Personalized Two-sided Dose Interval

In many clinical practices, the goal of medical interventions or therapies is often to maintain clinical measures within a desirable range, rather than maximizing or minimizing their values. To achieve this, it may be more practical to recommend a therapeutic dose interval rather than a single dose for a given patient. Since different patients may respond differently to the same dosage of medication, the therapeutic dose interval needs to be personalized based on each patient's unique characteristics. However, this problem is challenging as it requires jointly learning the lower and upper bound functions for personalized dose intervals. Currently, there are no methods available that are suitable to address this challenge. To fill this gap, we propose a novel loss function that converts the task of learning personalized two-sided dose intervals into a risk minimization problem. The loss function is defined over a tensor product reproducing kernel Hilbert space and is doubly-robust to misspecification of nuisance functions. We establish statistical properties of estimated dose interval functions that directly minimize the empirical risk associated with the loss function. Our simulation and a real-world application of personalized warfarin dose intervals show that our proposed direct estimation method outperforms naive indirect regression-based methods.