Mixture and nonmixture cure fraction models assuming discrete lifetimes: Application to a pelvic sarcoma dataset

Different cure fraction models have been used in the analysis of lifetime data in presence of cured patients. This paper considers mixture and nonmixture models based on discrete Weibull distribution to model recurrent event data in presence of a cure fraction. The novelty of this study is the use of a discrete lifetime distribution in place of usual existing continuous lifetime distributions for lifetime data in presence of cured fraction, censored data, and covariates. In the verification of the fit of the proposed model it is proposed the use of randomized quantile residuals. An extensive simulation study is considered to evaluate the properties of the estimates of the parameters related to the proposed model. As an illustration of the proposed methodology, it is considered an application considering a medical dataset related to lifetimes in a retrospective cohort study conducted by Puchner et al. (2017) that consists of 147 consecutive cases with surgical treatment of a sarcoma of the pelvis between the years of 1980 and 2012.