On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risks

A new estimation method is proposed founded upon a nonlinear conjugate gradient‐type algorithm having an efficient line search technique for cure rate models with competing risks, which are subject to elimination. An extensive simulation study is carried out to compare the performance of the proposed algorithm with some existing algorithms, including other conjugate gradient‐type algorithms and the expectation maximization algorithm. For this purpose, it is assumed that the initial competing risks follow an exponentially weighted Poisson distribution. In particular, it is shown that that the proposed algorithm produces estimates that are more accurate and efficient (i.e., the bias and root mean square errors are smaller), specifically with respect to the parameters related to the cure rate. Although for the purpose of simulation study an exponentially weighted Poisson competing risks distribution is assumed, the proposed algorithm incorporates a generic framework that can accommodate any competing risks distribution. Finally, a real data application is provided.