The natural and statistically exact modification of our approach would compute, for each trait, Bayes factors for sets of SNPs rather than single SNPs (up to N SNPs jointly to accommodate for N distinct associations per trait). However, this approach has two drawbacks. Firstly, the interpretation of the resulting posterior probabilities is more challenging in situations where some but not all of the variants are shared across both traits. More importantly, the typical approach consists of publishing single variant summary statistics, which would prevent the use of standard summary statistics, a key feature of our approach.
