Confidence Intervals, p‑Values, and Caveats: Regulator‑Ready Statistical Phrasing for ML Claims

1) What Regulators Want: Specific, Bounded, Decision-Linked Claims

Regulatory reviewers read statistical claims with a practical question in mind: Can this evidence support a decision about safe and effective use in a defined context? For machine learning (ML) systems in healthcare or other high-stakes domains, this means claims must be specific (what metric, for which population, under what conditions), bounded (with uncertainty expressed and limitations acknowledged), and linked to a decision (how the result informs clinical or operational action). The aim is not to showcase best-case performance but to present reliable, replicable evidence that holds under foreseeable conditions.

Regulators expect that numbers come with guardrails. This includes the uncertainty around metrics, the statistical framework under which inference was made, and the precise study conditions. Vague statements such as “the model performs well” or “the result is significant” are insufficient. Instead, a compliant claim quantifies performance with a confidence interval (CI), states the inferential frame (e.g., superiority, non-inferiority, or equivalence), and articulates the target population and the endpoints that matter. This triangulation helps reviewers understand not only the central estimate but also the plausible range of performance and how that range supports—or does not support—a regulatory decision.

Decision-linked phrasing is critical. A regulatory decision concerns fit-for-use: Is the model adequate for the intended population, setting, and purpose? Evidence statements must therefore tie metrics to use decisions. This is where bounded language matters: “consistent with,” “compatible with,” “supports but does not prove,” and “does not exclude” signal that statistical outputs are tools for judging plausibility rather than proofs of truth. Regulators are alert to overclaiming; overstated conclusions can undermine credibility, even when the underlying data are strong.

Finally, regulators expect transparency about limits. Model performance is sensitive to dataset composition, drift over time, calibration in deployment, and fairness across subgroups. A regulator-ready claim integrates these caveats proactively. The absence of such caveats can be seen as a red flag suggesting that the evidence may not be transportable beyond the exact study conditions. Thus, the structure of a compliant claim links the metric and its uncertainty to the decision context and explicitly names the boundaries of that inference.

2) CI and p-Value Roles with Acceptable Phrasing Patterns

CIs and p-values serve different purposes. Confidence intervals communicate the precision and plausible range of an estimated quantity. They answer: given the data and assumptions, what range of values for the metric is reasonably compatible with the evidence? A narrow CI suggests precise estimation; a wide CI suggests uncertainty. Crucially, CIs help readers assess clinical plausibility. For example, if the lower bound of a sensitivity CI is below a clinically acceptable threshold, the claim may not support deployment, even if the point estimate is high.

P-values quantify the strength of evidence against a null hypothesis within a prespecified hypothesis-testing framework. A small p-value signals that the observed data would be unusual if the null were true. However, a p-value does not measure effect size, clinical importance, or the probability the hypothesis is true. It must be interpreted with caution: a “statistically significant” result is not necessarily clinically meaningful, and a “non-significant” result does not prove no effect.

Regulator-ready phrasing distinguishes these roles and avoids common pitfalls:

• For CIs: “Estimate [metric] = X (95% CI: L to U), indicating that values as low as L and as high as U are compatible with these data under the model’s assumptions.” This emphasizes compatibility and uncertainty rather than certainty.
• For p-values: “Under the prespecified null hypothesis, the data provide evidence against the null (p = p0),” or “The data are insufficient to reject the null (p = p0).” Avoid saying “proves” or “demonstrates” without tying the result back to decision thresholds and clinical relevance.

Acceptable phrasing patterns link CIs and p-values to decisions:

• “The estimate meets the predefined performance threshold; the 95% CI lower bound exceeds the threshold, supporting the claim under the superiority framework.” This ties uncertainty to a decision rule.
• “Although the point estimate exceeds the threshold, the 95% CI includes values below the threshold; therefore, the evidence is insufficient to support superiority.” This prevents overclaiming based on a single number.
• “The non-inferiority margin M was prespecified; the 95% CI upper bound does not cross M, supporting non-inferiority.” Here, the CI’s relation to a predefined margin is the basis for the claim.

