Inference on the mixed effect additive-multiplicative hazard model for clustered failure time data

In survival analysis, data from different hospital or treatment center may be collected. The individuals from the same hospital are grouped into a cluster, and they have similarity. An additive-multiplicative hazard model was developed for the clustered failure time. A mixed effect was added to the model denoting the correlation among the cluster. The individuals in the same cluster share the same effect. Estimating equation method was applied to obtainthe estimator. Asymptotic properties were given and proved. Some simulation was conducted to verify the performance of the estimate under the finite sample. Real data was illustrated using the model and the proposed method.