When drawing causal inference from observational data, there is 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. Works along this line often make various parametric assumptions on U, for the sake of mathematical and computational simplicity. In this article, we substantively further this line of research by developing a valid sensitivity analysis that leaves the distribution of U unrestricted. Our semiparametric estimator has three desirable features compared to many existing methods in the literature. First, our method allows for a larger and more flexible family of models, and mitigates observable implications (Franks et al., 2019). Second, our methods work seamlessly with any primary analysis that models the outcome regression parametrically. Third, our method is easy to use and interpret. 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.
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