Approaches to the Estimation of the Local Average Treatment Effect in a Regression Discontinuity Design

Regression discontinuity designs (RD designs) are used as a method for causal inference from observational data, where the decision to apply an intervention is made according to a 'decision rule' that is linked to some continuous variable. Such designs are being increasingly developed in medicine. The local average treatment effect (LATE) has been established as an estimator of the intervention effect in an RD design, particularly where a design's 'decision rule' is not adhered to strictly. Estimating the variance of the LATE is not necessarily straightforward. We consider three approaches to the estimation of the LATE: two-stage least squares, likelihood-based and a Bayesian approach. We compare these under a variety of simulated RD designs and a real example concerning the prescription of statins based on cardiovascular disease risk score.