Sensitivity of the hazard ratio to nonignorable treatment assignment in an observational study

In non-randomized studies, estimation of treatment effects generally requires adjustment for imbalances in observed covariates. One such method, based on the propensity score, is useful in many applications but may be biased when the assumption of strongly ignorable treatment assignment is violated. Because it is not possible to evaluate this assumption from the data, it is advisable to assess the sensitivity of conclusions to violations of strong ignorability. Lin et al. (Biomet. 1998; 54:948-963) have implemented this idea by investigating how an unmeasured covariate may affect the conclusions of an observational study. We extend their method to assess sensitivity of the treatment hazard ratio to hidden bias under a range of covariate distributions. We derive simple formulas for approximating the true from the apparent treatment hazard ratio estimated under a specific survival model, and assess the validity of these formulas in simulation studies. We demonstrate the method in an analysis of SEER-Medicare data on the effects of chemotherapy in elderly colon cancer patients.