Mendelian randomization analysis with pleiotropy-robust log-linear model for binary outcomes

Mendelian randomization (MR) is a statistical technique that uses genetic variants as instrumental variables to infer causality between traits. In dealing with a binary outcome, there are two challenging barriers on the way toward a valid MR analysis, that is, the inconsistency of the traditional ratio estimator and the existence of horizontal pleiotropy. Recent MR methods mainly focus on handling pleiotropy with summary statistics. Many of them cannot be easily applied to one-sample MR. We propose two novel individual data-based methods, respectively named random-effects and fixed-effects MR-PROLLIM, to surmount both barriers. These two methods adopt risk ratio (RR) to define the causal effect for a continuous or binary exposure. The random-effects MR-PROLLIM models correlated pleiotropy, accounts for variant selection, and allows weaker instruments. The fixed-effects MR-PROLLIM can function with only a few selected variants. We demonstrate in this study that the random-effects MR-PROLLIM exhibits high statistical power while yielding fewer false-positive detections than its competitors. The fixed-effects MR-PROLLIM generally performs at an intermediate level between the classical median and mode estimators. In our UK Biobank data analyses, we also found (i) the MR ratio method tended to underestimate binary exposure effects to a large extent; (ii) about 26.5% of the trait pairs were detected to have significant correlated pleiotropy; (iii) the pleiotropy-sensitive method showed estimated relative biases ranging from -103.7% to 178.0% for inferred non-zero effects. MR-PROLLIM exhibits the potential to facilitate a more rigorous and robust MR analysis for binary outcomes. ### Competing Interest Statement The authors have declared no competing interest.