Why no additive hazards models?

The intuitively attractive additive hazards model is compared with the proportional hazards and accelerated failure time models. The lack of identifiability limits the use of the model and prevents the application of regression versions using covariates. Fortunately, data analysis based on nonhomogeneous Poisson processes or on proportional hazards is likely to yield most of the information available in the data, even though they: (1) do not necessarily represent the underlying process; and (2) even seem unlikely in certain situations. In particular, proportional hazards modeling appears very robust and requires few assumptions