Effect of misspecification of regression models in the analysis of survival data

The accelerated life and proportional hazards families of models are widely used in the analysis of survival data. We examine the question: if interest lies in the qualitative effect on failure of various explanatory variables, how critical is the choice of model family in assessing the relative importance of the explanatory variables? We consider small effects. When censoring is independent of the explanatory variables, to first order the regression parameters are proportional under the alternative models. This is not true when the censoring varies appreciably with the explanatory variables. Some higher-order theory is examined for the special case of the two-sample problem.