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Updated: Jun 24, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Quantitative risk stratification in Markov chains with limiting conditional distributions.

David C Chan1, Philip K Pollett, Milton C Weinstein

  • 1Department of Economics, Massachusetts Institute of Technology, Cambridge, MA, USA. dcchan@partners.org

Medical Decision Making : an International Journal of the Society for Medical Decision Making
|April 2, 2009
PubMed
Summary
This summary is machine-generated.

Limiting conditional distributions quantitatively assess patient risk in progressive diseases. This Markov chain model helps identify high-risk patients for targeted treatments and predict outcomes for broader populations.

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Last Updated: Jun 24, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

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Published on: September 16, 2022

Establishing a Competing Risk Regression Nomogram Model for Survival Data
04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Area of Science:

  • Mathematical modeling in healthcare
  • Biostatistics
  • Clinical decision support

Background:

  • Patient risk stratification is crucial for clinical decision-making.
  • Limiting conditional distributions quantify patient proportions in disease states within Markov chains.
  • These distributions offer a quantitative approach to risk stratification.

Purpose of the Study:

  • To establish conditions for positive limiting conditional distributions in general Markov chains.
  • To develop a framework for risk stratification using these distributions.
  • To apply the framework to a clinical example for treatment indications.

Main Methods:

  • Establishing existence conditions for positive limiting conditional distributions.
  • Developing a general framework for risk stratification.
  • Applying the framework to infer patient risk in clinical trials and predict outcomes for expanded treatment populations.

Main Results:

  • A positive limiting conditional distribution exists if early-stage patients have the lowest risk of progression or death.
  • Outcomes and population risk are interchangeable within the general framework.
  • Clinical trials likely selected the top quintile of patient risk; expanded treatment may be cost-effective.

Conclusions:

  • Limiting conditional distributions are suitable for quantitative risk stratification in Markov models of progressive diseases.
  • The framework effectively characterizes patient risk in clinical trials.
  • This approach can predict outcomes for diverse patient populations.