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.

翻译：考虑灵敏度分析，以评估在具有时变治疗和协变量的纵向研究中，顺序未测量混杂下反事实结局均值及平均处理效应的最坏可能值。我们构建了多个多周期灵敏度模型，以放宽相应版本的顺序无混杂假设。其中，基本灵敏度模型仅涉及反事实结局，而联合与乘积灵敏度模型则同时涉及反事实协变量与结局。通过凸优化方法，我们建立并比较了在总体水平上仅依赖观测数据的清晰界限与保守界限的显式表达。这些结果首次实现了从横截面设置中边际灵敏度模型到纵向情境的满意推广。