Back to the Future: Controlling for Future Treatments to Assess Hidden Bias

Felix Elwert, University of Wisconsin-Madison

Hidden bias from unobserved confounding is a central problem of causal inference from observational data. One strategy for mitigating hidden bias previously employed in population sciences is to control for future (i.e. post-outcome) values of the treatment. The basic idea is that the unobserved confounders affecting treatment likely also affect future values of the treatment. If so, future values of the treatment can proxy for the unmeasured confounder, and controlling for the proxy may remove part of the bias. Drawing on the theory of directed acyclic graphs we state the nonparametric conditions under which this strategy succeeds in reducing bias, and when it does not. We also state some parametric considerations and explain how future treatments can be used to detect the direction of bias. Centrally, we sketch a new parametric test for the presence of unobserved confounding. We illustrate these results with an empirical example.