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

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.

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.

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 Predicting the cure rate of breast cancer using a new regression model with four regression structures

2017 ◽  
Vol 27 (11) ◽  
pp. 3207-3223 ◽  
Author(s):  
Thiago G Ramires ◽  
Gauss M Cordeiro ◽  
Michael W Kattan ◽  
Niel Hens ◽  
Edwin MM Ortega
Keyword(s):  
Breast Carcinoma ◽  
Regression Model ◽  
Additive Model ◽  
Real Data ◽  
Cure Rate ◽  
Time Model ◽  
Data Set ◽  
Explanatory Variables ◽  
Diagnostic Measures ◽  
Cure Fraction

Cure fraction models are useful to model lifetime data with long-term survivors. We propose a flexible four-parameter cure rate survival model called the log-sinh Cauchy promotion time model for predicting breast carcinoma survival in women who underwent mastectomy. The model can estimate simultaneously the effects of the explanatory variables on the timing acceleration/deceleration of a given event, the surviving fraction, the heterogeneity, and the possible existence of bimodality in the data. In order to examine the performance of the proposed model, simulations are presented to verify the robust aspects of this flexible class against outlying and influential observations. Furthermore, we determine some diagnostic measures and the one-step approximations of the estimates in the case-deletion model. The new model was implemented in the generalized additive model for location, scale and shape package of the R software, which is presented throughout the paper by way of a brief tutorial on its use. The potential of the new regression model to accurately predict breast carcinoma mortality is illustrated using a real data set.

Cure fraction estimation from the mixture cure models for grouped survival data

2004 ◽  
Vol 23 (11) ◽  
pp. 1733-1747 ◽  
Author(s):  
Binbing Yu ◽  
Ram C. Tiwari ◽  
Kathleen A. Cronin ◽  
Eric J. Feuer
Keyword(s):  
Survival Data ◽  
Cure Fraction ◽  
Cure Models

scholarly journals Exponentiated Exponential-Exponentiated Weibull Linear Mixed Distribution: Properties and Applications

2020 ◽  
pp. 517-527
Author(s):  
Salman Abbas ◽  
Muhammad Mohsin ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Real Life ◽  
Moment Generating Function ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Coefficient Of Skewness

In this article we have discussed linear mixing of two exponentiated distribution. The proposed model is named as exponentiated exponential-exponentiated Weibull (EE-EW) distribution. The proposed distribution generalize several existing distributions. We study several characteristics of the proposed distribution including moment, moment generating function, reliability and hazard rate functions. An empirical study is presented for mean, variance, coefficient of skewness, and coefficient of kurtosis. The method of maximum likelihood is used for the estimation of parameters. For the illustration purpose, we have use two real-life data set for application. The results justify the capability of the new model.

On the use of the modified power series family of distributions in a cure rate model context

2019 ◽  
Vol 29 (7) ◽  
pp. 1831-1845
Author(s):  
Diego I Gallardo ◽  
Yolanda M Gómez ◽  
Héctor W Gómez ◽  
Mário de Castro
Keyword(s):  
Power Series ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Marrow Transplant ◽  
Rate Model ◽  
Cure Rate ◽  
Data Set ◽  
Cure Rate Models ◽  
Cure Rate Model

In this paper, we propose a generalization of the power series cure rate model for the number of competing causes related to the occurrence of the event of interest. The model includes distributions not yet used in the cure rate models context, such as the Borel, Haight and Restricted Generalized Poisson distributions. The model is conveniently parameterized in terms of the cure rate. Maximum likelihood estimation based on the Expectation Maximization algorithm is discussed. A simulation study designed to assess some properties of the estimators is carried out, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a bone marrow transplant data set is presented.

scholarly journals Variable selection for mixture and promotion time cure rate models

2016 ◽  
Vol 27 (7) ◽  
pp. 2185-2199 ◽  
Author(s):  
Abdullah Masud ◽  
Wanzhu Tu ◽  
Zhangsheng Yu
Keyword(s):  
Variable Selection ◽  
Failure Time ◽  
Operating Characteristics ◽  
Cure Rate ◽  
Time Data ◽  
Cure Rate Models ◽  
Cure Models ◽  
Selection Operators ◽  
Selection For ◽  
Using Data

Failure-time data with cured patients are common in clinical studies. Data from these studies are typically analyzed with cure rate models. Variable selection methods have not been well developed for cure rate models. In this research, we propose two least absolute shrinkage and selection operators based methods, for variable selection in mixture and promotion time cure models with parametric or nonparametric baseline hazards. We conduct an extensive simulation study to assess the operating characteristics of the proposed methods. We illustrate the use of the methods using data from a study of childhood wheezing.

Joint longitudinal and time-to-event cure models for the assessment of being cured

2019 ◽  
Vol 29 (4) ◽  
pp. 1256-1270
Author(s):  
Antoine Barbieri ◽  
Catherine Legrand
Keyword(s):  
Survival Data ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Medical Intervention ◽  
Time To Event ◽  
Mixture Cure Model ◽  
Longitudinal Measurements ◽  
Cure Fraction ◽  
Cure Models ◽  
Latent Structures

Medical time-to-event studies frequently include two groups of patients: those who will not experience the event of interest and are said to be “cured” and those who will develop the event and are said to be “susceptible”. However, the cure status is unobserved in (right-)censored patients. While most of the work on cure models focuses on the time-to-event for the uncured patients (latency) or on the baseline probability of being cured or not (incidence), we focus in this research on the conditional probability of being cured after a medical intervention given survival until a certain time. Assuming the availability of longitudinal measurements collected over time and being informative on the risk to develop the event, we consider joint models for longitudinal and survival data given a cure fraction. These models include a linear mixed model to fit the trajectory of longitudinal measurements and a mixture cure model. In simulation studies, different shared latent structures linking both submodels are compared in order to assess their predictive performance. Finally, an illustration on HIV patient data completes the comparison.

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