  The regression discontinuity design (RDD) is a quasi-experimental design that can be used to identify and estimate the causal effect of a treatment using observational data. In an RDD, a pre-specified rule is used for treatment assignment, whereby a subject is assigned to the treatment (control) group whenever their observed value of a specific continuous variable is greater than or equal to (is less than) a fixed threshold. Sharp RDDs occur when guidelines are strictly adhered to and fuzzy RDDs occur when the guidelines or not strictly adhered to. In this paper, we take a rigorous decision theoretic approach to formally study causal effect identification and estimation in both sharp and fuzzy RDDs. We use the language and calculus of conditional independence to express and explore in a clear and precise manner the conditions implied by each RDD and investigate additional assumptions under which the identification of the average causal effect at the threshold can be achieved. We apply the methodology in an example concerning the relationship between statins (a class of cholesterol-lowering drugs) and low density lipoprotein (LDL) cholesterol using a real set of primary care data. 
Regression Discontinuity Designs: A Decision Theoretic Approach