A global partial likelihood estimation in the additive Cox proportional hazards model

• We propose a global partial likelihood method to estimate the additive Cox model.
• We show that the proposed estimator is consistent, asymptotically normal and achieves semiparametric efficiency bound.
• Simulation studies show that our proposed estimator has much less mean squared error than the existing methods.
• The proposed method is applied to the “nursing home” data set analyzed by Morris et al. (1994), we extra find that the gender effect is significant on the time to stay at nursing homes over all observation ages, and that the married patients older than 80 years old are less likely to stay at nursing homes. These are not identified by the existing methods.

The additive Cox model has been considered by many authors. However, the existing methods are either inefficient or their asymptotical properties are not well developed. In this article, we propose a global partial likelihood method to estimate the additive Cox model. We show that the proposed estimator is consistent and asymptotically normal. We also show that the linear functions of the estimated nonparametric components achieve semiparametric efficiency bound. Simulation studies show that our proposed estimator has much less mean squared error than the existing methods. Finally, we apply the proposed approach to the “nursing home” data set (Morris et al. 1994).