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

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Abstract
Two problems that arise in making causal inferences for nonmortality outcomes such as bronchopulmonary dysplasia (BPD) are unmeasured confounding and censoring by death, ie, the outcome is observed only when subjects survive. In randomized experiments with noncompliance and no censoring by death, instrumental variable (IV) methods can be used to control for the unmeasured confounding. But, when there is censoring by death, the average causal treatment effect cannot be identified under usual assumptions but can be studied for a specific subpopulation by using sensitivity analysis with additional assumptions. However, evaluating the local average treatment effect (LATE) in observational studies with censoring by death problems while controlling for unmeasured confounding is not well studied. We develop a novel sensitivity analysis method based on IV models for studying the LATE. Specifically, we present the identification results under an additional assumption and propose a three‐step procedure for the LATE estimation. Also, we propose an improved two‐step procedure by simultaneously estimating the instrument propensity score (ie, the probability of instrument given covariates) and the parameters induced by the assumption. We show with simulation studies that the two‐step procedure can be more robust and efficient than the three‐step procedure. Finally, we apply our sensitivity analysis methods to a study on the effect of delivery at high‐level neonatal intensive care units on the risk of BPD.

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