A Sequential Quadratic Hamiltonian-Based Estimation Method for Box-Cox Transformation Cure Model

TL;DR

This paper introduces a new gradient-free sequential quadratic Hamiltonian (SQH) algorithm for estimating parameters in the Box-Cox transformation cure model, demonstrating its superior accuracy and efficiency over existing methods through simulations and real data application.

Contribution

The paper presents the SQH algorithm as a novel, gradient-free approach that outperforms the non-linear conjugate gradient method in estimating BCT cure model parameters.

Findings

SQH yields estimates with smaller bias and RMSE.

SQH requires less CPU time than NCG.

SQH provides more accurate cure rate estimates.

Abstract

We propose an enhanced estimation method for the Box-Cox transformation (BCT) cure rate model parameters by introducing a generic maximum likelihood estimation algorithm, the sequential quadratic Hamiltonian (SQH) scheme, which is based on a gradient-free approach. We apply the SQH algorithm to the BCT cure model and, through an extensive simulation study, compare its model fitting results with those obtained using the recently developed non-linear conjugate gradient (NCG) algorithm. Since the NCG method has already been shown to outperform the well-known expectation maximization algorithm, our focus is on demonstrating the superiority of the SQH algorithm over NCG. First, we show that the SQH algorithm produces estimates with smaller bias and root mean square error for all BCT cure model parameters, resulting in more accurate and precise cure rate estimates. We then demonstrate that, being gradient-free, the SQH algorithm requires less CPU time to generate estimates compared to the NCG algorithm, which only computes the gradient and not the Hessian. These advantages make the SQH algorithm the preferred estimation method over the NCG method for the BCT cure model. Finally, we apply the SQH algorithm to analyze a well-known melanoma dataset and present the results.