This article considers an extension of the existing survival model with an immune
proportion known as a latent data (LD) model. Random effects are introduced
in this LD model. A generalized linear mixed model using a penalized quasi
likelihood approach for the parameter estimates is proposed. The model enables
the prediction of the random effect and retains the proportional hazard property
of the LD model. Application of the method is carried out on two real data
sets. A simulation study is conducted to evaluate the model’s performance. Two
different types of censoring are considered. The results show that the estimates
have relatively small bias in all cases and the method works equally well in both
the random and fixed censoring cases.