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An R-Based Landscape Validation of a Competing Risk Model
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The semi-competing risk problem revisited.

Ross L Prentice1, Aaron K Aragaki2

  • 1Fred Hutchinson Cancer Center and University of Washington, Seattle, WA, USA. rprentic@whi.org.

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|April 27, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces methods to jointly analyze disease incidence and death, crucial when death is a competing risk in clinical trials. It proposes a hazard ratio statistic for assessing treatment effects on both outcomes simultaneously.

Keywords:
Cause-specific hazard functionCox regressionDependent censoringDual outcome hazard ratesHazard rate modelsMultivariate failure timesSemi-competing risksVolterra integral equation

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Clinical Trials

Background:

  • Clinical trials and cohort studies frequently assess treatment effects or exposure associations with disease risk.
  • Death is often a competing risk, complicating analysis when it's a major health concern.
  • Assuming death as independent right-censoring may be inappropriate, necessitating joint analysis of disease and death.

Purpose of the Study:

  • To present modeling approaches for jointly analyzing disease incidence and death.
  • To develop methods that account for death as a competing risk in survival analysis.
  • To propose a summary statistic for covariate effects on joint disease and death outcomes.

Main Methods:

  • Utilizing type-specific (cause-specific) hazard functions.
  • Modeling marginal hazard rates for disease-free survival and death.
  • Employing Cox models for various hazard functions, including dual outcome hazard functions.
  • Proposing a hazard ratio summary statistic for joint effects.

Main Results:

  • Demonstrated modeling approaches for joint analysis of disease and competing risks.
  • Illustrated the application of Cox models for disease-free survival and death.
  • Proposed a novel hazard ratio statistic for evaluating combined effects on incidence and mortality.
  • Analysis of Women's Health Initiative hormone therapy trials provided practical illustration.

Conclusions:

  • Jointly modeling disease incidence and death is essential when death is a competing risk.
  • The proposed methods and hazard ratio statistic offer a comprehensive approach to analyzing treatment effects.
  • These methods are valuable for studies where major diseases and mortality are key outcomes.