Jump Interval-Learning for Individualized Decision Making with Continuous Treatments
Authors: Hengrui Cai, Chengchun Shi, Rui Song, Wenbin Lu; 24(140):1−92, 2023.
Abstract
This paper introduces jump interval-learning, a method for developing an individualized interval-valued decision rule (I2DR) that maximizes expected outcomes in the continuous treatment setting. Unlike traditional individualized decision rules (IDRs) that recommend a single treatment, the proposed I2DR yields an interval of treatment options for each individual, providing greater flexibility in practical implementation. The jump interval-learning method estimates the conditional mean of the outcome based on the treatment and covariates using jump penalized regression, and derives the optimal I2DR based on the estimated outcome regression function. The regressor can be either linear for clear interpretation or a deep neural network to capture complex treatment-covariate interactions. The jump interval-learning algorithm efficiently computes the outcome regression function using dynamic programming. The statistical properties of the resulting I2DR are established for both piecewise and continuous outcome regression functions. Additionally, a procedure is developed to infer the mean outcome under the (estimated) optimal policy. The proposed I2DR is validated through extensive simulations and a real data application to a Warfarin study.
[abs]
[code]