A New Estimation Algorithm for Box-Cox Transformation Cure Rate Model and Comparison With EM Algorithm

TL;DR

This paper introduces a novel estimation algorithm based on the non-linear conjugate gradient method for the Box-Cox transformation cure rate model, demonstrating its advantages over the traditional EM algorithm through simulations and real data analysis.

Contribution

The paper presents a new NCG-based estimation procedure for the Box-Cox cure rate model, improving parameter estimation especially when the likelihood surface is flat.

Findings

NCG algorithm outperforms EM in simulation studies

NCG allows simultaneous parameter maximization in flat likelihood regions

Application to melanoma data shows better model fit with NCG

Abstract

In this paper, we develop a new estimation procedure based on the non-linear conjugate gradient (NCG) algorithm for the Box-Cox transformation cure rate model. We compare the performance of the NCG algorithm with the well-known expectation maximization (EM) algorithm through a simulation study and show the advantages of the NCG algorithm over the EM algorithm. In particular, we show that the NCG algorithm allows simultaneous maximization of all model parameters when the likelihood surface is flat with respect to a Box-Cox model parameter. This is a big advantage over the EM algorithm, where a profile likelihood approach has been proposed in the literature that may not provide satisfactory results. We finally use the NCG algorithm to analyze a well-known melanoma data and show that it results in a better fit.