Shared frailty model (${\lambda }_{ik}(t)=Y_{ik}(t)V_i{h}_{0k}(t)e^{z_i^{\mathsf{T}}\beta }$)

A shared frailty model assigns the same latent positive hazard multiplier $V_i$ to correlated event histories or group members. Gamma or lognormal frailty distributions are common examples. Modeling dependence through this latent effect yields conditional covariate effects; integrating out frailty can change the form of marginal hazards. Eligibility and event history still have to be encoded in the at-risk indicator.