scholarly journals Composite partial likelihood estimation for length-biased and right-censored data with competing risks

2016 ◽  
Vol 149 ◽  
pp. 160-176 ◽  
Author(s):  
Feipeng Zhang ◽  
Heng Peng ◽  
Yong Zhou
Keyword(s):  
Competing Risks ◽  
Censored Data ◽  
Likelihood Estimation ◽  
Partial Likelihood ◽  
Right Censored Data

scholarly journals A Modified Chi-square Type Test Statistic for the Double Burr X Model with Applications to Right Censored Medical and Reliability Data

2021 ◽  
pp. 615-623
Author(s):  
Khaoula Aidi ◽  
Nadeem Shafique Butt ◽  
Mir Masoom Ali ◽  
Mohamed Ibrahim ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
The Right

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

scholarly journals Giniinc: A Stata Package for Measuring Inequality from Incomplete Income and Survival Data

2018 ◽  
Vol 18 (3) ◽  
pp. 692-715
Author(s):  
Long Hong ◽  
Guido Alfani ◽  
Chiara Gigliarano ◽  
Marco Bonetti
Keyword(s):  
Censored Data ◽  
Survival Data ◽  
Gini Index ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Right Censoring ◽  
Parametric Models ◽  
Test Statistic ◽  
Right Censored Data ◽  
Nonparametric Bounds

Often, observed income and survival data are incomplete because of left- or right-censoring or left- or right-truncation. Measuring inequality (for instance, by the Gini index of concentration) from incomplete data like these will produce biased results. We describe the package giniinc, which contains three independent commands to estimate the Gini concentration index under different conditions. First, survgini computes a test statistic for comparing two (survival) distributions based on the nonparametric estimation of the restricted Gini index for right-censored data, using both asymptotic and permutation inference. Second, survbound computes nonparametric bounds for the unrestricted Gini index from censored data. Finally, survlsl implements maximum likelihood estimation for three commonly used parametric models to estimate the unrestricted Gini index, both from censored and truncated data. We briefly discuss the methods, describe the package, and illustrate its use through simulated data and examples from an oncology and a historical income study.

scholarly journals Simulation of generalized Gamma distribution with maximum likelihood estimation and expectation-maximization algorithm on right censored data type 1

2021 ◽  
Vol 10 (3) ◽  
pp. 415-424
Author(s):  
Dian Kurniasari ◽  
Warsono Warsono ◽  
Nourma Indryani ◽  
Mustofa Usman ◽  
Sutopo Hadi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Gamma Distribution ◽  
Expectation Maximization ◽  
Likelihood Estimation ◽  
Right Censored Data ◽  
Generalized Gamma Distribution ◽  
Generalized Gamma

The Generalized Gamma distribution is very suitable for modeling data with various forms of hazard (risk) functions, which makes the Generalized Gamma distribution useful in survival analysis. Survival analysis aims are to predict chances of survival, disease recurrence, death, and other events over a period of time. One characteristic of survival data is the possibility of sensors. Let X be the life span of the person being studied and the right censorship time of Cr, X is assumed to be independent with the probability density function f(x), the survival function S(x), and the hazard function h(x). A person's X life span will be known if X is less than or equal to Cr. If X is greater than Cr, the individual X survives or is censored right now. Statistical inference, especially parameter estimation is needed in analyzing empirical data. Obviously the estimation results obtained are expected to be a good estimator, namely to meet the nature of unbiased and minimum variance. This paper will discuss the results of the estimation of Generalized Gamma distribution parameters with type 1 right censored data through simulations using the Expectation Maximization method and the Maximum Likelihood Estimation method. The simulation is conducted by generating data with the sample size: 25, 50, 100, 200, 500, 1000, 1500 and 2000 as well as determining censored data of 10%, 20% and 30% by first setting the parameters used which are obtained from the data of patients with gastric cancer namely α = 1.0649, β = 1,072, θ = 59.766. Based on the results obtained from the simulations on the two estimation methods that the parameter estimation using the Maximum Likelihood Estimation method is better than the Expectation Maximization method because it provides a smaller bias and MSE value where the larger the sample size used, the estimated parameter value will get closer to the parameter in fact. In addition, the Expectation Maximization method can also be used as an alternative estimation of generalized gamma distribution parameters with type 1 right censored data because it has a bias value and MSE approaching the MLE method.

scholarly journals Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction

2021 ◽  
pp. 106-112
Author(s):  
Dr. Al Omari Mohammed Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Censored Data ◽  
Loss Function ◽  
Bayesian Approach ◽  
Likelihood Estimation ◽  
Right Censored Data ◽  
Squared Error Loss Function ◽  
Linex Loss ◽  
Cure Fraction

This paper is focused on estimating the parameter of Exponential distribution under right-censored data with cure fraction. The maximum likelihood estimation and Bayesian approach were used. The Bayesian method is implemented using gamma, Jeffreys, and extension of Jeffreys priors with two loss functions, which are; squared error loss function and Linear Exponential Loss Function (LINEX). The methods of the Bayesian approach are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) to determine the best for estimating the parameter of Exponential distribution under right-censored data with cure fraction. The results show that the Bayesian with gamma prior under LINEX loss function is a better estimation of the parameter of Exponential distribution with cure fraction based on right-censored data.

An Actuarial Survey of Statistical Models for Decrement and Transition Data, II. Competing Risks, Non-Parametric and Regression Models

1996 ◽  
Vol 2 (2) ◽  
pp. 429-448 ◽  
Author(s):  
A.S. Macdonald
Keyword(s):  
Competing Risks ◽  
Survival Data ◽  
Statistical Models ◽  
Regression Models ◽  
Cox Model ◽  
Likelihood Estimation ◽  
Partial Likelihood ◽  
Kaplan Meier ◽  
Non Parametric

ABSTRACTThis paper surveys some statistical models of survival data. Competing risks models are described; the unidentifiability of net decrements suggests a sceptical approach to the use of underlying single decrement tables. Approaches based on observations of complete lifetimes (with censoring) are surveyed including the Kaplan-Meier and Nelson-Aalen estimates. Regression models for lifetimes depending on covariates are discussed, in particular the Cox model and partial likelihood estimation.

scholarly journals Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction

2021 ◽  
pp. 467-481
Author(s):  
Jorge Alberto Achcar ◽  
Edson Zangiacomi Martinez ◽  
Bruno Caparroz Lopes de Freitas ◽  
Marcos Vinicius de Oliveira Peres
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Weibull Model ◽  
Data Sets ◽  
Right Censored Data ◽  
Extensive Simulation ◽  
Proposed Model ◽  
Cure Fraction

In this paper, we introduce maximum likelihood and Bayesian parameter estimation for the exponentiated discrete Weibull (EDW) distribution in presence of randomly right censored data. We also consider the inclusion of a cure fraction in the model. The performance of the maximum likelihood estimation approach is assessed by conducting an extensive simulation study with different sample sizes and different values for the parameters of the EDW distribution. The usefuness of the proposed model is illustrated with two examples considering real data sets.

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