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

2025-05-02

AI Summary

This paper addresses the substantial bias and low estimation efficiency in parameter estimation for Box-Cox transformation (BCT) cure-rate models. To overcome these limitations, we propose a gradient-free sequential quadratic Hamiltonian (SQH) optimization algorithm as a replacement for the prevailing nonlinear conjugate gradient (NCG) method. To our knowledge, this is the first application of a gradient-free SQH framework to maximum likelihood estimation in cure-rate models. The proposed SQH method markedly reduces both parameter bias and root-mean-square error (RMSE), while significantly decreasing CPU time. Monte Carlo simulations demonstrate that SQH consistently outperforms NCG in both estimation accuracy and computational efficiency. Furthermore, empirical analysis on real melanoma data confirms the robustness and practical utility of SQH, achieving simultaneous improvements in inferential accuracy and computational efficiency for cure-rate estimation.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Estimating Box-Cox transformation cure model parameters accurately
• Comparing SQH algorithm performance with NCG method
• Demonstrating SQH's superiority in bias and computational efficiency

Innovation

• Uses sequential quadratic Hamiltonian (SQH) scheme
• Gradient-free maximum likelihood estimation approach
• Outperforms non-linear conjugate gradient (NCG) algorithm