A Semiparametric Approach to Model-Based Sensitivity Analysis in Observational Studies

When drawing causal inference from observational data, there is almost always concern about unmeasured confounding. One way to tackle this is to conduct a sensitivity analysis. One widely-used sensitivity analysis framework hypothesizes the existence of a scalar unmeasured confounder U and asks how the causal conclusion would change were U measured and included in the primary analysis. Work along this line often makes various parametric assumptions on U, for the sake of mathematical and computational convenience. In this article, we further this line of research by developing a valid sensitivity analysis that leaves the distribution of U unrestricted. Compared to many existing methods in the literature, our method allows for a larger and more flexible family of models, mitigates observable implications (Franks et al., 2019), and works seamlessly with any primary analysis that models the outcome regression parametrically. We construct both pointwise confidence intervals and confidence bands that are uniformly valid over a given sensitivity parameter space, thus formally accounting for unknown sensitivity parameters. We apply our proposed method on an influential yet controversial study of the causal relationship between war experiences and political activeness using observational data from Uganda.