Bayesian Lifetime Regression with Multi-type Group-shared Latent Heterogeneity

Products manufactured from the same batch or utilized in the same region often exhibit correlated lifetime observations due to the latent heterogeneity caused by the influence of shared but unobserved covariates. The unavailable group-shared covariates involve multiple different types (e.g., discrete, continuous, or mixed-type) and induce different structures of indispensable group-shared latent heterogeneity. Without carefully capturing such latent heterogeneity, the lifetime modeling accuracy will be significantly undermined. In this work, we propose a generic Bayesian lifetime modeling approach by comprehensively investigating the structures of group-shared latent heterogeneity caused by different types of group-shared unobserved covariates. The proposed approach is flexible to characterize multi-type group-shared latent heterogeneity in lifetime data. Besides, it can handle the case of lack of group membership information and address the issue of limited sample size. Bayesian sampling algorithm with data augmentation technique is further developed to jointly quantify the influence of observed covariates and group-shared latent heterogeneity. Further, we conduct comprehensive numerical study to demonstrate the improved performance of proposed modeling approach via comparison with alternative models. We also present empirical study results to investigate the impacts of group number and sample size per group on estimating the group-shared latent heterogeneity and to demonstrate model identifiability of proposed approach for different structures of unobserved group-shared covariates. We also present a real case study to illustrate the effectiveness of proposed approach.