  Two problems that arise in making causal inferences for non-mortality
outcomes such as bronchopulmonary dysplasia (BPD) are unmeasured confounding
and censoring by death, i.e., the outcome is only observed when subjects
survive. In randomized experiments with noncompliance, instrumental variable
methods can be used to control for the unmeasured confounding without censoring
by death. 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, in observational studies, evaluation of the local average
treatment effect (LATE) in censoring by death problems with unmeasured
confounding is not well studied. We develop a novel sensitivity analysis method
based on instrumental variable 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
(i.e., the probability of instrument given covariates) and the parameters
induced by the assumption. We have shown 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 of the
effect of delivery at high-level neonatal intensive care units on the risk of
BPD.
