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On the parameter estimation of Box-Cox transformation cure model.

Suvra Pal1, Souvik Roy1

  • 1Department of Mathematics, University of Texas at Arlington, 411 S Nedderman Drive, Arlington, Texas, 76019, USA.

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Summary

We introduce a new estimation method for Box-Cox transformation (BCT) cure rate models using a non-linear conjugate gradient (NCG) algorithm. This NCG approach offers more accurate cure rate inference and faster computation compared to the expectation maximization (EM) algorithm.

Keywords:
line searchlong-term survivorsmelanomaprofile likelihood

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Survival Analysis

Background:

  • Cure rate models are essential for analyzing time-to-event data where a portion of the population may never experience the event.
  • The Box-Cox transformation (BCT) cure rate model is a widely used statistical tool for such analyses.
  • Existing estimation methods, like the expectation maximization (EM) algorithm, can face challenges with parameter estimation, especially with flat likelihood surfaces.

Purpose of the Study:

  • To propose and evaluate an improved estimation method for the parameters of the Box-Cox transformation (BCT) cure rate model.
  • To compare the performance of the proposed method against the existing expectation maximization (EM) algorithm.
  • To demonstrate the advantages of the new method in terms of accuracy, precision, and computational efficiency.

Main Methods:

  • Development of a generic maximum likelihood estimation algorithm using a non-linear conjugate gradient (NCG) method.
  • Incorporation of an efficient line search technique within the NCG algorithm.
  • Simulation studies to compare the NCG algorithm with the EM algorithm for BCT cure models.
  • Application of the NCG algorithm to a real-world melanoma dataset.

Main Results:

  • The proposed NCG algorithm allows simultaneous maximization of all model parameters, overcoming limitations of the EM algorithm on flat likelihood surfaces.
  • The NCG algorithm yields smaller bias and root mean square error for cure rate-associated parameters, leading to more accurate inference.
  • For large sample sizes, the NCG algorithm demonstrates reduced CPU time due to requiring only gradient computation, not the Hessian.
  • Analysis of melanoma data shows a better model fit using the NCG algorithm compared to the EM algorithm.

Conclusions:

  • The non-linear conjugate gradient (NCG) method is a superior estimation technique for Box-Cox transformation (BCT) cure rate models compared to the expectation maximization (EM) algorithm.
  • The NCG algorithm provides more precise and accurate estimation of cure rate parameters and is computationally more efficient.
  • The proposed NCG method is recommended for practical application in BCT cure rate modeling.