Nonparametric binary instrumental variable analysis of competing risks data

In both observational studies and randomized trials with noncompliance, unmeasured confounding may exist which may bias treatment effect estimates. Instrumental variables (IV) are a popular technique for addressing such confounding, enabling consistent estimation of causal effects. This paper proposes nonparametric IV estimators for censored time to event data that may be subject to competing risks. A simple, plug-in estimator is introduced using nonparametric estimators of the cumulative incidence function, with confidence intervals derived using asymptotic theory. To provide an overall test of the treatment effect, an integrated weighted difference statistic is suggested, which is applicable to data with and without competing risks. Simulation studies demonstrate that the methods perform well with realistic samples sizes. The methods are applied to assess the effect of infant or maternal antiretroviral therapy on transmission of HIV from mother to child via breastfeeding using data from a large, recently completed randomized trial in Malawi where noncompliance with assigned treatment may confound treatment effect estimates.