Related Experiment Video
Updated: Oct 19, 2025

Competing-Risk Nomogram for Predicting Cancer-Specific Survival in Multiple Primary Colorectal Cancer Patients after Surgery
Published on: September 27, 2024
Prognosis of cancer survivors: estimation based on differential equations
Pål C Ryalen1, Bjørn Møller2, Christoffer H Laache3
1Department of Mathematics, EPFL, Station 8, CH-1015 Lausanne, Switzerland.
Abstract:
We present a method for estimating several prognosis parameters for cancer survivors. The method utilizes the fact that these parameters solve differential equations driven by cumulative hazards. By expressing the parameters as solutions to differential equations, we develop generic estimators that are easy to implement with standard statistical software. We explicitly describe the estimators for prognosis parameters that are often employed in practice, but also for parameters that, to our knowledge, have not been used to evaluate prognosis. We then apply these parameters to assess the prognosis of five common cancers in Norway.
Related Concept Videos
Cancer Survival Analysis
Survival Curves
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...
Actuarial Approach
Consider the example of a high-risk surgical procedure with significant early-stage mortality. A two-year clinical study is conducted,...
Comparing the Survival Analysis of Two or More Groups
Kaplan-Meier Approach
Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

