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

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18 Scopus citations


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 trade-off 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 well as or better than the model selected through cross-validation. Finally, stacked survival models are applied to a well-known German breast cancer study.

Original languageEnglish (US)
Pages (from-to)537-549
Number of pages13
Issue number3
StatePublished - Jul 1 2015

Bibliographical note

Publisher Copyright:
© 2015 The Author 2015. Published by Oxford University Press. All rights reserved.


  • Bias-variance trade-off
  • Brier score
  • Cross-validation
  • Stacked regressions
  • Survival ensembles
  • Survival prediction.


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