Bayesian modelling for binary outcomes in the Regression Discontinuity Design

TL;DR

This paper introduces a Bayesian approach to estimate causal effects in Regression Discontinuity designs with binary outcomes, addressing issues of negative confidence bounds and outperforming traditional methods.

Contribution

It develops a novel Bayesian estimator for the risk ratio in RD designs with binary outcomes, incorporating prior constraints to improve inference.

Findings

Bayesian estimator prevents negative confidence bounds.

Method compares favorably with estimating equation and GMM methods.

Applied to statins and LDL cholesterol data.

Abstract

The Regression Discontinuity (RD) design is a quasi-experimental design which emulates a randomised study by exploiting situations where treatment is assigned according to a continuous variable as is common in many drug treatment guidelines. The RD design literature focuses principally on continuous outcomes. In this paper we exploit the link between the RD design and instrumental variables to obtain a causal effect estimator, the risk ratio for the treated (RRT), for the RD design when the outcome is binary. Occasionally the RRT estimator can give negative lower confindence bounds. In the Bayesian framework we impose prior constraints that prevent this from happening. This is novel and cannot be easily reproduced in a frequentist framework. We compare our estimators to those based on estimating equation and generalized methods of moments methods. Based on extensive simulations our methods compare favourably with both methods. We apply our method on a real example to estimate the effect of statins on the probability of Low-density Lipoprotein (LDL) cholesterol levels reaching recommended levels.