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" estimates 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 regularisation parameters and convex combination coefficients 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 existing 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.

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