Approaches to risk ratio estimation in a regression discontinuity design: Application to the prescription of statins for cholesterol reduction in UK primary care.

In recent years regression discontinuity designs have been used increasingly for the estimation of treatment effects in observational medical data where a rule-based decision to apply treatment is taken using a continuous assignment variable. Most regression discontinuity design applications have focused on effect estimation where the outcome of interest is continuous, with scenarios with binary outcomes receiving less attention, despite their ubiquity in medical studies. In this work, we develop an approach to estimation of the risk ratio in a fuzzy regression discontinuity design (where treatment is not always strictly applied according to the decision rule), derived using common regression discontinuity design assumptions. This method compares favourably to other risk ratio estimation approaches: the established Wald estimator and a risk ratio estimate from a multiplicative structural mean model, with promising results from extensive simulation studies. A demonstration and further comparison are made using a real example to evaluate the effect of statins (where a statin prescription is made based on a patient's 10-year cardiovascular disease risk score) on low-density lipoprotein cholesterol reduction in UK Primary Care.