Semi-parametric additive risk models: application to injury duration study.

In survival analysis, the Cox model is a multiplicative model and widely used in survival analysis. However, the assumption of proportional hazards in the Cox multiplicative model is a crucial one that needs to be fulfilled for the results to be meaningful. When proportionality is a questionable assumption, an alternative but less widely used method is additive model. The additive hazards model assumes that covariates act in an additive manner on an unknown baseline hazard rate. Using the emergency department (ED) visits data, we demonstrated the additive hazards regression models and showed the differences in estimates obtained by the additive hazards models and the Cox model. In our study, the Cox model gave a higher estimate than the additive hazards model. However, both models revealed similar results with regard to covariates selected to remain in the model and the estimated survival functions based on the Cox and additive hazards models were almost identical. Since Cox and additive hazards models give different aspects of the association between risk factors and the study outcome, it seems desirable to use together to give a more comprehensive understanding of data.