Upgrading survival models with CARE

TL;DR

This paper introduces CARE, a method for improving survival risk prediction by combining external estimators with new data through convex aggregation, supported by theoretical guarantees and empirical validation.

Contribution

We develop CARE, a novel convex aggregation approach for survival models that adaptively combines external estimators with new data, with proven convergence properties.

Findings

CARE achieves at least as good as the best individual estimators.

Theoretical bounds demonstrate optimal convergence rates.

Empirical results show improved cardiovascular risk prediction.

Abstract

Clinical risk prediction models are regularly updated as new data, often with additional covariates, become available. We propose CARE (Convex Aggregation of relative Risk Estimators) as a general approach for combining existing "external" estimators with a new data set in a time-to-event survival analysis setting. Our method initially employs the new data to fit a flexible family of reproducing kernel estimators via penalised partial likelihood maximisation. The final relative risk estimator is then constructed as a convex combination of the kernel and external estimators, with the convex combination coefficients and regularisation parameters selected using cross-validation. We establish high-probability bounds for the $L_2$-error of our proposed aggregated estimator, showing that it achieves a rate of convergence that is at least as good as both the optimal kernel estimator and the best external model. Empirical results from simulation studies align with the theoretical results, and we illustrate the improvements our methods provide for cardiovascular disease risk modelling. Our methodology is implemented in the Python package care-survival.