On the comparison of risk of death according to different stages of breast cancer via the long-term exponentiated Weibull hazard model

Abstract

Long-term survivor models have been extensively used for modelling time-to-event data with a significant proportion of patients who do not experience poor outcome. In this paper, we propose a new long-term survivor hazard model, which accommodates comprehensive families of cure rate models as particular cases, including modified Weibull, exponentiated Weibull, Weibull, exponential and Rayleigh distribution, among others. The maximum likelihood estimation procedure is presented. A simulation study evaluates bias and mean square error of the considered estimation procedure as well as the coverage probabilities of the parameters asymptotic and bootstrap confidence intervals. A real Brazilian dataset on breast cancer illustrates the methodology. From the practical point of view, under our modelling, we provide a parameter that works as a metric to quantify and compare the risk between different stages of the disease. We emphasize that, we developed an online platform for oncologists to calculate the probability of survival of patients diagnosed with breast cancer according to the stage of the disease in real time.