Fig. 3: Power for association tests by env-MR-MEGA and MR-MEGA when female and male cohorts have different smoking patterns, under different ancestral heterogeneity settings.

When smoking proportions clearly differed between male and female cohorts, env-MR-MEGA gained greater power to detect association compared to MR-MEGA. In the mixed direction pattern, where not all male cohorts share high smoking proportions, both West-central Africa and South Africa scenarios contain one male cohort with a lower smoking proportion. Within West-central Africa and South Africa scenarios, comparing the same direction and the mixed direction patterns, the gains in power to detect association by env-MR-MEGA in the same direction pattern exceeded those in the mixed direction pattern. “MR_MEGA_assoc_SD” and “env_MR_MEGA_assoc_SD” correspond to the same direction pattern, while “MR_MEGA_assoc_MD” and “env_MR_MEGA_assoc_MD” correspond to the mixed direction pattern. Power was assessed at P < 5 × 10⁻⁸ and based on 1000 replications with unequal sample sizes (≥3000 in each cohort).