Part II of Keys, Anderson & Grande’s classic metabolic-ward series: controlled feeding experiments in groups of healthy men (22 per arm) across dietary cholesterol intakes of 50-1450 mg/day, combined with comparable data pooled from four other institutions. Least-squares fit across 19 dietary-cholesterol comparisons gave the founding dose-response equation ΔSerum-Cholesterol = 1.5·(√C2 − √C1), where C is dietary cholesterol (mg/1000 kcal) — a square-root (concave, diminishing-returns) relationship, not a linear one. This equation, later folded into the combined Keys and Hegsted equations, is the quantitative backbone the whole feeding-trial tradition builds on. relevance_note: The foundational metabolic-ward dose-response equation for dietary cholesterol → serum cholesterol, establishing both that cholesterol raises cholesterol and that the effect is concave/diminishing at higher intake.
Methodology
Part II of the Keys/Anderson/Grande metabolic-ward series: controlled feeding in healthy men (~22 per arm at Minnesota) across dietary-cholesterol intakes of ~50-1450 mg/day, pooled with comparable data from four other institutions; the founding dose-response equation is a least-squares fit over 19 dietary-cholesterol comparisons. (Full text not retrieved — 1965, paywalled; extracted from the step-2 summary plus the corroborated equation form.)
Results
O-28 - Serum cholesterol rises with dietary cholesterol intake in controlled metabolic-ward feeding
The founding metabolic-ward dose-response result: under tightly controlled feeding, adding dietary cholesterol raises serum cholesterol, and the raw comparisons already show the effect flattening at higher intakes (the basis for fitting a square-root rather than linear form). Full text was not retrieved (1965, paywalled); the finding is extracted from the source’s step-2 summary and is among the most independently corroborated results in nutrition (Clarke 1997 meta-analysis of 395 experiments).
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Part II of the Keys/Anderson/Grande metabolic-ward series: controlled feeding in healthy men (~22 per arm at Minnesota) across dietary-cholesterol intakes of ~50-1450 mg/day, pooled with comparable data from four other institutions; the founding dose-response equation is a least-squares fit over 19 dietary-cholesterol comparisons. (Full text not retrieved — 1965, paywalled; extracted from the step-2 summary plus the corroborated equation form.)
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Dose-response model
A-9 - Keys square-root dose-response equation makes the dietary-cholesterol effect concave (diminishing returns)
The fitted model is ΔChol = 1.5·(Z2 − Z1) where Z = √C and C is dietary cholesterol in mg/1000 kcal (corroborated verbatim form; the same term enters the combined Keys equation ΔChol = 1.2·(2ΔS − ΔP) + 1.5·ΔZ). Treating serum cholesterol as f(C) = 1.5·√C, the marginal effect is df/dC = 1.5/(2·√C) = 0.75/√C, which strictly decreases as C rises — this is the mathematical content of “diminishing returns / concavity.” Worked illustration: raising C from 100 to 200 mg/1000 kcal gives Δ = 1.5·(√200 − √100) = 1.5·(14.14 − 10.0) = 6.2 units, whereas raising C from 400 to 500 gives Δ = 1.5·(√500 − √400) = 1.5·(22.36 − 20.0) = 3.5 units — a smaller rise for the same 100-unit increment at higher baseline. The inference bears on the feeding observation (O-28): the same data that show cholesterol rising with intake, read through this concave fit, imply that at habitual dietary-cholesterol intakes an extra egg’s worth of cholesterol moves serum cholesterol only modestly. The relation is a fitted mathematical form; its validity as a description is what steps 6/8 assess, but the concavity → small-marginal-effect implication is arithmetic given the form.
Validity verdict — approved (checked)
Traced the load-bearing step myself (elementary, author-blind). Take the form as premised: f(C) = 1.5·√C. Then df/dC = 1.5 · (1/2) · C^(−1/2) = 0.75/√C, which is strictly decreasing in C — the derivative falls monotonically, i.e. the function is strictly concave (f” = −0.375·C^(−3/2) < 0 for C > 0). Strict concavity is precisely the mathematical content of “each additional unit of intake raises serum cholesterol less at higher baseline intake,” so the reason→conclusion link is definitional, not merely suggestive. The two worked increments check arithmetically: 1.5·(√200 − √100) = 1.5·(14.142 − 10) = 6.21 vs 1.5·(√500 − √400) = 1.5·(22.361 − 20) = 3.54 — same 100-unit increment yields a smaller rise at higher baseline, confirming the monotone-decreasing marginal. The trailing “at habitual intakes the marginal effect is therefore small” is a weaker quantitative rider that also survives: plugging habitual C into 0.75/√C gives a modest per-unit slope, and even a discrete egg-sized jump reads through the concave form as a diminished increment. No undercutting defeater breaks the concavity→diminishing-returns step conditional on the fitted form (whether the √-form is the true dose-response is a premise-truth question priced downstream, not a validity issue). Holds as stated.
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