A sequential quadratic Hamiltonian‐based estimation method for Box‐Cox transformation cure model

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 indicate that the SQH algorithm performs favorably compared with the NCG method for estimation in the BCT cure model. Finally, we apply the SQH algorithm to analyze a well-known melanoma dataset and present the results.