A Flexible Ensemble Learning Method for Survival Extrapolation

Ran Dai, Jihyun Ma, Meijing Wu, Yabing Mai, Weili He

Research output: Contribution to journalArticlepeer-review


Objectives: Survival extrapolation is an important statistical concept for estimating long-term survival from short-term clinical trial data. It is widely used in health technology assessment (HTA). Survival extrapolation is often performed by fitting one or two parametric models selected based on experience or selecting a model based on some goodness of fit statistics from a predefined collection of models. The main challenge in survival extrapolation is that the result is sensitive to model misspecification. In this study, we aim to propose a new approach that has a robust performance for survival extrapolation. Methods: We propose a new method called Ensemble Learning for Survival Extrapolation (ELSE). Instead of selecting one best model from a predefined collection, ELSE builds an ensemble model based on a collection of models from the model library. Under this framework, we construct a point estimate of the long-term survival with a weighted average of the estimates of all candidate models and derive confidence intervals using nonparametric bootstrap. Results: With our extensive numerical simulation studies, the proposed ELSE method shows better performance than the traditionally used model selection procedure based on Akaike Information Criterion (AIC). With a real data application to the Therapeutically Applicable Research to Generate Effective Treatment Wilms Tumor project (TARGET-WT) data, the ELSE method produces better survival extrapolation results in point estimate accuracy and confidence interval coverage. Conclusions: We developed an ensemble learning method for survival extrapolation (ELSE) which is robust for the underline data model and has good real data performance.

Original languageEnglish (US)
Pages (from-to)580-588
Number of pages9
JournalTherapeutic Innovation and Regulatory Science
Issue number3
StatePublished - May 2023


  • Bootstrap
  • Ensemble learning
  • Health technology assessment
  • Survival analysis
  • Survival extrapolation

ASJC Scopus subject areas

  • Pharmacology, Toxicology and Pharmaceutics (miscellaneous)
  • Public Health, Environmental and Occupational Health
  • Pharmacology (medical)


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