  Inferring the causal effect of a non-randomly assigned exposure on an outcome
requires adjusting for common causes of the exposure and outcome to avoid
biased conclusions. Notwithstanding the efforts investigators routinely make to
measure and adjust for such common causes (or confounders), some confounders
typically remain unmeasured, raising the prospect of biased inference in
observational studies. Therefore, it is crucial that investigators can
practically assess their substantive conclusions' relative (in)sensitivity to
potential unmeasured confounding. In this article, we propose a sensitivity
analysis strategy that is informed by the stability of the exposure effect over
different, well-chosen subsets of the measured confounders. The proposal
entails first approximating the process for recording confounders to learn
about how the effect is potentially affected by varying amounts of unmeasured
confounding, then extrapolating to the effect had hypothetical unmeasured
confounders been additionally adjusted for. A large set of measured confounders
can thus be exploited to provide insight into the likely presence of unmeasured
confounding bias, albeit under an assumption about how data on the confounders
are recorded. The proposal's ability to reveal the true effect and ensure valid
inference after extrapolation is empirically compared with existing methods
using simulation studies. We demonstrate the procedure using two different
publicly available datasets commonly used for causal inference.
