Fig. 2

Directed acyclic graph. MR, Mendelian randomization; BMI, body mass index; MV, multivariable. We use hypothesis-free MR to explore the potential effect of age at menarche (X) on outcomes (Y), by using SNPs that robustly relate to age at menarche as instrumental variables (Z). The directed acyclic graph shows our key assumptions for the different genetic risk scores we use in our analyses. The black lines show this main analysis; the heavily weighted black line indicated the effects we are interested in. The MR assumption that Z does not relate to Y other than through X may be violated because of the known associations between some of the age at menarche SNPs and BMI. The genetic instrument Z could be associated with the outcome due to horizontal pleiotropy via child BMI, either via its relation to adult BMI or directly (blue dashed arrows). These paths could bias our MR results. Z could also be related to BMI via vertical pleiotropy through a path from Z to X, from X to adult BMI, and from it to Y (green dashed-dotted arrows). This path implies adult BMI is part of the causal path from age at menarche to Y and would not bias our results. We used four approaches to exploring these possibilities (table). We have not systematically explored other horizontally pleiotropic pathways that could bias our results (red dotted line)