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Bayes Estimator of Survival Probability from Randomly Censored Observations with Weibull Distribution of Time to Death
Author(s) -
Pandey M.
Publication year - 1987
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710290422
Subject(s) - statistics , mathematics , censoring (clinical trials) , estimator , weibull distribution , kaplan–meier estimator , bayes' theorem , joint probability distribution , bayes estimator , survival analysis , mean squared error , bayesian probability
This paper deals with Bayes estimation of survival probability when the data are randomly censored. Such a situation arises in case of a clinical trial which extends for a limited period T. A fixed number of patients ( n ) are observed whose times to death have identical Weibull distribution with parameters β and θ. The maximum times of observation for different patients are also independent uniform variables as the patients arrive randomly throughout the trial. For the joint prior distribution of (β, θ) as suggested by Sinha and Kale (1980, page 137) Bayes estimator of survival probability at time t (0< t < T ) has been obtained. Considering squared error loss function it is the mean of the survival probability with respect to the posterior distribution of (β, θ). This estimator is then compared with the maximum likelihood estimator, by simulation, for various values of β, θ and censoring percentage. The proposed estimator is found to be better under certain conditions.