DOI: 10.1097/EDE.0000000000000256

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Issn Print: 1044-3983

Publication Date: 2015/03/01


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Three Approaches to Causal Inference in Regression Discontinuity Designs

Jacob Bor; Ellen Moscoe; Till Bärnighausen

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Author Information: jbor@bu.edu

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Regression discontinuity designs offer a rigorous approach to causal inference when an exposure is assigned (at least in part) by a threshold rule on a continuous assignment variable. For example, antiretroviral therapy is prescribed for HIV patients when their CD4 count falls below some threshold.1 Treatment assignment based on a threshold rule leads to a natural experiment: for a subpopulation of patients, both potential outcome means — E[Y(1)] if treated, E[Y(0)] if not treated — can be estimated. We have recently published an introduction to regression discontinuity for epidemiologists and a clinical application in this journal.1 In their thoughtful commentary on our article,1 Vandenbroucke and le Cessie write that regression discontinuity “may produce valid causal inferences, at least under some assumptions.”2p738 We would like to comment on the nature of the assumptions required for causal inference in regression discontinuity designs, as there has been considerable historical evolution in perspectives on this matter.3 We describe three distinct approaches to inference in regression discontinuity designs, listed in order from the strongest (least plausible) to weakest (most easily met) assumptions required. The differences in these approaches turn on the assumptions made about the potential outcome conditional expectation functions (POCEFs) — E[Y(1)|Z] and E[Y(0)|Z] — which describe how the potential outcome means change with the assignment variable, Z.
The “local randomization” interpretation obtained from approach (3) may be justified in many clinical applications. For example, in our application, CD4 counts are measured with noise. For patients with true CD4 counts close to the threshold, random noise randomizes patients to treatment eligibility or ineligibility; CD4 counts were obtained directly from the lab and we found no evidence of systematic manipulation.1 In applications, where the assignment variable is measured without much error (eg, height, age, or geographic location), threshold rules still yield plausible natural experiments, which can be analyzed using regression discontinuity designs under the stronger assumption of continuity in POCEFs at the cut-off, approach (2). In a departure from some of the earlier regression discontinuity literature cited by Vandenbroucke and le Cessie2 most recent regression discontinuity studies5 have eschewed the strong assumptions required for inference on global causal effects, ie approach (1), in favor of local inference at the threshold, ie approaches (2) and (3). Generalizability to other (sub-) populations (eg, to obtain a global causal effect) is then a matter of external—not internal—validity. Regardless of the approach to causal inference, the causal parameter estimated and the assumptions required for a causal interpretation should be clearly stated in all regression discontinuity applications.
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