Bayesian survival model induced by frailty for lifetime with long‐term survivors

It is introduced the proportional hazards frailty model to allow a discrete distribution for the frailty variable. Frailty zero can be interpreted as being immune or cured. It is defined a class of survival models induced by a discrete frailty having a mixed Poisson distribution, which can account for unobserved dispersion. Further, a new regression to evaluate the effects of covariates in the cure fraction is constructed. Several former cure survival models are special cases of the proposed modeling framework. The inferential approach is based on Bayesian methods. Some simulation results are provided to assess the performance of the new regression. Its importance is illustrated by means of an application to colorectal cancer data.