We consider the model selection problem of the dependency between the?terminal event and the non-terminal event under semi-competing risks data. When the relationship between the two events is unspecified, the inference on the non-terminal event is not identifiable. We cannot make inference on the non-terminal event without extra assumptions. Thus, an association model for?semi-competing risks data is necessary, and it is important to select an appropriate dependence model for a data set. We construct the likelihood function for semi-competing risks data to select an appropriate dependence model. From?simulation studies, it shows the performance of the proposed approach is well. Finally, we apply our method to a bone marrow transplant data set.
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