  We propose a model-free framework for sensitivity analysis of individual
treatment effects (ITEs), building upon ideas from conformal inference. For any
unit, our procedure reports the $\Gamma$-value, a number which quantifies the
minimum strength of confounding needed to explain away the evidence for ITE.
Our approach rests on the reliable predictive inference of counterfactuals and
ITEs in situations where the training data is confounded. Under the marginal
sensitivity model of Tan (2006), we characterize the shift between the
distribution of the observations and that of the counterfactuals. We first
develop a general method for predictive inference of test samples from a
shifted distribution; we then leverage this to construct covariate-dependent
prediction sets for counterfactuals. No matter the value of the shift, these
prediction sets (resp. approximately) achieve marginal coverage if the
propensity score is known exactly (resp. estimated). We describe a distinct
procedure also attaining coverage, however, conditional on the training data.
In the latter case, we prove a sharpness result showing that for certain
classes of prediction problems, the prediction intervals cannot possibly be
tightened. We verify the validity and performance of the new methods via
simulation studies and apply them to analyze real datasets.
