Frailty-Augmented Logistic-Weighted Lomax Mixture regression for survival analysis

We propose the Frailty-Augmented Logistic-Weighted Lomax Mixture (F-LLoM), a finite-mixture survival model that combines gamma frailty within components with covariate-dependent multinomial logistic mixing weights. After integrating out the frailty, each component follows a Lomax (Pareto II) distribution, enabling flexible modeling of heavy-tailed survival times and latent heterogeneity, while covariates affect both tier membership and within-tier hazard scales. We derive identifiability conditions, moment expressions, and tail properties, and develop a censoring-aware expectation–maximization (EM) algorithm for right-censored data. In simulation studies with sample sizes between 500 and 1000 and censoring rates up to 20%, the Bayesian information criterion consistently selected the true number of components, and the EM algorithm showed stable convergence with well-calibrated predictions. An application to the Rossi recidivism dataset illustrates the practical implementation of the model and favors a parsimonious specification. The proposed framework provides a practical and interpretable approach for analyzing heterogeneous and heavy-tailed survival data.