scholarly journals Cure Models with Exponentiated Weibull Exponential Distribution for the Analysis of Melanoma Patients

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1926
Author(s):  
Mohamed Elamin Abdallah Mohamed Elamin Omer ◽  
Mohd Rizam Abu Bakar ◽  
Mohd Bakri Adam ◽  
Mohd Shafie Mustafa
Keyword(s):  
Survival Data ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Cure Rate ◽  
Cure Rate Models ◽  
Cure Model ◽  
Mixture Cure Model ◽  
Cure Models ◽  
Exponentiated Weibull ◽  
Melanoma Patients

In the survival data analysis, commonly, it is presumed that all study subjects will eventually have the event of concern. Nonetheless, it tends to be unequivocally expected that a fraction of these subjects will never expose to the event of interest. The cure rate models are usually used to model this type of data. In this paper, we introduced a maximum likelihood estimates analysis for the four-parameter exponentiated Weibull exponential (EWE) distribution in the existence of cured subjects, censored observations, and predictors. Aiming to include the fraction of unsusceptible (cured) individuals in the analysis, a mixture cure model, and two non-mixture cure models—bounded cumulative hazard model, and geometric non-mixture model with EWE distribution—are proposed. The mixture cure model provides a better fit to real data from a Melanoma clinical trial compared to the other two non-mixture cure models.

scholarly journals Application of Modified Generalized–Gamma Mixture Cure Model in the Analysis of Ovarian Cancer Data

2021 ◽  
Vol 2123 (1) ◽  
pp. 012041
Author(s):  
Serifat A. Folorunso ◽  
Timothy A.O. Oluwasola ◽  
Angela U. Chukwu ◽  
Akintunde A. Odukogbe
Keyword(s):  
Ovarian Cancer ◽  
Survival Data ◽  
Information Criterion ◽  
Cure Model ◽  
Modeling And Analysis ◽  
Cancer Data ◽  
Mixture Cure Model ◽  
Generalized Gamma ◽  
Ovarian Cancer Data ◽  
Cure Models

Abstract The modeling and analysis of lifetime for terminal diseases such as cancer is a significant aspect of statistical work. This study considered data from thirty-seven women diagnosed with Ovarian Cancer and hospitalized for care at theDepartment of Obstetrics and Gynecology, University of Ibadan, Nigeria. Focus was on the application of a parametric mixture cure model that can handle skewness associated with survival data – a modified generalized-gamma mixture cure model (MGGMCM). The effectiveness of MGGMCM was compared with existing parametric mixture cure models using Akaike Information Criterion, median time-to-cure and variance of the cure rate. It was observed that the MGGMCM is an improved parametric model for the mixture cure model.

Semi-Parametric Cure Rate Proportional Odds Models with Spatial Frailties for Interval-Censored Data

2019 ◽  
Vol 11 (03n04) ◽  
pp. 1950005
Author(s):  
Yiqi Bao ◽  
Vicente G. Cancho ◽  
Francisco Louzada ◽  
Adriano K. Suzuki
Keyword(s):  
Censored Data ◽  
Real Data ◽  
Interval Censored Data ◽  
Spatial Correlations ◽  
Cure Rate ◽  
Proportional Odds ◽  
Data Set ◽  
Cure Rate Models ◽  
Cure Models ◽  
Interval Censored

In this work, we proposed the semi-parametric cure rate models with independent and dependent spatial frailties. These models extend the proportional odds cure models and allow for spatial correlations by including spatial frailty for the interval censored data setting. Moreover, since these cure models are obtained by considering the occurrence of an event of interest is caused by the presence of any nonobserved risks, we also study the complementary cure model, that is, the cure models are obtained by assuming the occurrence of an event of interest is caused when all of the nonobserved risks are activated. The MCMC method is used in a Bayesian approach for inferential purposes. We conduct an influence diagnostic through the diagnostic measures in order to detect possible influential or extreme observations that can cause distortions on the results of the analysis. Finally, the proposed models are applied to the analysis of a real data set.

On a Class of Transmuted Distributions to Model Survival Data with a Cure Fraction

2021 ◽  
Vol 73 (2) ◽  
pp. 106-126
Author(s):  
G. Asha ◽  
C. S. Soorya
Keyword(s):  
Survival Data ◽  
Likelihood Function ◽  
Real Life ◽  
Estimation Of Parameters ◽  
Cure Rate ◽  
Data Set ◽  
Cure Rate Models ◽  
Subject Classifications ◽  
Cure Fraction ◽  
Cure Models

Modelling time to event data, when there is always a proportion of the individuals, commonly referred to as immunes who do not experience the event of interest, is of importance in many biomedical studies. Improper distributions are used to model these situations and they are generally referred to as cure rate models. In the literature, two main families of cure rate models have been proposed, namely the mixture cure models and promotion time cure models. Here we propose a new model by extending the mixture model via a generating function by considering a shifted Bernoulli distribution. This gives rise to a new class of popular distributions called the transmuted class of distributions to model survival data with a cure fraction. The properties of the proposed model are investigated and parameters estimated. The Bayesian approach to the estimation of parameters is also adopted. The complexity of the likelihood function is handled through the Metropolis-Hasting algorithm. The proposed method is illustrated with few examples using different baseline distributions. A real life data set is also analysed. AMS subject classifications: 62N02, 62F15

