The E-value is the minimum strength of association, on the risk-ratio scale, that an unmeasured confounder would need with both the exposure and the outcome, beyond the measured covariates, to fully explain away an observed association or shift a confidence bound to a chosen value. Using the pooled per-egg HR 0.98 (0.92-1.04): shifting the lower bound 0.92 up to 1.01 (a positive association) requires a confounder associated with both egg intake and CVD by RR >=1.43; shifting the upper bound 1.04 down to 0.99 (an inverse association) requires RR >=1.28. Confounders of RR 1.43 are substantial relative to the diet/lifestyle confounders already adjusted, so the null is moderately robust: weak residual confounding cannot manufacture a materially positive egg-CVD association (supporting H-21). This is a bound on required confounding strength, not proof of no causation, and it depends on the point estimate sitting near the null.
Validity assessment (step 6)
Traced the arithmetic with VanderWeele’s E-value E = 1/RR + sqrt((1/RR)(1/RR - 1)) applied to the CI bounds. Lower bound 0.92: 1/0.92 = 1.087, sqrt(1.087 x 0.087) = 0.307, E ~= 1.39 to reach null, a touch more (~1.43) to reach 1.01 — matches the stated 1.43. Upper bound 1.04: E ~= 1.04 + sqrt(1.04 x 0.04) = 1.04 + 0.204 = 1.24 to null, ~1.28 to reach 0.99 — matches. The definition and the directional reading are correct, and the conclusion is a proper bound (“only confounding of at least this strength could overturn the null”). No defeater breaks the step; the argument correctly flags that it is a bound, not proof, and that it depends on the near-null point estimate. The one soft spot is the interpretive label “fairly strong / substantial” for RR ~1.43 (an E-value that VanderWeele-style would call only modest, cf. A-20) — but that qualifier does not affect the validity of the bound itself. approved / checked.