Abstract
The time to event or survival time usually follows certain skewed probability distributions. These distributions encounter vital role using the Bayesian framework to analyze and project the maximum life expectancy in order to inform decision-making. The Bayesian method provides a flexible framework for monitoring the randomized clinical trials to update what is already known using prior information about specific phenomena under uncertainty. Additionally, medical practitioners can use the Bayesian estimators to measure the probability of time until tumor recurrence, time until cardiovascular death, and time until AIDS for HIV patients by considering the prior information. However, in clinical trials and medical studies, censoring is present when an exact event occurrence time is not known. The present study aims to estimate the parameters of Gumbel type-II distribution based on the type-II censored data using the Bayesian framework. The Bayesian estimators cannot be obtained in explicit forms, and therefore we use Lindley’s approximation based on noninformative prior and various loss functions such as squared error loss function, general entropy loss function, and LINEX (linear exponential) loss function. The maximum likelihood and Bayesian estimators are compared in terms of mean squared error by using the simulation study. Furthermore, two data sets about remission times (in months) of bladder cancer patients and survival times in weeks of 61 patients with inoperable adenocarcinoma of the lung are analyzed for illustration purposes.
Highlights
In medical research, data supporting the time until the occurrence of a particular event, such as the death of a patient, are frequently encountered
From the results of the simulation study, conclusions are drawn regarding the behavior of the estimators, which are summarized as follows: (i) In terms of mean squared error (MSE), the ML and Bayesian estimators become closer by increasing the sample sizes
Medical data are generally skewed to the right, and positively skewed distributions can be most suitable for describing unimodal medical data
Summary
Data supporting the time until the occurrence of a particular event, such as the death of a patient, are frequently encountered Such data are referred to as survival time data which has generally right-skewed distribution, and Gumbel type-II distribution can be used for this purpose. Erefore, generally, such experiments are preplanned and purposeful to save time and cost of these testing Data obtained from such experiments are called censored. Abbas et al [6] worked on Gumbel type-II distribution and obtained the Bayes estimators under different loss functions. Sultana et al [9] worked on a threecomponent mixture of Gumbel type-II distribution using Bayesian estimation under different priors such as informative and noninformative.
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