  The principal stratification has become a popular tool to address a broad
class of causal inference questions, particularly in dealing with
non-compliance and truncation-by-death problems. The causal effects within
principal strata which are determined by joint potential values of the
intermediate variable, also known as the principal causal effects, are often of
interest in these studies. Analyses of principal causal effects from observed
data in the literature mostly rely on ignorability of the treatment assignment,
which requires practitioners to accurately measure as many as covariates so
that all possible confounding sources are captured. However, collecting all
potential confounders in observational studies is often difficult and costly,
the ignorability assumption may thus be questionable. In this paper, by
leveraging available negative controls that have been increasingly used to deal
with uncontrolled confounding, we consider identification and estimation of
causal effects when the treatment and principal strata are confounded by
unobserved variables. Specifically, we show that the principal causal effects
can be nonparametrically identified by invoking a pair of negative controls
that are both required not to directly affect the outcome. We then relax this
assumption and establish identification of principal causal effects under
various semiparametric or parametric models. We also propose an estimation
method of principal causal effects. Extensive simulation studies show good
performance of the proposed approach and a real data application from the
National Longitudinal Survey of Young Men is used for illustration.
