| Summary: | Survival data often arise in longitudinal studies, and the survival process and the longitudinal process may be related to each other. Thus, it is desirable to jointly model the survival process and the longitudinal process to avoid possible biased and inefficient inferences from separate inferences. We consider mixed effects models (LME, GLMM, and NLME models) for the longitudinal process, and Cox models and accelerated failure time (AFT) models for the survival process. The survival model and the longitudinal model are linked through shared parameters or unobserved variables. We consider joint likelihood method and two-step methods to make joint inference for the survival model and the longitudinal model. We have proposed linear approximation methods to joint models with GLMM and NLME submodels to reduce computation burden and use existing software. Simulation studies are conducted to evaluate the performances of the joint likelihood method and two-step methods. It is concluded that the joint likelihood method outperforms the two-step methods.
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