Beyond the Cutoff: a Graphical Approach to Combining Multiple Fuzzy Regression Discontinuity Designs

Music City Center 

Regression discontinuity design (RDD) allows for robust estimation of the local average treatment effect at the cutoff. However, the effect has limited generalizability beyond that cutoff. To tackle this limitation, we propose a method to combine data from multiple fuzzy RDDs with the same score and outcome variables. Our work is motivated by the Dutch Arthroplasty Register dataset, which contains data on primary total hip replacement (THA) from Dutch hospitals. As hospitals use varying age-based cutoff points to decide on the fixation type in THA, we can estimate the treatment effect for a broader population. The key challenge in integrating the data is the presence of compliance groups, which are an inherent part of any fuzzy RDD. We take a rigorous novel graphical approach, which has not yet been exploited in the context of regression discontinuity design. We model the compliance types to depend on population characteristics rather than on specific hospitals. This approach allows us to view the hospital selection as a conditional instrumental variable. Finally, we propose a doubly robust estimator of the treatment effect that exploits local estimates at the cutoff points.

Regression discontinuity design

Causal inference

Multi-site observational study

Extrapolation

Instrumental variable 

IMS