Sensitivity models and bounds under sequential unmeasured confounding in longitudinal studies

TL;DR

This paper develops new sensitivity models and bounds for assessing the impact of unmeasured confounding in longitudinal studies with time-varying treatments, using convex optimization to derive explicit bounds.

Contribution

It introduces several multi-period sensitivity models that relax sequential unconfounding assumptions and provides explicit bounds based solely on observed data.

Findings

Established explicit bounds for counterfactual outcomes and treatment effects.

Compared sharp and conservative bounds across different sensitivity models.

Generalized marginal sensitivity analysis to longitudinal settings.

Abstract

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.