  Estimating an individual treatment effect (ITE) is essential to personalized
decision making. However, existing methods for estimating the ITE often rely on
unconfoundedness, an assumption that is fundamentally untestable with observed
data. To assess the robustness of individual-level causal conclusion with
unconfoundedness, this paper proposes a method for sensitivity analysis of the
ITE, a way to estimate a range of the ITE under unobserved confounding. The
method we develop quantifies unmeasured confounding through a marginal
sensitivity model [Ros2002, Tan2006], and adapts the framework of conformal
inference to estimate an ITE interval at a given confounding strength. In
particular, we formulate this sensitivity analysis problem as a conformal
inference problem under distribution shift, and we extend existing methods of
covariate-shifted conformal inference to this more general setting. The result
is a predictive interval that has guaranteed nominal coverage of the ITE, a
method that provides coverage with distribution-free and nonasymptotic
guarantees. We evaluate the method on synthetic data and illustrate its
application in an observational study.