CIs and p-values should be interpreted consistently with the analytic plan. Subgroup analyses, multiplicity adjustments, and sensitivity analyses must be reflected in the phrasing. Regulators look for alignment between the statistical analysis plan and the language used to present results. Claims that ignore prespecified hypotheses or thresholds invite concern.

3) Applying to ML Metrics and Hypothesis Types

For ML evaluations, the core diagnostic or prognostic metrics—sensitivity, specificity, AUROC, PPV, and NPV—require careful presentation because each ties to different clinical risks and decision pathways. Regulators expect that each reported metric includes a CI and, when applicable, that hypothesis tests match prespecified objectives.

• Sensitivity and Specificity: These are conditional probabilities sensitive to prevalence and threshold choices. For regulator-ready phrasing, state the operating point (decision threshold), the dataset context, and the CI. If the claim concerns superiority, link the CI bounds to a predefined threshold. For non-inferiority, present the margin and demonstrate that the CI stays within it. Acknowledge that sensitivity improvements may increase false positives; do not imply improved sensitivity guarantees better outcomes without endpoint evidence.

• AUROC: This threshold-agnostic measure summarizes ranking ability but does not reflect calibration or clinical utility at specific thresholds. Regulators typically view AUROC as a supportive metric rather than a sole basis for claims. Pair AUROC with its CI and specify whether it supports, but does not determine, clinical utility. Avoid implying that a high AUROC ensures adequate real-world performance.

• PPV and NPV: These are prevalence-dependent and particularly sensitive to the study population. Present CIs and clearly define the prevalence and case mix. A regulator-ready statement clarifies that PPV/NPV in the test set may not generalize if the deployment prevalence differs. For claims tied to PPV/NPV thresholds, note the acceptable range of population prevalence and how deviations may alter predictive values.

Hypothesis frameworks must be explicit:

• Superiority: Define a threshold or comparator (standard of care, prior device) and show that the CI demonstrates performance exceeding that benchmark in a clinically meaningful way. A significant p-value alone is not enough; the CI must be consistent with a meaningful gain.
• Non-inferiority: Define a margin representing the largest acceptable deficit relative to the comparator. The choice of margin should be justified based on clinical considerations, historical data, or consensus. The CI must not cross this margin; phrasing should emphasize compatibility with being no worse than the margin.
• Equivalence: Define a two-sided margin. The CI must lie entirely within the equivalence bounds. Avoid suggesting equivalence unless the interval supports it on both sides.

Calibration and decision thresholds are integral. An ML system can rank well (high AUROC) but be poorly calibrated, leading to misleading probabilities. Regulator-ready phrasing acknowledges whether calibration was assessed and whether recalibration was used. Declare whether thresholds were prespecified or derived from the data, and how that choice impacts multiplicity and overfitting risks.

When presenting time-to-event or longitudinal predictions, define the time horizon, censoring approach, and performance stability over time. A CI around time-dependent metrics (e.g., time-dependent AUC) should be reported, with clarity about the window of applicability. For resource allocation or triage tools, explain how thresholds map to actions and what the plausible range of false positives/negatives implies for patient flow and safety.

4) Adding Required Caveats and Regulator-Ready Rewrites

Transparent caveats are not optional. They are essential to align claims with how the model will be used and monitored. Regulators expect that limitations are integrated into the main claims rather than relegated to an appendix.

Key caveat domains:

