Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks of disease and death. The shared frailty models have been suggested to analyze the bivariate data on related survival times (e.g., matched pairs experiments, twin or family data). This paper introduces the shared Inverse Gaussian (IG) frailty model with baseline distribution as Weibull exponential, Lomax, and Logistic exponential. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the actual values of the parameters with the estimated values. Also, we apply these models to a real-life bivariate survival data set of McGilchrist and Aisbett [1] related to the kidney infection data, and a better model is suggested for the data.
Keywords:
Bayesian model comparison, Inverse gaussian frailty, Lomax distribution, Logistic exponential distribution, MCMC, Shared frailty, Weibull exponential distribution.
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Authors:Bentham Science Books