A study on comparisons of additive regression frailty models to counter heterogeneity: Bayesian strategies and case study

Historically, the primary goal of conventional survival study methods has been to reduce the frequency of failures over time. If the associated observed and unobserved variables are not known when studying such events, this can have detrimental effects. Frailty models offer a tempting solution for investigating the impact of unknown variables in such a case. In this article, we assume that frailty affects the hazard rate. We find that the weighted Lindley frailty models, which use general versions of the Weibull and log-logistic type II distributions as the baseline distributions, are a reliable method for ensuring the influence of endogenous variability. The parameters involved are estimated according to different loss functions using the Bayesian structure as the basis of Markov Chain Monte Carlo. Bayesian evaluation strategies are then implemented to evaluate the models. The results are demonstrated on known data of kidney infections. It is shown that the novel models outperform those based on the inverse Gaussian and gamma frailty distributions.