Robustness of Fuzzy Regression Discontinuity Designs under Imperfect Compliance

This paper studies the robustness of fuzzy regression discontinuity designs under imperfect compliance with clinical assignment rules. When treatment assignment based on a biomarker threshold is probabilistic, the cutoff indicator can be interpreted as an instrumental variable identifying a Local Average Treatment Effect. A Monte Carlo simulation calibrated to a cardiovascular risk setting is used to evaluate the local two stage least squares fuzzy regression discontinuity estimator under controlled violations of its identifying assumptions. We consider departures from continuity of potential outcomes at the cutoff, reductions in first stage strength, and violations of monotonicity. The results show that, under approximate continuity and sufficiently strong first stages, the estimator recovers the target local effect with limited bias and near nominal coverage. Weak first stages mainly reduce precision, whereas violations of continuity lead to severe bias even when the instrument is strong. Monotonicity violations increase variability and reduce coverage. Overall, the findings highlight that fuzzy regression discontinuity designs provide reliable local causal inference only under carefully assessed assumptions.