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A New Non-Linear Conjugate Gradient Algorithm for Destructive Cure Rate Model and a Simulation Study: Illustration

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  • 1Department of Mathematics, University of Texas at Arlington, TX, 76019, USA.

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Summary

We introduce a novel projected non-linear conjugate gradient (PNCG) algorithm for survival analysis with competing risks and a cure fraction. Our method outperforms the expectation maximization (EM) algorithm and other optimization techniques in simulations.

Keywords:
EM algorithmconstrained optimizationfirst-order necessary conditionsline-searchlong-term survivors

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Modeling

Background:

  • Survival models with competing risks and cure fractions are crucial in many fields.
  • The expectation maximization (EM) algorithm is a common method for parameter estimation in these models.
  • Existing optimization algorithms may have limitations in efficiency and applicability.

Purpose of the Study:

  • To propose a new estimation methodology using a projected non-linear conjugate gradient (PNCG) algorithm.
  • To develop a general PNCG algorithm for survival models with competing risks and a cure fraction.
  • To compare the performance of the proposed PNCG algorithm against the EM algorithm and other existing methods.

Main Methods:

  • Development of a projected non-linear conjugate gradient (PNCG) algorithm with an efficient line search.
  • Application of the PNCG algorithm to a survival model incorporating a proportion cure under a competing risks setup.
  • Extensive Monte Carlo simulation studies for performance comparison.
  • Analysis of a real-world melanoma dataset.

Main Results:

  • The proposed PNCG algorithm demonstrates superior performance compared to the expectation maximization (EM) algorithm.
  • Simulations show the advantages of the PNCG methodology over other available R software package optimization algorithms.
  • The algorithm is flexible and can accommodate various competing risks distributions, exemplified with a negative binomial distribution.

Conclusions:

  • The novel PNCG algorithm offers an efficient and advantageous alternative for estimating parameters in survival models with competing risks and cure fractions.
  • The methodology is robust and performs well across different scenarios, as evidenced by simulation studies.
  • The proposed algorithm provides a valuable tool for analyzing complex survival data, such as in the melanoma dataset example.