On adjustment for auxiliary covariates in additive hazard models for the analysis of randomized experiments

We consider additive hazard models (Aalen, 1989) for the effect of a randomized treatment on a survival outcome, adjusting for auxiliary baseline covariates. We demonstrate that the Aalen least squares estimator of the treatment effect parameter is asymptotically unbiased, even when the hazard's dependence on time or on the auxiliary covariates is misspecified, and even away from the null hypothesis of no treatment effect. We moreover show that adjustment for auxiliary baseline covariates does not change the asymptotic variance of the Aalen least squares estimator of the effect of a randomized treatment. We conclude that, in view of its robustness against model misspecification, Aalen least squares estimation is attractive for evaluating treatment effects on a survival outcome in randomized experiments, and that the primary reasons to consider baseline covariate adjustment in such settings may be the interest in subgroup effects, or the need to adjust for informative censoring or for baseline imbalances. Our results also shed light on the robustness of Aalen least squares estimators against model misspecification in observational studies.