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Updated: Oct 11, 2025

Establishing a Competing Risk Regression Nomogram Model for Survival Data
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Comparing current and emerging practice models for the extrapolation of survival data: a simulation study and

Benjamin Kearns1, Matt D Stevenson2, Kostas Triantafyllopoulos3

  • 1School of Health and Related Research. Regent Court (ScHARR), The University of Sheffield, 30 Regent Street, Sheffield, S1 4DA, UK. B.Kearns@sheffield.ac.uk.

BMC Medical Research Methodology
|November 28, 2021
PubMed
Summary

Flexible survival models like GAMs and DSMs show promise for improving future survival estimates in medical treatment funding decisions. However, good within-sample fit does not guarantee accurate long-term extrapolations, especially with limited data.

Keywords:
ExtrapolationForecastingSurvival analysis

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Area of Science:

  • Biostatistics
  • Health Economics
  • Medical Data Analysis

Background:

  • Accurate survival estimates are crucial for medical treatment funding decisions.
  • Current standard parametric models are used for survival extrapolations.
  • Emerging flexible survival models offer improved within-sample fit.

Purpose of the Study:

  • To assess if emerging flexible survival models provide improved extrapolations compared to current practice.
  • To evaluate the performance of various survival models in predicting long-term outcomes.

Main Methods:

  • A simulation study using a mixture-Weibull model with varying follow-up and sample sizes.
  • A case-study involving long-term follow-up data from a prostate cancer trial.
  • Comparison of current practice models, Royston Parmar models (RPMs), Fractional Polynomials (FPs), Generalised Additive Models (GAMs), and Dynamic Survival Models (DSMs).

Main Results:

  • Emerging models demonstrated better within-sample fit than current practice models.
  • Generalised Additive Models (GAMs) and Dynamic Survival Models (DSMs) showed improved extrapolations in data-rich scenarios.
  • Fractional Polynomials (FPs) yielded poor extrapolations, while RPMs were similar to current practice. All models struggled with short follow-up data.

Conclusions:

  • Good within-sample fit does not ensure reliable extrapolation performance.
  • Generalised Additive Models (GAMs) and Dynamic Survival Models (DSMs) are potential candidates for extrapolation alongside current methods.
  • Further research is needed to optimize the use of flexible models and external evidence for improved survival extrapolations.