Background

Mendelian randomization (MR) applies instrumental variable (IV) methods to observational data using a genetic variant as an IV. Several Monte-Carlo studies investigate the performance of MR methods with binary outcomes, but few consider them in conjunction with binary risk factors.

Objective

To develop a novel MR estimator for scenarios with a binary risk factor and outcome; and compare to existing MR estimators via simulations and real data analysis.

Methods

A bivariate Bernoulli distribution is adapted to the IV setting. Empirical bias and asymptotic coverage probabilities are estimated via simulations. The proposed method is compared to the Wald method, two-stage predictor substitution (2SPS), two-stage residual inclusion (2SRI), and the generalized method of moments (GMM). An analysis is performed using existing data from the CLEAR study to estimate the potential causal effect of smoking on rheumatoid arthritis risk in African Americans.

Results

Bias was low for the proposed method and comparable to 2SPS. The Wald method was often biased towards the null. Coverage was adequate for the proposed method, 2SPS, and 2SRI. Coverage for the Wald and GMM methods was poor in several scenarios. The causal effect of ever smoking on rheumatoid arthritis risk was not statistically significant using a variety of genetic instruments.

Conclusions

Simulations suggest the proposed MR method is sound with binary risk factors and outcomes, and comparable to 2SPS and 2SRI in terms of bias. The proposed method also provides more natural framework for hypothesis testing compared to 2SPS or 2SRI, which require ad-hoc variance adjustments.