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

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.

Regression discontinuity designs in healthcare research

“…Similarly, to estimate the impact of statin use on low density lipoprotein cholesterol levels, Geneletti et al exploited guideline driven differences in statin prescribing for those with just less or just greater than 20% 10 year risk of a cardiovascular event (as determined by a standard risk calculator). 16 Though the benefits of early antiretroviral treatment and statins are both well established in the medical literature, regression discontinuity studies provide a better sense of what could happen in the real world, which is free of biases to external validity introduced 3 . This is a relevant and important phenomenon that may be missed in randomized controlled trials, where attempts are made to explicitly minimize attrition in both treatment and control groups.…”

Bayesian Modelling for Binary Outcomes in the Regression Discontinuity Design

“…The increase in probability is more gradual but there is a distinct jump at the threshold. On the basis of these plots we would be happy to proceed to an RD design analysis of the data with LDL cholesterol level as a continuous outcome variable (Geneletti et al ., ).…”

“…The model described above has the interaction model denominator:whereandWe also consider an interaction model where the denominator is based on a flexible binomial model as used in Geneletti et al . (). In this model the prior information is used to create distance between the two elements in the denominator of the fraction in the RRT in equation .…”

“…The increase in probability is more gradual but there is a distinct jump at the threshold. On the basis of these plots we would be happy to proceed to an RD design analysis of the data with LDL cholesterol level as a continuous outcome variable (Geneletti et al, 2015). We now show the plots for the two binary outcomes of interest: LDL cholesterol dropping below 2 mmol l −1 for high risk patients and below 3 mmol l −1 for healthy patients.…”

“…A regression discontinuity (RD) design is a quasi-experimental method for treatment effect estimation, which was introduced in the 1960s in Thistlethwaite and Campbell (1960) and is widely used in economics and related social sciences (Imbens and Lemieux, 2008) and more recently in the medical sciences (Geneletti et al, 2015;Bor et al, 2014;Smith et al, 2015;Moscoe et al, 2015;Linden et al, 2006). The RD design has become of interest in the context of public health as it enables the use of routinely gathered medical data to evaluate the causal effects of drugs when these are prescribed according to well-defined decision rules.…”