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Title: Comparison between the marginal hazard models and sub-distribution hazard models with an assumed copula Authors:  Takeshi Emura - Chang Gung University (Taiwan) [presenting]
Jia-Han Shih - National Central University (Taiwan)
Il Do Ha - Pukyong National University (Korea, South)
Abstract: For analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, different types of the Cox model have been proposed to estimate the effect of covariates on each of the three different hazard functions. Many authors studied the difference between the cause-specific hazard and the sub-distribution hazard. However, the study on the marginal hazard function is limited partly due to its model identifiability issue. We apply the assumed copula approach to deal with the model identifiability issue, and compare between the sub-distribution hazard and the marginal hazard function. We establish the mathematical relationship between the two hazard functions by using an assumed copula. We then extend our results to clustered semi-competing risks data. We implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package. We analyze four datasets for illustration.