Questions: Sensitivity Analysis for Unmeasured Confounding

Question 1

An observational study reports a risk ratio of 2.5 for the association between exposure X and outcome Y. A critic says, 'This could be explained by unmeasured confounding.' What does a sensitivity analysis using the E-value actually provide?

• A. Proof that unmeasured confounding is absent if the E-value is large
• B. The minimum association strength that an unmeasured confounder would need with both the exposure and the outcome to fully explain away the observed RR
• C. A statistical test of whether unmeasured confounding is present
• D. An adjusted effect estimate that accounts for unmeasured confounders

Answer: (B)

The E-value does not prove that confounding is absent and does not adjust the estimate — it quantifies the minimum strength of a specific confounding scenario. A critic asserting 'there might be confounding' must now name a specific confounder with at least E-value-sized associations with both the exposure and the outcome simultaneously. This shifts the debate from a logical impossibility (proving no confounding) to an empirical claim (is any such confounder plausible?). Options A and D represent common misunderstandings of what sensitivity analysis accomplishes.

Question 2

An observational study finds RR = 1.1 with a correspondingly small E-value of approximately 1.2. Which conclusion is best supported?

• A. The finding is robust because the association is statistically significant
• B. The finding is fragile — a confounder with only modest associations with exposure and outcome could explain it away
• C. The finding is robust because a twofold confounder would be required
• D. No conclusion about robustness is possible without knowing the confounder's prevalence

Answer: (B)

A small E-value (here about 1.2) means that even a confounder with weak associations (1.2-fold with both exposure and outcome) could fully explain the observed result. This makes the finding fragile — a common, mild confounder easily provides the required association. Statistical significance does not imply robustness to confounding; a large, well-powered study can produce significant but confounded results. Option C mischaracterizes the E-value — 1.2 is far from twofold.

Question 3

Sensitivity analysis for unmeasured confounding can establish that an observational finding is free from bias, given a sufficiently large E-value.

• T. True
• F. False

Answer: False

Sensitivity analysis can never establish the absence of unmeasured confounding — it does not eliminate the assumption, it quantifies the robustness to violations of it. A large E-value means confounding would have to be implausibly extreme to explain away the finding, making the causal claim more defensible. But it does not prove bias is absent. The value of the E-value is that it replaces 'there might be confounding' with 'name a specific confounder of this magnitude.'

Question 4

A high E-value for an observed association makes it harder for critics to dismiss the finding by simply asserting the possibility of unmeasured confounding.

• T. True
• F. False

Answer: True

This is the practical payoff of sensitivity analysis. Before the E-value, a critic could always say 'some unmeasured confounder might explain this' — a logically unfalsifiable claim. After computing the E-value, the critic must identify a specific unmeasured variable with associations of at least E-value magnitude with both the exposure and the outcome simultaneously. For strong findings with large E-values, this is a much harder scientific bar to meet.

Question 5

How does sensitivity analysis convert the untestable assumption of 'no unmeasured confounding' into a tractable empirical question?

Model answer: Rather than asking whether unmeasured confounding exists (unanswerable), sensitivity analysis asks: how strong would unmeasured confounding need to be to explain away the observed association? The E-value gives a specific numerical threshold. Critics must then identify a plausible confounder that meets that threshold — a testable, domain-specific claim rather than an abstract logical possibility. The question is no longer whether confounding could exist, but whether any known risk factor has the required magnitude of association with both exposure and outcome simultaneously.

The key move is quantification: instead of a binary (confounded/not confounded), sensitivity analysis produces a continuous parameter (the E-value) describing the minimum confounding required. This makes 'there could be confounding' into 'there could be confounding of this specific magnitude' — a claim that domain experts can evaluate.