Bayesian Estimation in Shared Compound Negative Binomial Frailty Models

ABSTRACT Frailty models are used in survival analysis to model unobserved heterogeneity. To study such heterogeneity by the inclusion of a random term called the frailty is assumed to multiply hazards of all subjects in the shared frailty. We study compound negative binomial distribution as frailty distribution and two different baseline distributions namely Pareto and linear failure rate distribution in this paper. A simulation study is done to compare the true values of parameters with the estimated value. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters of the proposed models. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better model

Modeling survival data using frailty models

This book presents the basic concepts of survival analysis and frailty models, covering both fundamental and advanced topics. It focuses on applications of statistical tools in biology and medicine, highlighting the latest frailty-model methodologies and applications in these areas. After explaining the basic concepts of survival analysis, the book goes on to discuss shared, bivariate, and correlated frailty models and their applications. It also features nine datasets that have been analyzed using the R statistical package. Covering recent topics, not addressed elsewhere in the literature, this book is of immense use to scientists, researchers, students and teachers

Modelling heterogeneity for bivariate survival data by the log-normal distribution

We propose a bivariate Weibull regression model with heterogeneity (frailty or random effect) which is generated by log-normal distribution. We assume that the bivariate survival data follow bivariate Weibull of [Hanagal, D.D., 2004. Parametric bivariate regression analysis based on censored samples: A Weibull model. Economic Quality Control 19, 83--90]. There are some interesting situations like survival times in genetic epidemiology, dental implants of patients and twin births (both monozygotic and dizygotic) where genetic behaviour (which is unknown and random) of patients follows known frailty distribution. These are the situations which motivate to study this particular model. We propose two-stage maximum likelihood estimation for hierarchical likelihood in the proposed model. We present a small simulation study to compare these estimates with the true value of the parameters and it is observed that these estimates are very close to the true values of the parameters. We also compare theoretical standard errors with Monte Carlo standard errors and theoretical coverage probabilities with Monte Carlo coverage probabilities.

Bivariate Weibull regression model based on censored samples

Bivariate Weibull model, Parametric regression, Survival times,

Some inference results in an absolutely continuous multivariate exponential model of Block

In this paper, we obtain MLEs of the parameters and of large sample test for testing independence and symmetry of k components in the k + 1 parameter version of an absolutely continuous multivariate exponential distribution (ACMVED) of Block (1975).ACMVED Fisher information GLRT MLE

Software reliability growth models

This book presents the basic concepts of software reliability growth models (SRGMs), ranging from fundamental to advanced level. It discusses SRGM based on the non-homogeneous Poisson process (NHPP), which has been a quite successful tool in practical software reliability engineering. These models consider the debugging process as a counting process characterized by its mean value function. Model parameters have been estimated by using either the maximum likelihood method or regression. NHPP SRGMs based on inverse Weibull, generalized inverse Weibull, extended inverse Weibull, generalized extended inverse Weibull, and delayed S-shaped have been focused upon. Review of literature on SRGM has been included from the scratch to recent developments, applicable in artificial neural networks, machine learning, artificial intelligence, data-driven approaches, fault-detection, fault-correction processes, and also in random environmental conditions. This book is designed for practitioners and researchers at all levels of competency, and also targets groups who need information on software reliability engineering

Generalised Lindley shared additive frailty regression model for bivariate survival data

Frailty models are the possible choice to counter the problem of the unobserved heterogeneity in individual risks of disease and death. Based on earlier studies, shared frailty models can be utilised in the analysis of bivariate data related to survival times (e.g. matched pairs experiments, twin or family data). In this article, we assume that frailty acts additively to the hazard rate. A new class of shared frailty models based on generalised Lindley distribution is established. By assuming generalised Weibull and generalised log-logistic baseline distributions, we propose a new class of shared frailty models based on the additive hazard rate. 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 applied for the comparison of models. We analyse kidney infection data and suggest the best model