A New Estimation Algorithm for Destructive Cure Model: Illustration with Exponentially Weighted Poisson Competing Risks.

We propose an improved estimation method for the destructive cure rate model by introducing a generic maximum likelihood algorithm, the sequential quadratic Hamiltonian (SQH) scheme, which employs a gradient-free optimization approach. The SQH algorithm is applied to the destructive cure model with exponentially weighted Poisson competing risks, and its performance is evaluated through a comprehensive simulation study. Specifically, we compare the model-fitting accuracy of SQH with the recently developed conjugate gradient line search (CGLS) algorithm. Given that the CGLS method has been shown to outperform the widely used expectation-maximization algorithm and other optimization routines available in R (e.g., optim, nlm, and Rcgmin), our focus is on assessing whether the SQH algorithm can offer further improvements. Simulation results show that the SQH algorithm yields parameter estimates with consistently lower bias and root mean square error, resulting in more accurate and precise cure rate estimation. Furthermore, due to its gradient-free nature, the SQH algorithm requires less CPU time than CGLS. These advantages position the SQH algorithm as a preferred estimation method over CGLS for the destructive cure rate model. To demonstrate its practical utility, we apply the SQH algorithm to a well-known melanoma dataset and present the analysis results.