Chairs: Werner Brannath and Annette Kopp-Schneider

Semiparametric Sensitivity Analysis: Unmeasured Confounding in Observational Studies
Daniel Scharfstein
Department of Population Health Sciences, University of Utah School of Medicine, USA

Establishing cause-effect relationships from observational data often relies on untestable assumptions. It is crucial to know whether, and to what extent, the conclusions drawn from non-experimental studies are robust to potential unmeasured confounding. In this paper, we focus on the average causal effect (ACE) as our target of inference. We build on the work of Franks et al. (2019) and Robins et al. (2000) by specifying non-identified sensitivity parameters that govern a contrast between the conditional (on measured covariates) distributions of the outcome under treatment (control) between treated and untreated individuals. We use semi-parametric theory to derive the non-parametric efficient influence function of the ACE, for fixed sensitivity parameters. We utilize this influence function to construct a one-step, split-sample bias-corrected estimator of the ACE. Our estimator depends on semi-parametric models for the distribution of the observed data; importantly, these models do not impose any restrictions on the values of sensitivity analysis parameters.  We establish that our estimator has $\sqrt{n}$ asymptotics.  We utilize our methodology to evaluate the causal effect of smoking during pregnancy on birth weight. We also evaluate the performance of estimation procedure in a simulation study.  This is joint work with Razieh Nabi, Edward Kennedy, Ming-Yueh Huang, Matteo Bonvini and Marcela Smid. 

Closing: Andreas Faldum, Werner Brannath / Annette Kopp-Schneider