24 Again, as would be expected given a causal relationship, we observed a positive r P between PDW and PD in the UKB, although the estimate was only marginally significant (r P ∼ 0.01, p = 8.44 × 10 −4 to 0.07 depending on prevalence; Data S1 ; Table S28 ), potentially because of the modest number of PD cases in the cohort (n = 1,323 compared with >5,000 for stroke).
Interestingly, the majority of these trait pairs (n = 60) did not have a significant genome-wide HDL- or LDSC-based r g , suggesting that meaningful local genetic correlations are common between traits with negligible genome-wide r g , and in most cases, a significant genome-wide r g reflects the presence of moderately significant local genetic correlations across the genome rather than highly significant local genetic correlations in specific genomic regions.