ESTIMATION OF CURE FRACTION FOR LOGNORMAL RIGHT CENSORED DATA WITH COVARIATES

2012 ◽  
Vol 09 ◽  
pp. 308-315
Author(s):  
FAUZIA ALI TAWEAB ◽  
NOOR AKMA IBRAHIM ◽  
BADER AHMAD I ALJAWADI
Keyword(s):  
Survival Data ◽  
Right Censoring ◽  
Parametric Estimation ◽  
Survival Models ◽  
Cure Rate ◽  
Cumulative Hazard ◽  
Cure Rate Models ◽  
Right Censored Data ◽  
Mixture Cure Model ◽  
Cure Fraction

In clinical studies, a proportion of patients might be unsusceptible to the event of interest and can be considered as cured. The survival models that incorporate the cured proportion are known as cure rate models where the most widely used model is the mixture cure model. However, in cancer clinical trials, mixture model is not the appropriate model and the viable alternative is the Bounded Cumulative Hazard (BCH) model. In this paper we consider the BCH model to estimate the cure fraction based on the lognormal distribution. The parametric estimation of the cure fraction for survival data with right censoring with covariates is obtained by using EM algorithm.

scholarly journals Diagnostic checks in mixture cure models with interval-censoring

2016 ◽  
Vol 27 (7) ◽  
pp. 2114-2131 ◽  
Author(s):  
Sylvie Scolas ◽  
Catherine Legrand ◽  
Abderrahim Oulhaj ◽  
Anouar El Ghouch
Keyword(s):  
Survival Data ◽  
Goodness Of Fit ◽  
Real Data ◽  
Interval Censoring ◽  
Data Set ◽  
Survival Distribution ◽  
Cure Model ◽  
Censored Survival Data ◽  
Mixture Cure Model ◽  
Interval Censored

Models for interval-censored survival data presenting a fraction of “cure” or “immune” patients have recently been proposed in the literature, particularly extending the mixture cure model to interval-censored data. However, little is known about the goodness-of-fit of such models. In a mixture cure model, the survival distribution of the entire population is improper and expressed in terms of the survival distribution of uncured individuals, i.e. the latency part of the model, and the probability to experience the event of interest, i.e. the incidence part. To validate a mixture cure model, assumptions made on both parts need to be checked, i.e. the survival distribution of uncured individuals, the link function used in the latency and the linearity of the covariates used in the both parts of the model. In this work, we investigate the Cox-Snell and deviance residuals and show how they can be adapted and used to perform diagnostics checks when all subjects are right- or interval-censored and some subjects are cured with unknown cure status. A large simulation study investigates the ability of these residuals to detect a departure from the assumptions of the mixture model. Developed techniques are applied to a real data set about Alzheimer’s disease.

scholarly journals New Flexible Regression Models Generated by Gamma Random Variables with Censored Data

2016 ◽  
Vol 5 (3) ◽  
pp. 9 ◽  
Author(s):  
Elizabeth M. Hashimoto ◽  
Gauss M. Cordeiro ◽  
Edwin M.M. Ortega ◽  
G.G. Hamedani
Keyword(s):  
Regression Model ◽  
Censored Data ◽  
Survival Data ◽  
Regression Models ◽  
Empirical Distribution ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Standard Normal Distribution ◽  
Model Parameters ◽  
Linear Regression Models

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models. 

scholarly journals Goodness-of-fit tests for the cure rate in a mixture cure model

Biometrika ◽  
2018 ◽  
Vol 106 (1) ◽  
pp. 211-227 ◽  
Author(s):  
U U Müller ◽  
I Van Keilegom
Keyword(s):  
Goodness Of Fit ◽  
Cure Rate ◽  
Cure Model ◽  
Mixture Cure Model ◽  
Goodness Of Fit Tests

scholarly journals A Non-Mixture Cure Model for Right Censored Data with Fréchet Distribution

2018 ◽  
Author(s):  
Durga Kutal ◽  
Lianfen Qian
Keyword(s):  
Censored Data ◽  
Real Data ◽  
Phase Iii ◽  
Likelihood Method ◽  
Model Parameters ◽  
Exponential Distributions ◽  
Right Censored Data ◽  
Cure Model ◽  
Mixture Cure Model ◽  
Allogeneic Marrow

This paper considers a non-mixture cure model for right censored data. It utilizes the maximum likelihood method to estimate model parameters in the non-mixture cure model. The simulation study is based on Fréchet susceptible distribution to evaluate the performance of the method. Comparing with Weibull and exponentiated exponential distributions, the non-mixture Fréchet distribution is shown to be the best in modeling a real data on allogeneic marrow HLA-matched donors and ECOG phase III clinical trial e1684 data.

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