Long-term survivor model with bivariate random effects: applications to bone marrow transplant and carcinoma study...

Cured patients (or the so-called long-term survivors) are increasingly being observed in clinical trial studies. As exemplified in two data sets, the bone marrow transplantation study for leukaemia patients and the multi-centre study for patients with carcinoma in the oropharynx, a considerable portion of the patients in these studies are deemed to be cured. With the presence of random hospital/centre effects, a long-term survivor model with bivariate random effects is proposed to analyse clustered survival data with a possible portion of cured patients. This model extends earlier work by allowing random effects in both the cured fraction and the hazard function parts to follow a bivariate normal distribution, which gives a generalized model with an additional correlation parameter governing the relationship between the recovery probability and the instantaneous failure rate due to the hospital/centre effects. By adopting the GLMM formulation, random effects are incorporated in the model via the linear predictor terms. REML estimation of parameters is achieved via the EM algorithm. Application to the two sets of data illustrates the usefulness of the proposed model. A simulation study is conducted to assess the performance of the estimators, under the proposed numerical estimation scheme.