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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
PubMed
Summary
This summary is machine-generated.

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.

Keywords:
Competing risksCure rateDestructive cure modelLong-term survivorsOptimization

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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.