Supplementary Material for: The Childhood Shield: How FLOW-MR Unravels the Causal Effects of Time-Varying BMI on Migraine

Objectives: To investigate the causal effects of body mass index (BMI) at different life stages (childhood and adulthood) on migraine and its subtypes. Background: While previous studies suggest BMI is a risk factor for migraine, it is unclear whether BMI influences migraine differently throughout the life course. The causal effect of childhood BMI may have obscured the association between adult BMI and migraine, making it difficult to determine the independent role of adult adiposity. Methods: We conducted a life-course Mendelian randomization (MR) study. Two-sample and conventional multivariable MR analyses were performed initially. Subsequently, FLOW-MR—a newly-developed three-sample multivariable MR method—was applied to estimate the direct, indirect, and total effects of BMI at childhood or adulthood on migraine. All estimates were scaled per 1-SD increase in BMI (SDs: 1.35 kg/m² at age 1; 1.78 kg/m² at age 8; 4.76 kg/m² in adulthood). Results: The causal effect of BMI on migraine is strictly dependent on the timing of exposure. First, we found no evidence that adult BMI influences the risk of either migraine subtype. Second, higher BMI at age 8 exerted a direct protective effect against migraine with aura (OR = 0.522). Third, BMI at age 1 exhibited a dual role: its direct risk-increasing effect (OR = 1.983) was offset by an indirect protective effect mediated through 8-year-old BMI (OR = 0.511), resulting in a null total effect on migraine with aura. Migraine without aura was unaffected by BMI at any life stage. Conclusion: The causal effect of BMI on migraine is dependent on developmental timing, challenging the conventional view of BMI as a uniform risk factor. We emphasize that the observed protective role of childhood BMI is a model-estimated association from genetic data, which does not constitute a recommendation to increase body weight in children.