Relative Sparsity for Medical Decision Problems

Existing statistical methods can be used to estimate a policy, or a mapping from covariates to decisions, which can then instruct decision makers. There is great interest in using such data-driven policies in healthcare. In healthcare, however, it is often important to explain to the healthcare provider, and to the patient, how a new policy differs from the current standard of care. This end is facilitated if one can pinpoint the aspects (i.e., parameters) of the policy that change most when moving from the standard of care to the new, suggested policy. To this end, we adapt ideas from Trust Region Policy Optimization. In our work, however, unlike in Trust Region Policy Optimization, the difference between the suggested policy and standard of care is required to be sparse, aiding with interpretability. In particular, we trade off between maximizing expected reward and minimizing the $L_1$ norm divergence between the parameters of the two policies. This yields "relative sparsity," where, as a function of a tuning parameter, $\lambda$, we can approximately control the number of parameters in our suggested policy that differ from their counterparts in the standard of care. We develop our methodology for the observational data setting. We propose a problem-specific criterion for selecting $\lambda$, perform simulations, and illustrate our method with a real, observational healthcare dataset, deriving a policy that is easy to explain in the context of the current standard of care. Our work promotes the adoption of data-driven decision aids, which have great potential to improve health outcomes.