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Updated: Sep 7, 2025

Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
The analysis of COVID-19 in-hospital mortality: A competing risk approach or a cure model?
Xiaonan Xue1, Omar Saeed2, Francesco Castagna2
1Department of Epidemiology & Population Health, Albert Einstein College of Medicine, New York, NY 10461, USA.
Insights
This study proposes cure models for in-hospital mortality, treating hospital discharge as a "cure" rather than a competing event. Cure models offer a more accurate analysis of COVID-19 patient outcomes, revealing differential treatment benefits.
Area of Science:
- Biostatistics
- Epidemiology
- Medical Statistics
Background:
- Competing risk models are common for in-hospital mortality, treating discharge as a competing event.
- However, discharge and death stem from the same disease process, making competing risk models potentially inaccurate.
- Cure models offer an alternative framework, viewing discharge as a sign of recovery or 'cure'.
Purpose of the Study:
- To propose and evaluate cure models for in-hospital mortality analysis.
- To compare cure models with traditional competing risk models.
- To investigate the impact of treatments on mortality and cure probabilities in COVID-19 patients.
Main Methods:
- Utilized mixture cure and promotion time cure models.
- Extended models to incorporate known cure status for discharged patients.
- Developed an Expectation-Maximization (EM) algorithm for the mixture cure model.
- Demonstrated the equivalence between competing risk and promotion time cure models.
- Applied models to a cohort of COVID-19 in-hospital patients with diabetes.
Main Results:
- The promotion time cure model indicated statin use improved overall survival.
- The mixture cure model revealed statin use reduced mortality in susceptible patients but improved cure probability only in older patients.
- Both cure models suggested treatments were more beneficial for older patients.
Conclusions:
- Cure models provide a more appropriate framework than competing risk models for analyzing in-hospital mortality when discharge signifies recovery.
- Findings highlight differential effects of treatments like statins based on patient age and susceptibility.
- Cure models offer valuable insights into disease processes and treatment efficacy in complex patient populations.
Abstract:
Competing risk analyses have been widely used for the analysis of in-hospital mortality in which hospital discharge is considered as a competing event. The competing risk model assumes that more than one cause of failure is possible, but there is only one outcome of interest and all others serve as competing events. However, hospital discharge and in-hospital death are two outcomes resulting from the same disease process and patients whose disease conditions were stabilized so that inpatient care was no longer needed were discharged. We therefore propose to use cure models, in which hospital discharge is treated as an observed "cure" of the disease. We consider both the mixture cure model and the promotion time cure model and extend the models to allow cure status to be known for those who were discharged from the hospital. An EM algorithm is developed for the mixture cure model. We also show that the competing risk model, which treats hospital discharge as a competing event, is equivalent to a promotion time cure model. Both cure models were examined in simulation studies and were applied to a recent cohort of COVID-19 in-hospital patients with diabetes. The promotion time model shows that statin use improved the overall survival; the mixture cure model shows that while statin use reduced the in-hospital mortality rate among the susceptible, it improved the cure probability only for older but not younger patients. Both cure models show that treatment was more beneficial among older patients.
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