IGHE and allergic disease: The respective effect estimated from MR-Egger regression (Fig. 3) were 0.97 for atopic dermatitis (95% CI 0.92–1.03; P = 0.375), 0.63 for IgE levels (95% CI 0.32–1.25; P = 0.184), 0.99 for asthma and hay fever (95% CI 0.72–1.36, P = 0.951) and 0.92 for self-reported allergy (95% CI 0.69–1.22; P = 0.540), with intercepts of −0.004 (95% CI −0.014 to 0.006, P = 0.396), 0.027 (95% CI 0.001 to 0.053, P = 0.042), −0.007 (95% CI −0.030 to 0.016, P = 0.542) and 0.017 (95% CI 0.003–0.031, P = 0.018).