Information Bounds for the Conditional Hazard Ratio in a Nested Family of Regression Models

Information bounds are obtained for a parametric treatment effect in a nested family of models for the conditional distribution of survival given confounding variables. The family extends from the fully parametric Weibull model to a completely nonparametric model for right-censored data and includes the Cox model and the stratified version of it. It is shown that, in certain special cases, there is no loss of information about the treatment effect when going from a fully parametric to a nonparametric specification of the conditional hazard function