Bayesian survival modeling with mixtures of inverse Gaussian frailties

We introduce a Bayesian framework for survival analysis that integrates frailty and mixture modeling. In our approach, a mixture of two inverse Gaussian (MIG) distributions is used as the frailty variable for bivariate failure times. The parameterization of the mixture directly specifies the mixing weights, and the Laplace transform is obtained in closed form, which facilitates efficient computation. Flexible baseline distributions are modeled using the generalized Weibull and generalized log-logistic families. Parameter estimation is performed in a fully Bayesian setting using Markov chain Monte Carlo (MCMC) algorithms, allowing for uncertainty quantification. The proposed methodology is illustrated through an analysis of a kidney dataset, where the use of MIG frailties results in improved model fit and predictive performance relative to conventional approaches.