Title: Collapsible Cox-regression and non-collapsible Aalen additive hazards regression
Authors: Sven Ove Samuelsen - University of Oslo (Norway) [presenting]
Abstract: It is well-known that the additive hazards model is collapsible, in the sense that when omitting one covariate from a model with two independent covariates, the marginal model is still an additive hazards model with the same regression coefficient. In contrast, for the proportional hazards model under the same covariate assumption, the marginal model is no longer a proportional hazards model and is not collapsible. These results, however, relate to the model specification and not to the regression estimates. We point out that if covariates in risk sets at all event times are independent then both Cox and Aalen regression estimates are collapsible, in the sense that there is no systematic change in the parameter estimates. Vice-versa, if this assumption fails, then the estimates will change systematically both for Cox and Aalen regression. In particular, if the data are generated by an Aalen model with censoring independent of covariates both Cox and Aalen regression is collapsible, but if generated by a proportional hazards model neither estimators are. We will also discuss settings where survival times are generated by proportional hazards models with censoring and truncation patterns providing uncorrelated covariates and hence collapsible Cox and Aalen regression estimates.