APOE and obesity due to melanocortin 4 receptor deficiency: When the participants were stratified by APOE genotype (ε4 non-carrier vs. ε4 carrier), both stratified groups showed significant associations between obesity and decreased risk of Aβ positivity only in the MH group (ε4 non-carrier: OR = 0.41, 95% CI 0.24–0.70; ε4 carrier: OR = 0.32, 95% CI 0.15–0.70) (Supplementary Fig. 2).