Destructive cure rate models under proportional odds and associated likelihood inference

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In this work, we introduce a flexible destructive cure rate model for lifetime data. We assume the number of competing causes of the event of interest to follow the Weighted Poisson distribution (including length-biased Poisson, negative binomial, and exponentially weighted Poisson [EWP]) and the lifetimes of the noncured individuals to follow a proportional odds survival model. The baseline odds distribution is considered to be either Weibull or log-logistic distribution. A damage distribution is introduced due to the fact that some of the competing causes may not remain active following treatment. The statistical inference is developed for this model under right-censored data. The maximum likelihood estimation of the model parameters is then developed with the full usage of expectation–maximization method. Model discrimination between destructive negative binomial cure rate model and destructive EWP cure rate model is carried out by likelihood-based criteria through AIC and BIC. An extensive simulation study is performed to evaluate the performance of all the models and inferential methods developed here. A real data example on cutaneous melanoma is analyzed for illustrative purpose.