This guest post is by Chris Wallace on the preprint Unbiased statistical testing of shared genetic control for potentially related traits, available from the arXiv here. This is a cross-post from her group’s blog.
We have a new paper on arXiv detailing some work on colocalisation analysis, a method to determine whether two traits share a common causal variant. This is of interest in autoimmune disease genetics as the associated loci of so many autoimmune diseases overlap 1, but, for some genes, it appears the causal variants are distinct. It is also relevant for integrating disease association and eQTL data, to understand whether association of a disease to a particular locus is mediated by a variant’s effect on expression of a specific gene, possibly in a specific tissue.
However, determining whether traits share a common causal variant as opposed to distinct causal variants, probably in some LD, is not straightforward. It is well established that regression coefficients are aymptotically unbiased. However, when a SNP has been selected because it is the most associated in a region, then coefficients do then tend to be biased away from the null, ie their effect is overestimated. Because SNPs need to be selected to describe the association in any region in order to do colocalisation analysis, and because the coefficient bias will differ between datasets, there could be a tendancy to call truly colocalising traits as distinct. In fact, application of a formal statistical test for colocalisation 2 in a naive manner could have a type 1 error rate around 10-20% for a nominal size of 5%. This of course suggests that our earlier analysis of type 1 diabetes and monocyte gene expression 3 needs to be revised because it is likely we will have falsely rejected some genes which mediate the type 1 diabetes association in a region.
In this paper, we demonstrate two methods to overcome the problem. One, possibly more attractive to frequentists, is to avoid the variable selection by performing the analysis on principle components which summarise the genetic variation in a region. There is an issue with how many components are required, and our simulations suggest enough components need to be selected to capture around 85% of variation in a region. Obviously, this leads to a huge increase in degrees of freedom but, surprisingly, the power was not much worse compared to our favoured option of averaging p values over the variable selection using Bayesian Model Averaging. The idea of averaging p values is possibly anathema to Bayesians and frequentists alike, but these “posterior predictive p values” do have some history, having been introduced by Rubin in 1984 4. If you are prepared to mix Bayesian and frequentist theory sufficiently to average a p value over a posterior distribution (in this case, the posterior is of the SNPs which jointly summarise the association to both traits), it’s quite a nice idea. We used it before 3 as an alternative to taking a profile likelihood approach to dealing with a nuisance parameter, instead calculating p values conditional on the nuisance parameter, and averaging over its posterior. In this paper, we show by simulation that it does a good job of maintaining type 1 error and tends to be more powerful than the principle components approach.
There are many questions regarding integration of data from different GWAS that this paper doesn’t address: how to do this on a genomewide basis, for multiple traits, or when samples are not independent (GWAS which share a common set of controls, for example). Thus, it is a small step, but a useful contribution, I think, demonstrating a statistically sound method of investigating potentially shared causal variants in individual loci in detail. And while detailed investigation of individual loci may be currently be less fashionable than genomewide analyses, those detailed analyses are crucial for fine resolution analysis.