Bayesian regression discontinuity designs: incorporating clinical knowledge in the causal analysis of primary care data.

Sara Geneletti,Aidan G. O'Keeffe,Gianluca Baio,Linda D. Sharples,Sylvia Richardson

doi:10.1002/sim.6486

Abstract

The regression discontinuity (RD) design is a quasi‐experimental design that estimates the causal effects of a treatment by exploiting naturally occurring treatment rules. It can be applied in any context where a particular treatment or intervention is administered according to a pre‐specified rule linked to a continuous variable. Such thresholds are common in primary care drug prescription where the RD design can be used to estimate the causal effect of medication in the general population. Such results can then be contrasted to those obtained from randomised controlled trials (RCTs) and inform prescription policy and guidelines based on a more realistic and less expensive context. In this paper, we focus on statins, a class of cholesterol‐lowering drugs, however, the methodology can be applied to many other drugs provided these are prescribed in accordance to pre‐determined guidelines. Current guidelines in the UK state that statins should be prescribed to patients with 10‐year cardiovascular disease risk scores in excess of 20%. If we consider patients whose risk scores are close to the 20% risk score threshold, we find that there is an element of random variation in both the risk score itself and its measurement. We can therefore consider the threshold as a randomising device that assigns statin prescription to individuals just above the threshold and withholds it from those just below. Thus, we are effectively replicating the conditions of an RCT in the area around the threshold, removing or at least mitigating confounding. We frame the RD design in the language of conditional independence, which clarifies the assumptions necessary to apply an RD design to data, and which makes the links with instrumental variables clear. We also have context‐specific knowledge about the expected sizes of the effects of statin prescription and are thus able to incorporate this into Bayesian models by formulating informative priors on our causal parameters. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Highlights

The regression discontinuity (RD) design is a quasi-experimental design that estimates the causal effects of a treatment by exploiting naturally occurring treatment rules
If we focus on an area close to the threshold, we have a situation that is analogous to a randomised controlled trial (RCT), resulting in removal or mitigation of confounding where we can identify and estimate causal effects of treatments in primary care
In the context of statin prescription this assumption will hold if the GPs adhere to the National Institute for Health and Care Excellence (NICE) treatment guidelines and Z is predictive of treatment T, i.e. they prescribe the treatment to patients with a 10 year risk score that exceeds 20% and do not prescribe statins to patients whose risk score is below 20%

Summary

Introduction

The regression discontinuity (RD) design is a quasi-experimental design that estimates the causal effects of a treatment by exploiting naturally occurring treatment rules. If we focus on an area close to the threshold, we have a situation that is analogous to a randomised controlled trial (RCT), resulting in removal or mitigation of confounding where we can identify and estimate causal effects of treatments in primary care. RD methods, while not providing as substantive evidence of a causal effect as an RCT, are cheaper to implement, can be typically applied to much larger datasets and are not subject to as many ethical constraints This could make such methods desirable in the overall accumulation of evidence regarding the effectiveness of a particular treatment, administered using strict prescription guidelines, on an outcome of interest in primary care. We introduce a Bayesian analysis of the RD design and illustrate its formulation, using an example on the prescription of statins in primary care.

The basics of the regression discontinuity design

Assumptions

Links with instrumental variables and causal effect estimators

Bayesian model specification

Local linear regression

Models for the average treatment effect

Models for the denominator of the local average treatment effect

Models for the local average treatment effect

Simulated data

Simulation–results

1: Low 3: High

Example: prescription of statins in UK primary care