Bayesian regression discontinuity designs: Incorporating clinicalknowledge in the causal analysis of primary care data

Abstract

The regression discontinuity (RD) design is a quasi-experimental designthat estimates the causal effects of a treatment by exploiting naturallyoccurring treatment rules. It can be applied in any context wherea particular treatment or intervention is administered accordingto a pre-specified rule linked to a continuous variable. Such thresholdsare common in primary care drug prescription where the RD designcan be used to estimate the causal effect of medication in the generalpopulation. Such results can then be contrasted to those obtainedfrom randomised controlled trials (RCTs) and inform prescriptionpolicy and guidelines based on a more realistic and less expensivecontext. In this paper we focus on statins, a class of cholesterol-loweringdrugs, however, the methodology can be applied to many other drugsprovided these are prescribed in accordance to pre-determined guidelines.NHS guidelines state that statins should be prescribed to patientswith 10 year cardiovascular disease risk scores in excess of 20%.If we consider patients whose scores are close to this thresholdwe find that there is an element of random variation in both therisk score itself and its measurement. We can thus consider the thresholda randomising device assigning the prescription to units just abovethe threshold and withholds it from those just below. Thus we areeffectively replicating the conditions of an RCT in the area aroundthe threshold, removing or at least mitigating confounding. We framethe RD design in the language of conditional independence which clarifiesthe assumptions necessary to apply it to data, and which makes thelinks with instrumental variables clear. We also have context specificknowledge about the expected sizes of the effects of statin prescriptionand are thus able to incorporate this into Bayesian models by formulatinginformative priors on our causal parameters.

Gianluca Baio
Gianluca Baio
Professor of Statistics and Health Economics