Personalised treatment assignment maximising expected benefit with smooth hinge loss

In personalised medicine, the goal is to make a treatment recommendation for each patient with a given set of covariates to maximise the treatment benefit measured by patient's response to the treatment. In application, such a treatment assignment rule is constructed using a sample training data consisting of patients’ responses and covariates. Instead of modelling responses using treatments and covariates, an alternative approach is maximising a response-weighted target function whose value directly reflects the effectiveness of treatment assignments. Since the target function involves a loss function, efforts have been made recently on the choice of the loss function to ensure a computationally feasible and theoretically sound solution. We propose to use a smooth hinge loss function so that the target function is convex and differentiable, which possesses good asymptotic properties and numerical advantages. To further simplify the computation and interpretability, we focus on the rules that are linear functions of covariates and discuss their asymptotic properties. We also examine the performances of our method with simulation studies and real data analysis.