  Instrumental variables (IV) are a useful tool for estimating causal effects
in the presence of unmeasured confounding. IV methods are well developed for
uncensored outcomes, particularly for structural linear equation models, where
simple two-stage estimation schemes are available. The extension of these
methods to survival settings is challenging, partly because of the nonlinearity
of the popular survival regression models and partly because of the
complications associated with right censoring or other survival features. We
develop a simple causal hazard ratio estimator in a proportional hazards model
with right censored data. The method exploits a special characterization of IV
which enables the use of an intuitive inverse weighting scheme that is
generally applicable to more complex survival settings with left truncation,
competing risks, or recurrent events. We rigorously establish the asymptotic
properties of the estimators, and provide plug-in variance estimators. The
proposed method can be implemented in standard software, and is evaluated
through extensive simulation studies. We apply the proposed IV method to a data
set from the Prostate, Lung, Colorectal and Ovarian cancer screening trial to
delineate the causal effect of flexible sigmoidoscopy screening on colorectal
cancer survival which may be confounded by informative noncompliance with the
assigned screening regimen.
