  Causal inference from observational data is crucial for many disciplines such
as medicine and economics. However, sharp bounds for causal effects under
relaxations of the unconfoundedness assumption (causal sensitivity analysis)
are subject to ongoing research. So far, works with sharp bounds are restricted
to fairly simple settings (e.g., a single binary treatment). In this paper, we
propose a unified framework for causal sensitivity analysis under unobserved
confounding in various settings. For this, we propose a flexible generalization
of the marginal sensitivity model (MSM) and then derive sharp bounds for a
large class of causal effects. This includes (conditional) average treatment
effects, effects for mediation analysis and path analysis, and distributional
effects. Furthermore, our sensitivity model is applicable to discrete,
continuous, and time-varying treatments. It allows us to interpret the partial
identification problem under unobserved confounding as a distribution shift in
the latent confounders while evaluating the causal effect of interest. In the
special case of a single binary treatment, our bounds for (conditional) average
treatment effects coincide with recent optimality results for causal
sensitivity analysis. Finally, we propose a scalable algorithm to estimate our
sharp bounds from observational data.
