Non-Mixture Cure Model Estimation in Bladder Cancer Patients: A Novel Approach with Exponentiated Weibull Exponential Distribution.

OBJECTIVE: Cure models are frequently used in survival analysis to account for a cured fraction in the data. When there is a cure rate present, researchers often prefer cure models over parametric models to analyse the survival data. These models enable the ability to define the probability distribution of survival durations for patients who are at risk. Various distributions can be considered for the survival times, such as Exponentiated Weibull Exponential (EWE), Exponential Exponential (EE), Weibull and lognormal distribution. The objective of this research is to choose the most appropriate distribution that accurately represents the survival times of patients who have not been cured. This will be accomplished by comparing various non-mixture cure models that are based on the EWE distribution with its sub-distributions, and distributions distinct from those belonging to the EWE distribution family. MATERIAL AND METHODS: A sample of 85 patients diagnosed with superficial bladder tumours was selected to be used in fitting the non-mixture cure model. In order to estimate the parameters of the suggested model, which takes into account the presence of a cure rate, censored data, and covariates, we utilized the maximum likelihood estimation technique using R software version 3.5.7. RESULT: Upon conducting a comparison of various parametric models fitted to the data, both with and without considering the cure fraction and without incorporating any predictors, the EE distribution yields the lowest AIC, BIC, and HQIC values among all the distributions considered in this study, (1191.921/1198.502, 1201.692/1203.387, 1195.851/1200.467). Furthermore, when considering a non-mixture cure model utilizing the EE distribution along with covariates, an estimated ratio was obtained between the probabilities of being cured for placebo and thiotepa groups (and its 95% confidence intervals) were 0.76130 (0.13914, 6.81863). CONCLUSION: The findings of this study indicate that EE distribution is the optimal selection for determining the duration of survival in individuals diagnosed with bladder cancer.

Utilization of a Mixture Cure Rate Model based on the Generalized Modified Weibull Distribution for the Analysis of Leukemia Patients.

OBJECTIVE: Cure rate models are survival models, commonly applied to model survival data with a cured fraction. In the existence of a cure rate, if the distribution of survival times for susceptible patients is specified, researchers usually prefer cure models to parametric models. Different distributions can be assumed for the survival times, for instance, generalized modified Weibull (GMW), exponentiated Weibull (EW), and log-beta Weibull. The purpose of this study is to select the best distribution for uncured patients' survival times by comparing the mixture cure models based on the GMW distribution and its particular cases. MATERIALS AND METHODS: A data set of 91 patients with high-risk acute lymphoblastic leukemia (ALL) followed for five years from 1982 to 1987 was chosen for fitting the mixture cure model. We used the maximum likelihood estimation technique via R software 3.6.2 to obtain the estimates for parameters of the proposed model in the existence of cure rate, censored data, and covariates. For the best model choice, the Akaike information criterion (AIC) was implemented. RESULTS: After comparing different parametric models fitted to the data, including or excluding cure fraction, without covariates, the smallest AIC values were obtained by the EW and the GMW distributions, (953.31/969.35) and (955.84/975.99), respectively. Besides, assuming a mixture cure model based on GMW with covariates, an estimated ratio between cure fractions for allogeneic and autologous bone marrow transplant groups (and its 95% confidence intervals) were 1.42972 (95% CI: 1.18614 - 1.72955). CONCLUSION: The results of this study reveal that the EW and the GMW distributions are the best choices for the survival times of Leukemia patients.
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