  We study user sentiment (reported via optional surveys) as a metric for fully
randomized A/B tests. Both user-level covariates and treatment assignment can
impact response propensity. We propose a set of consistent estimators for the
average and local treatment effects on treated and respondent users. We show
that our problem can be mapped onto the intersection of the missing data
problem and observational causal inference, and we identify conditions under
which consistent estimators exist. We evaluate the performance of estimators
via simulation studies and find that more complicated models do not necessarily
provide superior performance.
