Thin plate regression splines for treatment effect estimation in a local randomisation regression discontinuity design

A regression discontinuity (RD) design may be used for treatment effect estimation in observational settings, where a treatment or intervention is allocated using a threshold-based ‘decision rule’ that is linked to a continuous assignment variable. In a local randomisation framework, where the decision rule may be viewed as a quasi-randomisation device, treatment effect estimation at the threshold is often done using a two-stage least squares (TSLS) approach but this may be unsuitable when the assignment variable-outcome relationship is non-linear or unknown. The use of thin plate regression spline (TPRS) models for treatment effect estimation in an RD design under local randomisation is considered and explored. The TPRS model is fully flexible, completely data driven and does not require the pre-specification of the number or position of knots. Simulation studies are used to compare the performance of the TPRS method to TSLS estimation under varying relationships between the outcome and assignment variable. Results showed that the TPRS method produces less biased estimates of the treatment effect, especially when the underlying relationship is not linear. An example is shown where the method is used to estimate the effect of statins on low density lipoprotein (LDL) cholesterol level in a local randomisation RD design, using real data from UK Primary Care.