Causal Inference in Dynamic Thresholding Designs

Music City Center 

In modern medical practice, it is common to regularly monitor patients' fasting blood sugar, and declare them to have prediabetes (and encourage lifestyle changes) if this number crosses a pre-specified threshold. The sharp, threshold-based treatment policy suggests that we should be able to estimate the long-term benefit of care given to prediabetic patients by comparing health trajectories of patients with blood-sugar measurements right above and below the threshold. A naive regression-discontinuity analysis, however, is not applicable here, as it ignores the temporal dynamics of the problem where, e.g., a patient just below the threshold on one visit may become prediabetic (and receive treatment) following their next visit.

Here, we study dynamic thresholding designs in Markovian systems, and show that a regression-discontinuity estimator run on aggregate discounted outcomes can still be used to identify a relevant causal target, namely the policy gradient of moving the treatment threshold. We develop results for estimation and inference of this target, and discuss implications of our findings to interpretation of regression-discontinuity studies in preventive healthcare. More broadly, our results highlight the promise of adapting widely used observational study techniques to dynamic systems.

Regression discontinuity

Reinforcement learning

Markov decision process