  In survival analysis, cure models have gained much importance due to rapid
advancements in medical sciences. More recently, a subset of cure models,
called destructive cure models, have been studied extensively under competing
risks scenario wherein initial competing risks undergo a destructive process,
such as under a chemotherapy. In this article, we study destructive cure models
by assuming a flexible weighted Poisson distribution (exponentially weighted
Poisson, length biased Poisson and negative binomial distributions) for the
initial number of competing causes and with lifetimes of the susceptible
individuals following proportional hazards. The expectation-maximization (EM)
algorithm and profile likelihood approach are made use of for estimating the
model parameters. An extensive simulation study is carried out under various
parameter settings to examine the properties of the models, and the accuracy
and robustness of the proposed estimation technique. Effects of model
misspecification on the parameter estimates are also discussed in detail.
Finally, for the illustration of the proposed methodology, a real-life
cutaneous melanoma data set is analyzed.
