  We present two methods for bounding the probabilities of benefit and harm
under unmeasured confounding. The first method computes the (upper or lower)
bound of either probability as a function of the observed data distribution and
two intuitive sensitivity parameters which, then, can be presented to the
analyst as a 2-D plot to assist her in decision making. The second method
assumes the existence of a measured nondifferential proxy (i.e., direct effect)
of the unmeasured confounder. Using this proxy, tighter bounds than the
existing ones can be derived from just the observed data distribution.
