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The Regression Discontinuity (RD) design is a quasi-experimental design whichemulates a randomised study by exploiting situations where treatment isassigned according to a continuous variable as is common in many drug treatmentguidelines. The RD design literature focuses principally on continuousoutcomes. In this paper we exploit the link between the RD design andinstrumental variables to obtain a causal effect estimator, the risk ratio forthe treated (RRT), for the RD design when the outcome is binary. Occasionallythe RRT estimator can give negative lower confindence bounds. In the Bayesianframework we impose prior constraints that prevent this from happening. This isnovel and cannot be easily reproduced in a frequentist framework. We compareour estimators to those based on estimating equation and generalized methods ofmoments methods. Based on extensive simulations our methods compare favourablywith both methods. We apply our method on a real example to estimate the effectof statins on the probability of Low-density Lipoprotein (LDL) cholesterollevels reaching recommended levels.

Bayesian modelling for binary outcomes in the Regression Discontinuity Design