• Drift: Data distributions and clinical practices evolve. State whether the study environment matches anticipated deployment, whether temporal splits or external validation were used, and whether performance drift monitoring is planned. Acknowledge that estimates may degrade if prevalence or feature distributions shift.
• Calibration: Declare whether predicted probabilities are calibrated and at which stage (training vs. validation). If calibration differs by subgroup or over time, say so. Calibration affects PPV/NPV at specific thresholds, so connect calibration quality to decision reliability.
• Subgroups and Fairness: Present whether performance varies across prespecified subgroups (e.g., age, sex, race/ethnicity, site). If power is limited, say that subgroup CIs are wide and interpret accordingly. Avoid implying uniform performance if subgroup intervals do not support that inference.
• Missingness: Describe missing data handling (complete case, imputation, model-based methods) and how assumptions may affect performance. Clarify if missingness patterns differ across subgroups or sites, which could bias results.
• Generalizability: Specify the data sources, sites, and inclusion/exclusion criteria. Clarify that performance estimates are conditional on these features and may not generalize to different clinical workflows, devices, or prevalence profiles. If an external validation was conducted, explain its context and limitations.
• Multiplicity: If multiple metrics, endpoints, thresholds, or subgroups were evaluated, explain how you controlled the family-wise error or false discovery rate. Link claims to analyses that were prespecified and adjusted, and avoid definitive language for exploratory findings.

Regulator-ready phrasing integrates these caveats in-line with the evidence. The goal is to pair clarity with restraint: claims should reflect what the data can support and explicitly mark what they cannot. A single strong point estimate does not outweigh wide CIs, unaddressed calibration issues, or drift risks.

Before/after rewrites follow a consistent pattern. Start with an overbroad statement and transform it into a bounded, decision-linked claim that includes the metric, CI, hypothesis framework, and relevant caveats. Replace absolute language with compatibility language, and tie results to prespecified thresholds or margins. Ensure that subgroup and generalizability caveats are foregrounded. For example, shift from emphasis on statistical “significance” to alignment with clinically meaningful thresholds, and from general claims to population-specific claims with prevalence considerations.

A practical phrasing template helps maintain consistency:

• Intended use and context: “This model is intended for [population, setting, and decision], using [input data] at [time horizon].”
• Primary metric and uncertainty: “[Metric] = X (95% CI: L–U), assessed at [threshold or across thresholds], on [dataset description].”
• Hypothesis framework and decision rule: “Under the [superiority/non-inferiority/equivalence] framework, with [prespecified threshold/margin], the [CI bound] [exceeds/does not cross/fully lies within] the [threshold/margin], [supporting/not supporting] the claim.”
• Calibration and prevalence: “Predicted probabilities were [calibrated/not calibrated]; PPV/NPV are conditional on the observed prevalence [p%] and may differ under other prevalences.”
• Subgroups and fairness: “Subgroup analyses were [prespecified/exploratory]; performance was [consistent/inconclusive] across [subgroups], noting [wide CIs/limited power] where applicable.”
• Drift and monitoring: “External validation in [setting/time] showed [evidence]; performance may change with distributional shifts; monitoring and recalibration are planned under [protocol].”
• Multiplicity and endpoints: “Claims are based on [primary endpoint(s)] with [multiplicity control]; other analyses are exploratory and should be interpreted cautiously.”
• Boundary statement: “These findings support use in [specified context]; generalization beyond this context has not been established.”

By systematically applying this structure, ML claims become regulator-ready. The use of CIs to frame plausible ranges ensures that claims avoid overconfidence; the explicit hypothesis framework anchors interpretation; and transparent caveats communicate the boundaries within which the evidence is informative. The result is a set of statements that reviewers can evaluate directly against decision criteria, improving both clarity and trustworthiness.

In practice, disciplined phrasing encourages better study design. Knowing that the CI’s lower bound must exceed a clinically meaningful threshold pushes teams to plan adequate sample sizes and rigorous validation. Recognizing that PPV and NPV depend on prevalence leads to collecting deployment-representative data or modeling how performance translates across settings. Acknowledging drift encourages instituting monitoring plans ahead of time. Thus, regulator-ready language is not merely stylistic; it reflects and reinforces the scientific rigor needed for safe and effective ML deployment.

Ultimately, confidence intervals and p-values are tools for quantifying uncertainty and evidence, not for proving truth. Regulator-ready phrasing integrates them with hypothesis frameworks and essential caveats to articulate claims that are specific, bounded, and decision-linked. This alignment serves both the reviewer and the end users who rely on ML systems to make critical decisions. By adopting these practices, you present ML performance in a way that is transparent, clinically relevant, and suitable for regulatory evaluation.