  The Regression Discontinuity (RD) design is a quasi-experimental design which
emulates a randomised study by exploiting situations where treatment is
assigned according to a continuous variable as is common in many drug treatment
guidelines. The RD design literature focuses principally on continuous
outcomes. In this paper we exploit the link between the RD design and
instrumental variables to obtain a causal effect estimator, the risk ratio for
the treated (RRT), for the RD design when the outcome is binary. Occasionally
the RRT estimator can give negative lower confindence bounds. In the Bayesian
framework we impose prior constraints that prevent this from happening. This is
novel and cannot be easily reproduced in a frequentist framework. We compare
our estimators to those based on estimating equation and generalized methods of
moments methods. Based on extensive simulations our methods compare favourably
with both methods. We apply our method on a real example to estimate the effect
of statins on the probability of Low-density Lipoprotein (LDL) cholesterol
levels reaching recommended levels.
