Estimation of causal effects using instrumental variables with
nonignorable missing covariates: Application to effect of type of delivery
NICU on premature infants
Understanding how effective high-level NICUs (neonatal intensive care units
that have the capacity for sustained mechanical assisted ventilation and high
volume) are compared to low-level NICUs is important and valuable for both
individual mothers and for public policy decisions. The goal of this paper is
to estimate the effect on mortality of premature babies being delivered in a
high-level NICU vs. a low-level NICU through an observational study where there
are unmeasured confounders as well as nonignorable missing covariates. We
consider the use of excess travel time as an instrumental variable (IV) to
control for unmeasured confounders. In order for an IV to be valid, we must
condition on confounders of the IV---outcome relationship, for example, month
prenatal care started must be conditioned on for excess travel time to be a
valid IV. However, sometimes month prenatal care started is missing, and the
missingness may be nonignorable because it is related to the not fully measured
mother's/infant's risk of complications. We develop a method to estimate the
causal effect of a treatment using an IV when there are nonignorable missing
covariates as in our data, where we allow the missingness to depend on the
fully observed outcome as well as the partially observed compliance class,
which is a proxy for the unmeasured risk of complications. A simulation study
shows that under our nonignorable missingness assumption, the commonly used
estimation methods, complete-case analysis and multiple imputation by chained
equations assuming missingness at random, provide biased estimates, while our
method provides approximately unbiased estimates. We apply our method to the
NICU study and find evidence that high-level NICUs significantly reduce deaths
for babies of small gestational age, whereas for almost mature babies like 37
weeks, the level of NICUs makes little difference. A sensitivity analysis is
conducted to assess the sensitivity of our conclusions to key assumptions about
the missing covariates. The method we develop in this paper may be useful for
many observational studies facing similar issues of unmeasured confounders and
nonignorable missing data as ours.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS699 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
