Correlated destructive generalized power series cure rate models and associated inference with an application to a cutaneous melanoma data

2012 ◽  
Vol 56 (6) ◽  
pp. 1703-1713 ◽  
Author(s):  
Patrick Borges ◽  
Josemar Rodrigues ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Power Series ◽  
Cutaneous Melanoma ◽  
Cure Rate ◽  
Cure Rate Models ◽  
Generalized Power Series

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.

Relaxed Poisson cure rate models

2015 ◽  
Vol 58 (2) ◽  
pp. 397-415 ◽  
Author(s):  
Josemar Rodrigues ◽  
Gauss M. Cordeiro ◽  
Vicente G. Cancho ◽  
N. Balakrishnan
Keyword(s):  
Cure Rate ◽  
Cure Rate Models

Bayesian Approaches to Cure Rate Models

2005 ◽  
Author(s):  
Joseph G. Ibrahim ◽  
Ming-Hui Chen ◽  
Debajyoti Sinha
Keyword(s):  
Cure Rate ◽  
Bayesian Approaches ◽  
Cure Rate Models

On the Distribution of Sum of Independent Positive Binomial Variables

1970 ◽  
Vol 13 (1) ◽  
pp. 151-152 ◽  
Author(s):  
J. C. Ahuja
Keyword(s):  
Power Series ◽  
Inversion Formula ◽  
Probability Function ◽  
Random Variables ◽  
Random Variable ◽  
Characteristic Functions ◽  
Binomial Probability ◽  
Generalized Power Series ◽  
Alternative Derivation ◽  
Image Position

Let X1, X2, …, Xn be n independent and identically distributed random variables having the positive binomial probability function1where 0 < p < 1, and T = {1, 2, …, N}. Define their sum as Y=X1 + X2 + … +Xn. The distribution of the random variable Y has been obtained by Malik [2] using the inversion formula for characteristic functions. It appears that his result needs some correction. The purpose of this note is to give an alternative derivation of the distribution of Y by applying one of the results, established by Patil [3], for the generalized power series distribution.

scholarly journals Gradient and Likelihood Ratio Tests in Cure Rate Models

2016 ◽  
Vol 5 (4) ◽  
pp. 9 ◽  
Author(s):  
Hérica P. A. Carneiro ◽  
Dione M. Valença
Keyword(s):  
Likelihood Ratio ◽  
Asymptotic Properties ◽  
Information Matrix ◽  
Survival Models ◽  
Finite Sample ◽  
Cure Rate ◽  
Time Model ◽  
Cure Rate Models ◽  
Large Sample ◽  
Finite Samples

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently  a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we  performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.

Sign in / Sign up

Export Citation Format

Share Document