Abstract
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.
Highlights
Regression discontinuity designs (RD designs) have been developed as a method for causal inference in a variety of observational data settings (Berk & Leeuw, 1999; van der Klaauw, 2002, 2008; Lee, 2008)
The notion of an assignment variable ‘lying close’ to the threshold is quantified by the choice of a pre-specified bandwidth, h, such that only those subjects whose assignment variable values lie within a distance h of the intervention threshold are included in an RD design
Are similar for most bandwidths and dataset sizes and for each of the chosen non-adherence probabilities. This suggests that the likelihood-based approach taken to local average treatment effect (LATE) variance estimation accurately reflects the uncertainty in estimate of the LATE and that, when adopting a two-stage least squares approach, it is advisable to use the adjusted method for variance estimation at the threshold
Summary
Regression discontinuity designs (RD designs) have been developed as a method for causal inference in a variety of observational data settings (Berk & Leeuw, 1999; van der Klaauw, 2002, 2008; Lee, 2008). An intervention threshold may not be adhered to strictly, resulting in some subjects receiving (or not receiving) the intervention contrary to what would be indicated by their assignment variable This is known as a ‘fuzzy RD design’, and the estimation of the causal effect of the intervention must account for this ‘fuzziness’ present in the observed data. The LATE (1) is only valid within a population whose assignment variable values lie within a region close enough to the threshold for individuals to be considered exchangeable In econometrics, both the ATE and the LATE are typically estimated using a two-stage least squares regression approach (Imbens & Angrist, 1994; Angrist & Imbens, 1995; Imbens & Lemieux, 2008).
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