Estimating the causal effect of treatment in observational studies with survival time end points and unmeasured confounding

Estimation of the effect of a treatment in the presence of unmeasured confounding is a common objective in observational studies. The two-stage least squares instrumental variables procedure is frequently used but is not applicable to time-to-event data if some observations are censored. We develop a simultaneous equations model to account for unmeasured confounding of the effect of treatment on survival time subject to censoring. The identification of the treatment effect is assisted by instrumental variables (variables related to treatment but conditional on treatment, not to the outcome) and the assumed bivariate distribution underlying the data-generating process. The methodology is illustrated on data from an observational study of time to death following endovascular or open repair of ruptured abdominal aortic aneurysms. As the instrumental variable and the distributional assumptions cannot be jointly assessed from the observed data, we evaluate the sensitivity of the results to these assumptions.