A semiparametric model for the cause-specific hazard under risk proportionality

Semiparametric Cox proportional hazards models enjoy great popularity in empirical survival analysis. A semiparametric model for cause-specific hazards under a proportionality restriction across risks is considered, which has desired practical properties such as estimation by partial likelihood and an analytical solution for the copula-graphic estimator. The cause-specific and marginal hazards are shown to share functional form restrictions in this case. The model for the cause-specific hazard can be used for inference about parametric restrictions on the marginal hazard without the risk of misspecifying the latter and without knowing the risk dependence. After the class of parametric marginal hazards has been determined, it can be estimated in conjunction with the degree of risk dependence. Finite sample properties are investigated with simulations. An application to employment duration demonstrates the practicality of the approach.