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We seek to understand the probability an individual benefits from treatment(PIBT), an inestimable quantity that must be bounded in practice. Given theinnate uncertainty in the population-level bounds on PIBT, we seek to betterunderstand the margin of error for their estimation in order to discern whetherthe estimated bounds on PIBT are tight or wide due to random chance or not.Toward this goal, we present guarantees to the estimation of bounds on marginalPIBT, with any threshold of interest, for a randomized experiment setting or anobservational setting where propensity scores are known. We also derive resultsthat permit us to understand heterogeneity in PIBT across learnable sub-groupsdelineated by pre-treatment features. These results can be used to help withformal statistical power analyses and frequentist confidence statements forsettings where we are interested in assumption-lean inference on PIBT throughthe target bounds with minimal computational complexity compared to a bootstrapapproach. Through a real data example from a large randomized experiment, wealso demonstrate how our results for PIBT can allow us to understand thepractical implication and goodness of fit of an estimate for the conditionalaverage treatment effect (CATE), a function of an individual's baselinecovariates.

High confidence inference on the probability an individual benefits from  treatment using experimental or observational data with known propensity  scores