Combining parametric, semi-parametric, and non-parametric survival models with stacked survival models

TL;DR

This paper introduces stacked survival models that combine parametric, semi-parametric, and non-parametric estimators to improve conditional survival function estimation, demonstrating superior performance through simulations and real data application.

Contribution

The paper proposes a novel stacked survival modeling approach that adaptively combines different survival models, outperforming individual models and model selection methods.

Findings

Stacked survival models perform consistently well across various scenarios.

They outperform traditional model selection methods like cross-validation.

Application to breast cancer data illustrates practical utility.

Abstract

For estimating conditional survival functions, non-parametric estimators can be preferred to parametric and semi-parametric estimators due to relaxed assumptions that enable robust estimation. Yet, even when misspecified, parametric and semi-parametric estimators can possess better operating characteristics in small sample sizes due to smaller variance than non-parametric estimators. Fundamentally, this is a bias-variance tradeoff situation in that the sample size is not large enough to take advantage of the low bias of non-parametric estimation. Stacked survival models estimate an optimally weighted combination of models that can span parametric, semi-parametric, and non-parametric models by minimizing prediction error. An extensive simulation study demonstrates that stacked survival models consistently perform well across a wide range of scenarios by adaptively balancing the strengths and weaknesses of individual candidate survival models. In addition, stacked survival models perform as good as, or better than, the model selected through cross-validation. Lastly, stacked survival models are applied to a well-known German breast cancer study.