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

Abstract

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.

Keywords: Cure models; maximum likelihood estimation , Bladder cancer, Right-censored data.

Figure 1

(a) Overall Survival Function Obtained by Kaplan-Meier Technique for the Bladder Cancer Data. (b) Curves of survival functions for each type of treatments

Figure 2

A Comparison between Kaplan-Meier Estimates of the Survival Function and the Corresponding Anticipated Values Obtained from the Non-mixture Models for Various Probability Distributions (as indicated in Table 1, results). The diagonal red lines in the graph indicate a complete agreement between the product-limit estimates and the anticipated values

Figure 3

Panels (a) and (b) Display the Fitted Survival Curves Derived from the BCH Model Using the EWE Distribution and Its Sub-distributions for Bladder Cancer Data. The corresponding hazard functions are depicted in panels (c) and (d). In order to enable easy comparisons, all plots present curves based on the EWE distribution

Figure 4

Hazards Functions Derived from the Non-mixture Cure Model with the EE Distribution where a covariate (specifically, the type of treatment) is connected both to the probability of being cured, π, and the scale parameter α