Methodology Brief

Pre-specifying equivalence margins for dietary assessment non-inferiority claims

A methodology brief

Daniel Okafor, PhD, MS; Lars Henriksen, PhD
Published February 17, 2026

Background

Non-inferiority and equivalence claims are increasingly common in dietary assessment: a new image-based tool may be claimed to be “as accurate as” 24-hour recall, or a simplified diary method may be claimed to be “non-inferior” to a weighed-food record. Such claims are meaningful only if the equivalence margin - the maximum accuracy gap that would still count as “not worse” - is specified in advance and justified on clinical or operational grounds. When margins are selected after seeing the data, or chosen to be conveniently large, non-inferiority inference loses its interpretive content.

The Initiative’s convention is that equivalence margins are pre-specified in the protocol, justified, and reported in every non-inferiority paper drawing on Initiative data.

The Method

Margin specification format. Equivalence margins are specified on the scale of the primary accuracy outcome. For MAPE-based comparisons, the margin $\delta$ is a number of percentage points (for example, “the candidate method is non-inferior if the upper 95% CI on $\text{MAPE}{\text{candidate}} - \text{MAPE}{\text{reference}}$ is below +3 percentage points”). For mean bias, $\delta$ is in the outcome’s units (kcal, g).

Justification. Every margin must be justified on one of three grounds, documented in the protocol:

1. Clinical relevance. The margin corresponds to a difference plausibly capable of changing a clinical recommendation or an epidemiologic exposure classification. For example, an energy-estimation margin narrower than the typical within-person day-to-day variation in free-living intake.
2. Operational relevance. The margin corresponds to a difference that would change a decision about tool deployment (for example, adoption by a clinic or a public-health programme).
3. Historical precedent. The margin matches prior literature on the reference method’s own measurement error.

A pure “that’s what powered” justification is not acceptable; the margin drives the sample size, not the reverse.

Pre-specification vehicle. Margins are recorded in the public protocol (or preregistration) with a date stamp prior to data analysis. Any change to the margin after data collection begins must be disclosed and justified, and triggers a sensitivity analysis with the original margin.

One-sided vs. two-sided. Non-inferiority uses one-sided 97.5% CIs (equivalent to a two-sided 95%). Equivalence (bi-directional) uses two one-sided tests (TOST) with matched margins $\pm \delta$.

Analysis populations. The primary analysis is per-protocol for non-inferiority, with an intention-to-treat sensitivity analysis, reversing the usual convention for superiority trials, because per-protocol is conservative for non-inferiority.

Worked example

A protocol pre-specifies that a candidate image-based tool is non-inferior to 24-hour recall in estimating per-occasion energy if the upper bound of the 95% one-sided CI on the difference in MAPE is below +4 percentage points. The margin is justified on clinical-relevance grounds: a within-person day-to-day CV of about 25% implies a typical day-to-day energy variation well in excess of 4 percentage points of MAPE at the individual level.

Suppose the study enrols $n = 150$ and observes:

The upper CI bound on the MAPE difference (+1.4 pp) is below the pre-specified margin of +4 pp. The non-inferiority claim is supported at the pre-specified margin. The Initiative publication would report the margin, the justification, the upper CI bound, and a sensitivity analysis around the margin choice (for example, at +3 and +5 pp).

Common pitfalls

• Selecting a large margin to ensure the study is powered, without a substantive justification. This inverts the logic of non-inferiority.
• Changing the margin after inspecting the data. This is a form of hypothesising after results are known (HARKing) and invalidates inference.
• Confusing “no statistically significant difference” with non-inferiority. The two are distinct; absence of a significant difference does not establish non-inferiority without a margin.
• Using a two-sided 95% CI for a one-sided non-inferiority claim and thereby reporting a stricter test than claimed.
• Applying the intention-to-treat analysis as primary for non-inferiority. ITT tends to attenuate group differences, which is anti-conservative in this setting.
• Reporting non-inferiority at the overall level while showing adverse stratum-level differences in the secondary analyses, without acknowledging the conflict.

Recommended reporting

• The pre-specified margin, in the units of the primary outcome.
• The justification category (clinical, operational, historical) and the supporting reasoning.
• The date the margin was pre-specified and where it was recorded.
• The primary analysis population (per-protocol) and the ITT sensitivity analysis.
• The one-sided 95% CI (or equivalent) on the candidate-minus-reference difference.
• A sensitivity table at alternative margins around the pre-specified value.
• Any stratum-level analyses and whether the non-inferiority conclusion holds within each.

References

1. Okafor N, Henriksen D. Equivalence and non-inferiority inference in dietary assessment: a critical review. Stat Med. 2025;44(4):1010-1024.
2. Reinholt P. Margin justification in nutrition non-inferiority studies: a proposal. Nutrients. 2023;15(21):4620.
3. Henriksen D. Per-protocol versus intention-to-treat analysis in non-inferiority trials: a primer for nutrition researchers. Am J Clin Nutr. 2024;120(2):330-338.
4. Park S-H, Morales F. Within-person day-to-day variability in energy intake and its implication for equivalence margins. Br J Nutr. 2022;128(6):950-960.
5. Tanaka M. Two one-sided tests (TOST) for equivalence in dietary method comparison. Public Health Nutr. 2023;26(2):350-359.
6. Weiss R, Okafor N. Pre-registration of equivalence margins: practice and adherence. J Nutr. 2025;155(5):1212-1220.
7. Linde J. When non-inferiority claims exceed the evidence: three case studies. JMIR mHealth Uhealth. 2024;12(3):e52014.
8. Okafor N. A minimal checklist for non-inferiority reporting in nutrition technology validation. Nutrients. 2026;18(2):401.