Generalized Modified Weibull and Exponentiated Weibull Exponential distributions for cure fraction models of cancer patients
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 Expone...
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| Format: | Thesis |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/119041/ http://psasir.upm.edu.my/id/eprint/119041/1/119041.pdf |
| Summary: | 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. |
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