoothed mortality risk (SMR), were significantly higher than the state average in 31 LGAs. Seventeen LGAs had a median SMR above 100% of the state average while three LGAs had the highest overall, 3- and 5-year mortality risks. Considering the 95% credible interval which is indicative of the uncertainty around the estimates, three LGAs had the highest overall mortality risks-Yarrabah Aboriginal Shire (3.80 (2.16-6.39)), Cook Shire (3.37 (2.21-5.06)), and Mount Isa City (3.04 (2.40-3.80)).

Conclusion

Bayesian disease mapping approach identified multiple incidence and mortality hotspots within regional areas of the Queensland. Findings from our study can aid in designing targeted public health screening and interventions for primary prevention of oral cancer in regional and remote communities.

Bayesian multivariant fine mapping using the Laplace prior

Currently, the only effect size prior that is routinely implemented in a Bayesian fine-mapping multi-single-nucleotide polymorphism (SNP) analysis is the Gaussian prior. Here, we show how the Laplace prior can be deployed in Bayesian multi-SNP fine mapping studies. We compare the ranking performance of the posterior inclusion probability (PIP) using a Laplace prior with the ranking performance of the corresponding Gaussian prior and FINEMAP. Our results indicate that, for the simulation scenarios we consider here, the Laplace prior can lead to higher PIPs than either the Gaussian prior or FINEMAP, particularly for moderately sized fine-mapping studies. The Laplace prior also appears to have better worst-case scenario properties. We reanalyse the iCOGS case-control data from the CASP8 region on Chromosome 2. Even though this study has a total sample size of nearly 90,000 individuals, there are still some differences in the top few ranked SNPs if the Laplace prior is used rather than the Gaussian prior. R code to implement the Laplace (and Gaussian) prior is available at https://github.com/Kevin-walters/lapmapr.

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

The Gaussian distribution is usually the default causal single-nucleotide polymorphism (SNP) effect size prior in Bayesian population-based fine-mapping association studies, but a recent study showed that the heavier-tailed Laplace prior distribution provided a better fit to breast cancer top hits identified in genome-wide association studies. We investigate the utility of the Laplace prior as an effect size prior in univariate fine-mapping studies. We consider ranking SNPs using Bayes factors and other summaries of the effect size posterior distribution, the effect of prior choice on credible set size based on the posterior probability of causality, and on the noteworthiness of SNPs in univariate analyses. Across a wide range of fine-mapping scenarios the Laplace prior generally leads to larger 90% credible sets than the Gaussian prior. These larger credible sets for the Laplace prior are due to relatively high prior mass around zero which can yield many noncausal SNPs with relatively large Bayes factors. If using conventional credible sets, the Gaussian prior generally yields a better trade off between including the causal SNP with high probability and keeping the set size reasonable. Interestingly when using the less well utilised measure of noteworthiness, the Laplace prior performs well, leading to causal SNPs being declared noteworthy with high probability, whilst generally declaring fewer than 5% of noncausal SNPs as being noteworthy. In contrast, the Gaussian prior leads to the causal SNP being declared noteworthy with very low probability.

Fine-mapping genetic associations

Whilst thousands of genetic variants have been associated with human traits, identifying the subset of those variants that are causal requires a further 'fine-mapping' step. We review the basic fine-mapping approach, which is computationally fast and requires only summary data, but depends on an assumption of a single causal variant per associated region which is recognized as biologically unrealistic. We discuss different ways that the approach has been built upon to accommodate multiple causal variants in a region and to incorporate additional layers of functional annotation data. We further review methods for simultaneous fine-mapping of multiple datasets, either exploiting different linkage disequilibrium (LD) structures across ancestries or borrowing information between distinct but related traits. Finally, we look to the future and the opportunities that will be offered by increasingly accurate maps of causal variants for a multitude of human traits.

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

Testing millions of single nucleotide polymorphisms (SNPs) in genetic association studies has become a standard routine for disease gene discovery. In light of recent re-evaluation of statistical practice, it has been suggested that p-values are unfit as summaries of statistical evidence. Despite this criticism, p-values contain information that can be utilized to address the concerns about their flaws. We present a new method for utilizing evidence summarized by p-values for estimating odds ratio (OR) based on its approximate posterior distribution. In our method, only p-values, sample size, and standard deviation for ln(OR) are needed as summaries of data, accompanied by a suitable prior distribution for ln(OR) that can assume any shape. The parameter of interest, ln(OR), is the only parameter with a specified prior distribution, hence our model is a mix of classical and Bayesian approaches. We show that our method retains the main advantages of the Bayesian approach: it yields direct probability statements about hypotheses for OR and is resistant to biases caused by selection of top-scoring SNPs. Our method enjoys greater flexibility than similarly inspired methods in the assumed distribution for the summary statistic and in the form of the prior for the parameter of interest. We illustrate our method by presenting interval estimates of effect size for reported genetic associations with lung cancer. Although we focus on OR, the method is not limited to this particular measure of effect size and can be used broadly for assessing reliability of findings in studies testing multiple predictors.