Sensitivity Analysis for Causality
Also known as: sensitivity analysis, hidden-bias sensitivity analysis, Rosenbaum sensitivity analysis, omitted-variable sensitivity
Sensitivity analysis for causality assesses how robust a causal conclusion is to unobserved confounding. Rather than assuming all confounders are controlled, it asks: how strong would an unmeasured variable need to be to overturn the estimated effect? It is an indispensable robustness check after any quasi-experimental or observational causal analysis.
Key highlights
- Quantifies exactly how much unmeasured confounding would be required to overturn a finding, giving readers a calibrated sense of credibility.
- Applicable after many different causal estimators — matching, weighting, DiD, regression — without rerunning the primary analysis.
- Rosenbaum's Gamma and Cinelli-Hazlett robustness values are interpretable and can be benchmarked against observed covariates.
- Encourages transparent, honest reporting of uncertainty rather than false confidence in causal claims.
- Widely accepted by peer reviewers in economics, epidemiology, and the social sciences as a standard robustness check.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use sensitivity analysis whenever a causal claim rests on observational or quasi-experimental data where full randomisation was impossible. It is particularly important after propensity score matching, inverse probability weighting, DiD, or regression adjustment when an important confounder may not have been measured. Do not use it as a substitute for good research design — it augments, rather than rescues, a poorly designed study. Also not needed after a well-executed randomised controlled trial where confounding is eliminated by design.
Strengths & limitations
- Quantifies exactly how much unmeasured confounding would be required to overturn a finding, giving readers a calibrated sense of credibility.
- Applicable after many different causal estimators — matching, weighting, DiD, regression — without rerunning the primary analysis.
- Rosenbaum's Gamma and Cinelli-Hazlett robustness values are interpretable and can be benchmarked against observed covariates.
- Encourages transparent, honest reporting of uncertainty rather than false confidence in causal claims.
- Widely accepted by peer reviewers in economics, epidemiology, and the social sciences as a standard robustness check.
- Does not identify the actual unmeasured confounder — it only quantifies the threshold of concern, not whether that threshold is crossed.
- Rosenbaum's approach assumes a particular worst-case adversarial structure; real confounders may operate differently.
- A high critical Gamma is reassuring but does not rule out hidden bias — it only shows that bias would need to be very large.
- Interpretation requires judgment about what levels of confounding are 'plausible', which varies by domain and must be argued, not computed.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What does Gamma equal to 2 mean in Rosenbaum's framework?
It means two matched units could differ by a factor of 2 in their odds of receiving treatment due to an unmeasured confounder. If your conclusion survives Gamma = 2, the hidden bias would need to at least double the treatment odds before your finding disappears.
How is sensitivity analysis different from a placebo test?
A placebo test checks for spurious effects by applying the estimator to a group or outcome that should not be affected by the treatment. Sensitivity analysis instead quantifies how strong unmeasured confounding would need to be to invalidate the real estimate. Both are robustness checks but they address different threats to validity.
Do I need to run sensitivity analysis after a randomised experiment?
Generally no. Randomisation eliminates systematic confounding by design, so the concern that motivates sensitivity analysis does not apply. It is relevant for observational and quasi-experimental studies where treatment assignment was not randomised.
Which sensitivity framework should I use — Rosenbaum or Cinelli-Hazlett?
Use Rosenbaum's Gamma approach after matched designs. Use Cinelli and Hazlett's omitted-variable robustness values after regression-based analyses, since their partial R-squared parameterisation is natural in that context and allows benchmarking against observed covariates.
What counts as a 'robust' finding?
There is no universal threshold, but a common heuristic is that a Gamma above 1.5–2 (Rosenbaum) or robustness values exceeding those of the strongest measured covariate (Cinelli-Hazlett) indicate reasonable robustness. The argument must ultimately rest on domain knowledge about how strong plausible unmeasured confounders could be.
Sources
- 1.Rosenbaum, P. R. (2002). Observational Studies (2nd ed.). Springer.ISBN 978-0387989679
- 2.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.
You have read it. What now?
Cite this page
ScholarGate. (2026, June 3). Sensitivity Analysis for Causality. ScholarGate. https://scholargate.app/causal-inference/sensitivity-analysis-for-causality