Mendelian randomization (MR) 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. MR-PROLLIM adopts risk ratio (RR), which can be further converted to odds ratio (OR), to define the causal effect. The random-effects MR-PROLLIM allows correlated pleiotropy and weaker instruments. The fixed-effects MR-PROLLIM can be implemented 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 is less biased than the classical median estimator and higher powered than the classical mode estimator. We also found (i) the traditional ratio method tended to underestimate binary exposure effects to a large extent, and transforming MR-PROLLIM RR to OR provided better estimates; (ii) about 26.5% of the real trait pairs we analyzed were detected to have significant correlated pleiotropy; (iii) compared to random-effects MR-PROLLIM results, 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.