Generalized Modified Weibull and Exponentiated Weibull Exponential distributions for cure fraction models of cancer patients - Omer, Mohamed Elamin Abdallah Mohamed Elamin (2023)
This research aims to develop a parametric cure model for lifetime data in the presence of right and interval- censored data with fixed predictors. The research begins by extending the existing Mixture Cure Model (MCM), utilizing Generalized Modified Weibull (GMW) and Exponentiated Weibull Exponential (EWE) distributions to accommodate both right- and interval-censored data with fixed covariates. Bounded Cumulative Hazard (BCH) and the Geometric Non-Mixture Cure (GeNMC) models, are also explored, offering alternative approaches in cure modelling methodologies. These models are developed based on GMW and EWE distributions, are extended in the presence of right and interval censored data with fixed covariate. Maximum likelihood estimation (MLE) method is employed to estimate model parameters. Simulation studies are carried out to assess the performance of the MLE estimates. The MLE performance is evaluated using bias, standard error (SE), and root mean square error (RMSE) metrics across varying sample sizes and censoring proportions. The width of the interval (len) for the interval-censored data (observational gap times) is also being considered (len=0.5). The results of the simulation studies reveal increased bias, SE, and RMSE of the estimates with higher censoring proportions and decreased sample sizes. Moreover, the MLE demonstrates efficiency, evidenced by declining RMSE values with increasing sample sizes across all censoring proportions. To further support the findings of the simulation studies, four real-life datasets are utilized, sourced from cancer and smoking studies. The first dataset comprises of right-censored observations from a bladder cancer study. The second dataset is an interval-censored data taken from a smoking cessation study. This dataset includes smoking relapse times that were collected annually over a 5-year follow-up period from participants living in 51 zip code areas in the South Eastern region of Minnesota, USA. The third dataset includes right-censored data from a study on leukemia, focusing on treatment as the covariate. The fourth dataset is a rightcensored data related to melanoma cancer, considering sex, treatment, and age as covariates. Comparing the MCM, BCH, and GeNMC models based on GMW, EWE, Fr´echet, and Gompertz distributions using bladder data, the results indicate that the MCM, BCH, and GeNMC models based on the EWE distribution performed better than the other competing models in this study. While the GMW distribution with the three cure models provides a slightly better fit than the EWE distribution, considering smoking cessation data. For leukemia data, both GMW and EWE distributions emerge as best choices for modeling the survival times of susceptible patients. For the melanoma data, while all models show similar outcomes, the MCM model with the EWE distribution exhibits the best fit.