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Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
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A New Estimation Algorithm for Destructive Cure Model: Illustration with Exponentially Weighted Poisson Competing
Suvra Pal1,2, Souvik Roy1
1Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, United States.
Communications in Statistics: Simulation and Computation
|April 20, 2026
Summary
We introduce the sequential quadratic Hamiltonian (SQH) algorithm, a novel gradient-free method for estimating destructive cure rate models. SQH demonstrates superior accuracy and efficiency compared to existing algorithms, offering improved cure rate estimation.
Area of Science:
- Biostatistics
- Statistical modeling
- Survival analysis
Background:
- Cure rate models are essential for analyzing long-term survival data where a proportion of patients may be cured.
- Existing estimation methods, such as expectation-maximization (EM) and conjugate gradient line search (CGLS), have limitations in accuracy and computational efficiency.
- Accurate estimation is crucial for understanding disease progression and treatment effectiveness.
Purpose of the Study:
- To propose and evaluate a novel gradient-free maximum likelihood estimation algorithm, the sequential quadratic Hamiltonian (SQH) scheme.
- To compare the performance of the SQH algorithm against the conjugate gradient line search (CGLS) algorithm for destructive cure rate models.
- To assess the accuracy, precision, and computational efficiency of SQH for cure rate estimation.
Main Methods:
- Development and application of the sequential quadratic Hamiltonian (SQH) algorithm, a gradient-free optimization technique.
- Application of SQH to a destructive cure rate model incorporating exponentially weighted Poisson competing risks.
- Comprehensive simulation studies to compare SQH with the conjugate gradient line search (CGLS) algorithm.
Main Results:
- The SQH algorithm produced parameter estimates with consistently lower bias and root mean square error compared to CGLS.
- SQH demonstrated improved accuracy and precision in cure rate estimation.
- The gradient-free nature of SQH resulted in reduced CPU time compared to CGLS.
Conclusions:
- The sequential quadratic Hamiltonian (SQH) algorithm is a preferred estimation method over CGLS for destructive cure rate models due to its superior accuracy and efficiency.
- SQH offers a valuable alternative for statistical modeling in survival analysis, particularly for complex cure rate models.
- The practical utility of SQH was demonstrated through its application to a melanoma dataset.
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