Weighted Lindley Shared Regression Model for Bivariate Left Censored Data

Shikhar Tyagi (), Arvind Pandey () and Christophe Chesneau ()
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Shikhar Tyagi: Central University of Rajasthan
Arvind Pandey: Central University of Rajasthan
Christophe Chesneau: Université de Caen Normandie, LMNO

Sankhya B: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 9, 655-682

Abstract: Abstract Due to the lack of complete data in biological, epidemiological, and medical studies, analysis of censored data is very common among researchers. But analysis of bivariate censored data is not a regular mechanism. Because it is not necessary to always have independent bivariate data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in data. Ignoring observed and unobserved covariates could have negative consequences. But it is not easy to find out whether there is any effect of unobserved covariate or not. Shared frailty models are the viable choice to counter such a scenario. However, due to certain constraints such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty distribution weighted Lindley for reversed hazard rate setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under reversed hazard rate setup. Generalized exponential and exponential Gumbel baseline distributions are proposed as a useful tool for ensuring the effect of unobserved heterogeneity. The Bayesian paradigm of Markov Chain Monte Carlo methodology with flat and informative prior under different loss functions is used to estimate the model parameters. Subsequently, model comparisons are performed using Bayesian comparison techniques. The popular Australian twin data set is used to illustrate the results and to demonstrate that better models are recommended.

Keywords: Bayesian estimation; exponential Gumbel distribution; generalized exponential distribution; left censoring; Markov chain Monte Carlo; reversed hazard rate; weighted Lindley frailty.; Primary 62F10, 62F15; Secondary 62J02, 62H10, 62N02 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13571-022-00278-1

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