Generalized Lindley Shared Frailty Based on Reversed Hazard Rate

Abstract

Due to the unavailability of complete data in various circumstances in biological, epidemiological, and medical studies, the analysis of censored data is very common among practitioners. But the analysis of bivariate censored data is not a regular mechanism because it is not necessary to always have independent data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in the data. Ignoring observed and unobserved covariates may have objectionable consequences. But it is not easy to find that whether there is any effect of the unobserved covariate or not. Shared frailty models are the viable choice to counter such scenarios. However, due to certain restrictions 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 generalized Lindley (GL) for reversed hazard rate (RHR) setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under the RHR setup. By assuming exponential Gumbel (EG) and generalized inverted exponential (GIE) baseline distributions, we propose a new class of shared frailty models based on RHR. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been performed for the comparison of models. We analyze Australian twin data and suggest a better model.