scholarly journals Bayesian Estimations of Exponential Distribution Based on Interval-Censored Data with a Cure Fraction

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Al Omari Mohammed Ahmed
Keyword(s):  
Exponential Distribution ◽  
Censored Data ◽  
Bayesian Approach ◽  
Failure Time ◽  
Upper And Lower Bounds ◽  
Interval Censored Data ◽  
Squared Error ◽  
Cure Fraction ◽  
Interval Censored ◽  
The Bayesian Approach

Censored data are considered to be of the interval type where the upper and lower bounds of an event’s failure time cannot be directly observed but only determined between interval inspection times. The analyses of interval-censored data have attracted attention because they are common in the fields of reliability and medicine. A proportion of patients enrolled in clinical trials can sometimes be cured. In some instances, their symptoms mostly disappear without any recurrence of the disease. In this study, the proportion of such patients who are cured is estimated. Furthermore, the Bayesian approach under the gamma prior and maximum likelihood estimation (MLE) is used to estimate the cure fraction depending on the bounded cumulative hazard (BCH) model based on interval-censored data with an exponential distribution. The Bayesian approach uses three loss functions: squared error, linear exponential, and general entropy. These functions are compared with the MLE and used between estimators. Moreover, they are obtained using the mean squared error, which locates the best option to estimate the parameter of an exponential distribution. The results show that the BCH model and lambda parameter of the exponential distribution based on the interval-censored data can be best estimated using the Bayesian gamma prior with a positive loss function of the linear exponential.

Statistical analysis of bivariate interval-censored failure time data

2015 ◽  
Author(s):  
◽  
Qingning Zhou
Keyword(s):  
Statistical Analysis ◽  
Censored Data ◽  
Failure Time ◽  
Current Status Data ◽  
Current Status ◽  
Interval Censored Data ◽  
Time Data ◽  
Failure Times ◽  
Interval Censored ◽  
Status Data

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Interval-censored failure time data arise when the failure time of interest in a survival study is not exactly observed but known only to fall within some interval. One area that often produces such data is medical studies with periodic follow-ups, in which the medical condition of interest such as the onset of a disease is only known to occur between two adjacent examination times. An important special case of intervalcensored data is current status data which arise when each study subject is observed only once and the only information available is whether the failure event of interest has occurred or not by the observation time. The areas that often yield such data include tumorigenicity experiments and cross-sectional studies. Sometimes we refer to current status data as case I interval-censored data, and the general case as case II interval-censored data. The analysis of both case I and case II interval-censored data has recently attracted a great deal of attention and many procedures have been proposed for various issues related to it. However, there are still a number of problems that remain unsolved or lack approaches that are simpler, more efficient and apply to more general situations compared to the existing ones. This is especially the case for multivariate intervalcensored data which arise if there are multiple failure times of interest and all of them suffer intervalcensoring. This dissertation focuses on the statistical analysis for bivariate interval-censored data, including regression analysis, model selection and estimation of the association between failure times.

scholarly journals Bayesian Inference of the Weibull Model Based on Interval-Censored Survival Data

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chris Bambey Guure ◽  
Noor Akma Ibrahim ◽  
Mohd Bakri Adam
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Failure Time ◽  
Real Data ◽  
Weibull Model ◽  
Bayesian Estimator ◽  
Interval Censored Data ◽  
Weibull Parameters ◽  
Interval Censored

Interval-censored data consist of adjacent inspection times that surround an unknown failure time. We have in this paper reviewed the classical approach which is maximum likelihood in estimating the Weibull parameters with interval-censored data. We have also considered the Bayesian approach in estimating the Weibull parameters with interval-censored data under three loss functions. This study became necessary because of the limited discussion in the literature, if at all, with regard to estimating the Weibull parameters with interval-censored data using Bayesian. A simulation study is carried out to compare the performances of the methods. A real data application is also illustrated. It has been observed from the study that the Bayesian estimator is preferred to the classical maximum likelihood estimator for both the scale and shape parameters.

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