We compared the behaviour of our proposed test with that of proportional colocalisation testing [12], [14] in the specific case of a biomarker dataset with 10,000 samples (Figure 5, and also Figures S3 and S4). Broadly, in the case of either a single common causal variant or two distinct causal variants, our proposed method could infer the simulated hypotheses correctly (PP4 or PP3 >0.9) with good confidence, and PP3 >0.9 slightly more often than the proportional testing p-value <0.05. A key advantage in our Bayesian approach is the ability to distinguish evidence for colocalisation (i.e. high PP4) from a lack of power (i.e. high PP0, PP1 or PP2). In both of these cases (high PP4 or high PP0/PP1/PP2), the use of the proportional approach leads to failure to reject the null even though the interpretation of these situations should differ.
