On the relationship between the proportional hazards and accelerated failure time models in survival analysis

The slope parameters in the proportional hazards and accelerated failure time models are shown to be proportional if and only if the error variable in the accelerated failure time model has a generalized extreme value distribution. A differential equation relating the two score functions [phi](u) and [Phi](u) is established. The error distribution is characterized when [phi] (u) and [Phi](u) are linearly related; subject to this restriction, censored data linear rank procedures are studied.