  Sensitivity Analysis is a framework to assess how conclusions drawn from
missing outcome data may be vulnerable to departures from untestable underlying
assumptions. We extend the E-value, a popular metric for quantifying robustness
of causal conclusions, to the setting of missing outcomes. With motivating
examples from partially-observed Facebook conversion events, we present
methodology for conducting Sensitivity Analysis at scale with three
contributions. First, we develop a method for the Bayesian estimation of
sensitivity parameters leveraging noisy benchmarks(e.g., aggregated reports for
protecting unit-level privacy); both empirically derived subjective and
objective priors are explored. Second, utilizing the Bayesian estimation of the
sensitivity parameters we propose a mechanism for posterior inference of the
E-value via simulation. Finally, closed form distributions of the E-value are
constructed to make direct inference possible when posterior simulation is
infeasible due to computational constraints. We demonstrate gains in
performance over asymptotic inference of the E-value using data-based
simulations, supplemented by a case-study of Facebook conversion events.
