How wrong could unmeasured confounding make you?

Observed data cannot rule out a hidden confounder. They can tell you how strong one would have to be to change your conclusion, and you can compare that strength with the confounders you did measure.

Further reading: Ding P, VanderWeele TJ (2016). Sensitivity analysis without assumptions. Epidemiology 27(3):368–377; VanderWeele TJ, Ding P (2017). Sensitivity analysis in observational research: introducing the E-value. Annals of Internal Medicine 167(4):268–274; Cinelli C, Hazlett C (2020). Making sense of sensitivity: extending omitted variable bias. Journal of the Royal Statistical Society Series B 82(1):39–67. The bias factor, curves and E-values are exact formulas. The study is simulated with a fixed seed (n = 4,000, four independent binary covariates, a log-linear risk model and no unmeasured confounder); its estimates use standardization with an influence-function interval. Benchmarks are computed exactly in the population that generated it.