A Huber loss-based super learner with applications to healthcare expenditures

TL;DR

This paper introduces a robust super learner based on Huber loss for healthcare expenditure modeling, improving prediction accuracy especially in the presence of outliers and extreme values.

Contribution

It develops a Huber loss-based super learner with theoretical guarantees and practical methods for parameter tuning, enhancing cost estimation in healthcare data.

Findings

Improved prediction accuracy in healthcare expenditure data.

Robustness to outliers demonstrated in simulations and real data.

Theoretical bounds established for the proposed method.

Abstract

Complex distributions of the healthcare expenditure pose challenges to statistical modeling via a single model. Super learning, an ensemble method that combines a range of candidate models, is a promising alternative for cost estimation and has shown benefits over a single model. However, standard approaches to super learning may have poor performance in settings where extreme values are present, such as healthcare expenditure data. We propose a super learner based on the Huber loss, a "robust" loss function that combines squared error loss with absolute loss to down-weight the influence of outliers. We derive oracle inequalities that establish bounds on the finite-sample and asymptotic performance of the method. We show that the proposed method can be used both directly to optimize Huber risk, as well as in finite-sample settings where optimizing mean squared error is the ultimate goal. For this latter scenario, we provide two methods for performing a grid search for values of the robustification parameter indexing the Huber loss. Simulations and real data analysis demonstrate appreciable finite-sample gains in cost prediction and causal effect estimation using our proposed method.