Sensitivity Analysis Explorer

How strong would an unmeasured confounder need to be to explain away your result?

Causal Diagram
W Y X X = unmeasured confounder (dashed = hypothetical)
Observed Effect (W → Y)
What your study found (before worrying about confounding)
-1.001.00
γ : Confounder → Treatment (X → W)
How strongly X predicts who gets treated
-1.001.00
δ : Confounder → Outcome (X → Y)
How strongly X affects the outcome directly
-1.001.00
Omitted Variable Bias Formula
Observed = True Effect + Bias
Bias = γ × δ =
True Effect = − =
Effect Decomposition
Observed Effect
Bias (γ × δ)
True Causal Effect
Interpretation

Key insight: We can never prove the absence of unmeasured confounders. Sensitivity analysis asks: "How extreme would confounding need to be to change our conclusion?"
Try This
1. Set observed effect to −0.30 (exercise reduces heart disease risk)
2. Slowly increase γ and δ — how strong must the confounder be to erase the effect?
3. Notice: bias = γ × δ, so a moderate confounder on both dimensions creates more bias than a strong confounder on only one
The Science of Why — Causal Inference · Prof. Falco J. Bargagli-Stoffi · UCLA Fielding School of Public Health