Model-assisted sensitivity analysis for treatment effects under unmeasured confounding via regularized calibrated estimation

Understand

Consider sensitivity analysis for estimating average treatment effects under unmeasured confounding, assumed to satisfy a marginal sensitivity model.

• At the population level, we provide new representations for the sharp population bounds and doubly robust estimating functions, recently derived by Dorn, Guo, and Kallus.
• We also derive new, relaxed population bounds, depending on weighted linear outcome quantile regression.
• At the sample level, we develop new methods and theory for obtaining not only doubly robust point estimators for the relaxed population bounds with respect to misspecification of a propensity score model or an outcome mean regression model, but also model-assisted confidence intervals which are valid if the propensity score model is correctly specified, but the outcome quantile and mean regression models may be misspecified.