Instrumental Variable Estimation of Causal Risk Ratios and Causal Odds Ratios in Mendelian Randomization Analyses

Abstract

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.

Instrumental Variable Analysis in Epidemiologic Studies: An Overview of the Estimation Methods

“…These assumptions are illustrated in Figure 1. Along with these basic assumptions, there are other assumptions (i.e., homogeneous treatment effects, monotonicity) that are needed for point identification of IVestimates [14,19].…”

“…If the first-stage logistic model is not correctly specified, the estimates from the second-stage can be biased [54,55]. Also, note that this method may not provide the causal odds ratio due to the non-collapsibility of the OR [19].…”

“…SMMs are semi-parametric models and use IVs via G-estimation for identification and estimation of the causal parameter. This method involves the assumption of a conditional mean independence [14,19,[60][61][62] and does not make distributional assumptions about the exposure [19]. SMMs with an identity link is sometimes called additive SMMs and can be used for continuous outcomes and multiplicative SMMs with log-linear model can be used for positive-valued/binary outcomes in order to estimate the causal risk ratio [19,63].…”

“…This method involves the assumption of a conditional mean independence [14,19,[60][61][62] and does not make distributional assumptions about the exposure [19]. SMMs with an identity link is sometimes called additive SMMs and can be used for continuous outcomes and multiplicative SMMs with log-linear model can be used for positive-valued/binary outcomes in order to estimate the causal risk ratio [19,63]. Additionally, the logistic structural mean model (LSMM) developed by Vansteelandt and Goetghebeur [64] and Robins and Rotnitzky [65] can also be used for binary outcome in order to estimate causal odds ratio [19,63].…”

“…Over the last decade several reviews of IVanalysis were published, covering various aspects including the key assumptions, estimating parameters, possible IVs, estimation methods, reporting of the results, and the use of IVs in comparative effectiveness research [3,4,[12][13][14][15][16][17][18][19][20][21][22][23]. We summarized these reviews in Table 1.…”