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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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

Phuong Bui¹, Varun Jadhav¹, Suvra Pal^1,2

¹Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, United States.

Statistica Neerlandica

|July 14, 2026

Summary

We introduce a new gradient-free estimation method, the sequential quadratic Hamiltonian (SQH) scheme, for Box-Cox transformation (BCT) cure rate models. SQH offers improved accuracy and efficiency over existing methods, providing better cure rate estimates.

Keywords:

Box-Cox Transformation Cure rate Cutaneous melanoma Long-term survivors Optimization

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Area of Science:

Biostatistics
Statistical modeling
Computational statistics

Background:

Cure rate models are essential for analyzing data with a proportion of individuals who will never experience the event of interest.
The Box-Cox transformation (BCT) cure rate model is a flexible framework for such analyses.
Existing estimation methods, like expectation maximization (EM) and non-linear conjugate gradient (NCG), have limitations in accuracy and computational efficiency.

Purpose of the Study:

To propose and evaluate an enhanced estimation method for BCT cure rate model parameters.
To introduce the sequential quadratic Hamiltonian (SQH) algorithm, a gradient-free approach, for parameter estimation.
To demonstrate the superiority of the SQH algorithm over the NCG algorithm in terms of accuracy and computational speed.

Main Methods:

Application of the sequential quadratic Hamiltonian (SQH) algorithm for maximum likelihood estimation.
Extensive simulation studies to compare SQH with the non-linear conjugate gradient (NCG) algorithm.
Analysis of a real-world melanoma dataset using the proposed SQH algorithm.

Main Results:

The SQH algorithm yields estimates with smaller bias and root mean square error for all BCT cure model parameters.
SQH provides more accurate and precise cure rate estimates compared to NCG.
The gradient-free nature of SQH results in significantly less CPU time for estimation compared to NCG.
SQH demonstrates favorable performance against NCG for BCT cure model estimation.

Conclusions:

The sequential quadratic Hamiltonian (SQH) algorithm is a superior method for estimating parameters in Box-Cox transformation (BCT) cure rate models.
SQH offers enhanced accuracy, precision, and computational efficiency.
The proposed method shows promise for analyzing survival data with a cure fraction, as demonstrated on a melanoma dataset.