Fig. 3: Comparison of HyPrColoc and MOLOC computation time and posterior probability of colocalization.

(Left panel) Computation time (seconds) for HyPrColoc (yellow) and MOLOC (blue) to assess full colocalization across M ≤ 1000 traits in a region containing Q = 1000 SNPs. MOLOC was restricted to M ≤ 5 traits owing to the computational and memory burden of the MOLOC algorithm when M > 5. When M = 5, we summarise the computation time of MOLOC from 10 datasets - as it took around 1 hour to analyse a single dataset, in all other scenarios performance was summarised from 1000 datasets. Three reference lines are plotted: (i) Bell(M + 1), which denotes the theoretical cost of exhaustively enumerating all hypotheses; (ii) M², denoting quadratic cost and; (ii) M¹, denoting the linear complexity of the HyPrColoc algorithm. (Right panel) Distribution of the posterior probability of colocalization between all traits, i.e. the posterior probability of full colocalization (PPFC), using HyPrColoc (yellow) and MOLOC (blue) across M ∈ {2,3,4} traits. Error bars denote the 1st and 9th deciles and a point denotes the median value. Despite differences in the prior set-up between the methods, the median absolute relative difference between the two posterior probabilities was ≲ 0.005.