Bivariate lifetime modelling using copula functions in presence of mixture and non-mixture cure fraction models, censored data and covariates

2016 ◽  
Vol 11 (4) ◽  
pp. 261-276 ◽  
Author(s):  
Jorge Alberto Achcar ◽  
Edson Zangiacomi Martinez ◽  
José Rafael Tovar Cuevas
Keyword(s):  
Censored Data ◽  
Copula Functions ◽  
Cure Fraction ◽  
Fraction Models

scholarly journals Mixture and Non-Mixture Cure Fraction Models Based on Generalized Gompertz Distribution under Bayesian Approach

2016 ◽  
Vol 66 (1) ◽  
pp. 121-135 ◽  
Author(s):  
Prafulla Kumar Swain ◽  
Gurprit Grover ◽  
Komal Goel
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Bayesian Approach ◽  
New Drugs ◽  
Lifetime Data ◽  
Gompertz Distribution ◽  
Cure Fraction ◽  
Long Term Survivors ◽  
Fraction Models

Abstract The cure fraction models are generally used to model lifetime data with long term survivors. In a cohort of cancer patients, it has been observed that due to the development of new drugs some patients are cured permanently, and some are not cured. The patients who are cured permanently are called cured or long term survivors while patients who experience the recurrence of the disease are termed as susceptibles or uncured. Thus, the population is divided into two groups: a group of cured individuals and a group of susceptible individuals. The proportion of cured individuals after the treatment is typically known as the cure fraction. In this paper, we have introduced a three parameter Gompertz (viz. scale, shape and acceleration) or generalized Gompertz distribution in the presence of cure fraction, censored data and covariates for estimating the proportion of cure fraction through Bayesian Approach. Inferences are obtained using the standard Markov Chain Monte Carlo technique in openBUGS software.

scholarly journals Bivariate Weibull Distributions Derived From Copula Functions In The Presence Of Cure Fraction And Censored Data

2021 ◽  
Vol 14 (2) ◽  
pp. 295-316
Author(s):  
Em´ılio A. Coelho-Barros ◽  
Jorge Alberto Achcar ◽  
Josmar Mazucheli
Keyword(s):  
Censored Data ◽  
Weibull Distributions ◽  
Copula Functions ◽  
Cure Fraction

scholarly journals Cure fraction models using mixture and non-mixture models

2012 ◽  
Vol 51 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Jorge A. Achcar ◽  
Emílio A. Coelho-Barros ◽  
Josmar Mazucheli
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Mixture Models ◽  
Censored Data ◽  
Life Time ◽  
Time Data ◽  
Data Set ◽  
Cure Fraction ◽  
The Bayesian Approach

ABSTRACT We introduce the Weibull distributions in presence of cure fraction, censored data and covariates. Two models are explored in this paper: mixture and non-mixture models. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a life- time data set.

Bayesian cure fraction models with measurement error in the scale mixture of normal distribution

2020 ◽  
Vol 29 (9) ◽  
pp. 2411-2444
Author(s):  
Anna R S Marinho ◽  
Rosangela H Loschi
Keyword(s):  
Measurement Error ◽  
Normal Distribution ◽  
Measurement Errors ◽  
Error Variance ◽  
Scale Mixture ◽  
Time To Event Data ◽  
Proposed Model ◽  
Cure Fraction ◽  
Measurement Error Variance ◽  
Fraction Models

Cure fraction models have been widely used to model time-to-event data when part of the individuals survives long-term after disease and are considered cured. Most cure fraction models neglect the measurement error that some covariates may experience which leads to poor estimates for the cure fraction. We introduce a Bayesian promotion time cure model that accounts for both mismeasured covariates and atypical measurement errors. This is attained by assuming a scale mixture of the normal distribution to describe the uncertainty about the measurement error. Extending previous works, we also assume that the measurement error variance is unknown and should be estimated. Three classes of prior distributions are assumed to model the uncertainty about the measurement error variance. Simulation studies are performed evaluating the proposed model in different scenarios and comparing it to the standard promotion time cure fraction model. Results show that the proposed models are competitive ones. The proposed model is fitted to analyze a dataset from a melanoma clinical trial assuming that the Breslow depth is mismeasured.

scholarly journals A BIVARIATE GENERALIZED EXPONENTIAL DISTRIBUTION DERIVED FROM COPULA FUNCTIONS IN THE PRESENCE OF CENSORED DATA AND COVARIATES

2015 ◽  
Vol 35 (1) ◽  
pp. 165-186 ◽  
Author(s):  
Jorge Alberto Achcar ◽  
Fernando Antônio Moala ◽  
Mario Hissamitsu Tarumoto ◽  
Leandro Fernandes Coladello
Keyword(s):  
Exponential Distribution ◽  
Censored Data ◽  
Generalized Exponential Distribution ◽  
Copula Functions
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