Regression discontinuity threshold optimization

Treatments often come with thresholds, e.g. we are given statins if our cholesterol is above a certain threshold. But which statin administration threshold maximizes our quality of life adjusted years? More generally, which threshold would optimize the average expected outcome? Regression discontinuity approaches are used to measure the local average treatment effect (LATE) and more recently also the Marginal Threshold Treatment Effect (MTTE), which shows how marginal changes in the threshold can affect the LATE. We extend this idea to define the problem of optimizing a policy threshold, i.e. selecting a threshold that optimizes the cumulative effect of the treatment on the treated. We present an estimator of the optimal threshold based on a constrained optimization framework. We show how to use machine learning (Gaussian process regression) for non-linear estimation. We also extend the estimation to a conservative threshold that is unlikely to produce harm, and we show how to include policy cost constraints. We apply these results to estimate an optimal tip-maximizing threshold for tip suggestions in taxi cabs Haggag (2014).