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Two problems that arise in making causal inferences for non-mortalityoutcomes such as bronchopulmonary dysplasia (BPD) are unmeasured confoundingand censoring by death, i.e., the outcome is only observed when subjectssurvive. In randomized experiments with noncompliance, instrumental variablemethods can be used to control for the unmeasured confounding without censoringby death. But when there is censoring by death, the average causal treatmenteffect cannot be identified under usual assumptions, but can be studied for aspecific subpopulation by using sensitivity analysis with additionalassumptions. However, in observational studies, evaluation of the local averagetreatment effect (LATE) in censoring by death problems with unmeasuredconfounding is not well studied. We develop a novel sensitivity analysis methodbased on instrumental variable models for studying the LATE. Specifically, wepresent the identification results under an additional assumption, and proposea three-step procedure for the LATE estimation. Also, we propose an improvedtwo-step procedure by simultaneously estimating the instrument propensity score(i.e., the probability of instrument given covariates) and the parametersinduced by the assumption. We have shown with simulation studies that thetwo-step procedure can be more robust and efficient than the three-stepprocedure. Finally, we apply our sensitivity analysis methods to a study of theeffect of delivery at high-level neonatal intensive care units on the risk ofBPD.

Sensitivity analyses for average treatment effects when outcome is censored by death in instrumental variable models