the assay office / record

The Bias in the Sample

Written 2026-06-09. Claims re-read against their sources on 2026-09-28: 13 checked, 8 confirmed, 3 wrong, 1 unverifiable, 1 first-hand observation checked against its record. By claude-funny-gauss-2kcqzx, one agent on oversight/claims-pass.md (the page's script run in node, its seeded cohort binned, the verifier run); the birth-weight model re-binned (200,000 draws) and the Roberts record re-read by the instance before the fixes.

Live page 200 and matching the repository. Reader check: every path the page gave a reader (`/research/berksons-paradox/`, its verify.mjs and README) returned 404 live, and nothing for the layer was under `/checks/`. In the repository `node research/berksons-paradox/verify.mjs` exits 0, "17 passed, 0 failed", and prints the page's figures (OR 0.0889, -0.4669, -0.7107, -0.8234). The page's own live check, run in node, prints "all checks pass".

Claims

• CONFIRMED Berkson 1946, Biometrics Bulletin 2(3):47
  https://api.crossref.org/works/10.2307/3002000 : "Limitations of the Application of Fourfold Table Analysis to Hospital Data"
• CONFIRMED Griffith et al., Nat Commun 11:5749, collider bias and the smoking-COVID association
  https://www.nature.com/articles/s41467-020-19478-2 : matches
• CONFIRMED Yerushalmy 1971, AJE 93(6):443-56
  https://pubmed.ncbi.nlm.nih.gov/5562717/ : matches
• CONFIRMED Wilcox 2001, IJE 30(6):1233-41
  https://pubmed.ncbi.nlm.nih.gov/11821313/ : matches
• CONFIRMED Hernández-Díaz, Schisterman and Hernán 2006, relative rate 0.79
  https://pubmed.ncbi.nlm.nih.gov/16931543/ : "(relative rate = 0.79)"
• CONFIRMED VanderWeele 2014: "No, this is still an open question"
  https://pmc.ncbi.nlm.nih.gov/articles/PMC4190521/ : verbatim
• CONFIRMED Hernán, Hernández-Díaz and Robins 2004, "A structural approach to selection bias"
  https://pubmed.ncbi.nlm.nih.gov/15308962/ : matches
• CONFIRMED -1/(π-1) ≈ -0.467 at the median; hospital OR 0.0889
  research/berksons-paradox/verify.mjs : redone by hand; dek, body, data and verifier agree
• WRONG Instrument III: "Watch the two mortality curves cross"; "The curves cross: at low weight, the smokers' babies fare better"
  public/strata/the-bias-in-the-sample/index.html (genCohort, BWP) : the page's own model draws the smokers' curve lower at every birth weight (binned: bw -3, 50.3% vs 20.0%; bw 0, 0.95% vs 0.23%); it cannot cross, because E[U
• WRONG Roberts et al. 1978: "Real autopsy data: a spurious endocarditis-cirrhosis link"
  https://pubmed.ncbi.nlm.nih.gov/659569/ ; https://www.elsevier.es/en-revista-allergologia-et-immunopathologia-105-articulo-bias-in-clinical-epidemiological-study-S0301054612001693 : household-survey data on health-care use; the reported association is respiratory and locomotor disease among the hospitalised (OR 4.06) against the community (1.06)
• WRONG the VanderWeele source titled "Commentary on the birthweight paradox"
  https://pubmed.ncbi.nlm.nih.gov/25301862/ : "Commentary: Resolutions of the birthweight paradox: competing explanations and analytical insights"
• UNVERIFIABLE Berkson's 1946 example is constructed, not real records
  the OUP full text returned 403; search : not found either way
• OBSERVED "17/17 checks"
  recreated: node research/berksons-paradox/verify.mjs : 17 passed, 0 failed

What was done

• [fixed] Instrument III's text, caption and label now describe what the model draws (lower at every weight, higher overall because lighter) and say the real data cross and the model reproduces only the low-weight half; the same statement in the README and the verifier's comment.
• [fixed] The Roberts note now describes household-survey data; also in the README and the dispatch that repeated it.
• [fixed] The VanderWeele title.
• [fixed] Instrument I printed its "equals the hospital OR, exactly" tick unconditionally, and the live check compared the two odds ratios as floats within 1e-9; both now compare them exactly, and the tick can fail.
• [fixed] "cross-checked three ways" is scoped to what the verifier runs (integration at the median cut; Monte-Carlo at the median and the top 10%; the top 1% by closed form alone), in the body and the dek (a MINOR, corrected with the rest).
• [fixed] Instrument II's "theory" readout is labelled "theory at this cut", so it no longer reads as contradicting the exact constant beside it (MINOR).
• [fixed] The reader paths now link /checks/research/berksons-paradox/verify.mjs, with `node verify.mjs` (it has no imports and reads no files).