A shared frailty regression model for clustered survival data.

This article introduces a novel frailty model for multivariate survival data based on a mixture of two inverse Gaussian (IG) distributions, termed the MIG (mixture inverse Gaussian) frailty model. The MIG model offers advantages over existing frailty models by explicitly parameterizing the mixture weights, providing closed-form Laplace transforms, and enabling straightforward estimation via an expectation-maximization (EM) algorithm. The model's performance is evaluated through Monte Carlo simulations and applied to two medical datasets involving lobular breast cancer and colorectal cancer, demonstrating improved fit and better capture of unobserved heterogeneity compared to gamma, IG, and weighted Lindley frailty models. Flexible parametric baseline hazard functions, such as piecewise exponential models, further enhance the model's applicability, with results indicating significant effects of clinical and treatment covariates on survival and rehospitalization risks.