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

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.