  Consider sensitivity analysis to assess the worst-case possible values of
counterfactual outcome means and average treatment effects under sequential
unmeasured confounding in a longitudinal study with time-varying treatments and
covariates. We formulate several multi-period sensitivity models to relax the
corresponding versions of the assumption of sequential unconfounding. The
primary sensitivity model involves only counterfactual outcomes, whereas the
joint and product sensitivity models involve both counterfactual covariates and
outcomes. We establish and compare explicit representations for the sharp and
conservative bounds at the population level through convex optimization,
depending only on the observed data. These results provide for the first time a
satisfactory generalization from the marginal sensitivity model in the
cross-sectional setting.
