Instrumental variable estimation of causal risk ratios and causal odds ratios in Mendelian randomization analyses

In this paper, the authors describe different instrumental variable (IV) estimators of causal risk ratios and odds ratios with particular attention to methods that can handle continuously measured exposures. The authors present this discussion in the context of a Mendelian randomization analysis of the effect of body mass index (BMI; weight (kg)/height (m)(2)) on the risk of asthma at age 7 years (Avon Longitudinal Study of Parents and Children, 1991-1992). The authors show that the multiplicative structural mean model (MSMM) and the multiplicative generalized method of moments (MGMM) estimator produce identical estimates of the causal risk ratio. In the example, MSMM and MGMM estimates suggested an inverse relation between BMI and asthma but other IV estimates suggested a positive relation, although all estimates had wide confidence intervals. An interaction between the associations of BMI and fat mass and obesity-associated (FTO) genotype with asthma explained the different directions of the different estimates, and a simulation study supported the observation that MSMM/MGMM estimators are negatively correlated with the other estimators when such an interaction is present. The authors conclude that point estimates from various IV methods can differ in practical applications. Based on the theoretical properties of the estimators, structural mean models make weaker assumptions than other IV estimators and can therefore be expected to be consistent in a wider range of situations.