Daily step count, a plateau in all-cause mortality, and differences between women and men: prospective cohort study using NHANES accelerometry

Summary

Strengths

1. Data provenance is exact and independently reproducible

   Sec 2.2–2.4, 3.1; Figure 1; Table 2; Table 4

   From the public DEMO, PAXRAW_D and 2019 LMF files I rebuilt cohort A and reproduced all 18 flow numbers in Figure 1, n=2373 (1187/1186), 702 deaths (317/385), 28553 person-years, the weighted mean of 9254 steps/day and the spline knots 3014/7521/10458/16149 exactly (checks 01, 02). The statement that 2003–04 files contain no steps, which motivates imputation for cohort B, is correct (check 13). An approximate re-fit gives the same flattening shape, with HRs within 0.05 of Table 4.

2. Explicit, operational plateau definition with honest uncertainty

   Sec 2.9; Eq (1); Table 3

   Two estimators (hinge breakpoint and 90%-of-D point), the breakpoint re-profiled in every replicate so intervals carry location uncertainty, a boundary-share diagnostic, and a decision rule that allows 'absent' and 'not identifiable'. This goes beyond the visual reading of spline curves criticised in the Introduction. The decision rule was applied consistently: 0/79 labelled rows violate it (check 04).

3. Internally consistent, verifiable numbers

   Tables 3–7, 9–11; Sec 3.2–3.3

   Table 4 HRs are reproduced by a 3-coefficient RCS to within 0.004 (overall) and the nadir 14880 to within 32 steps (check 03). All 25 CIs are log-symmetric (check 08), all 15 F→P conversions and Holm values match (check 05), 22/22 Table 6 differences match (check 06), Table 7 arithmetic is exact (check 07), and 153 count identities hold (check 10). The hinge estimates agree with the spline (check 09).

4. Appropriate design-based inference and multiplicity control

   Sec 2.2, 2.7, 2.11; Table 5

   Wald F tests use the correct design degrees of freedom (15/30/32, confirmed from PSU and strata counts in check 01), and Holm correction is applied to the two primary hypotheses and reported side by side with the raw P in the abstract. Hip and wrist step counts are never pooled.

5. Sex question addressed on both relative and absolute scales

   Sec 2.10, 3.3; Tables 6–7

   Rather than reading 'no interaction' as 'no difference', the paper pre-specifies an equivalence margin and reports that equivalence was not established. It also gives standardised absolute risks (Table 7), which show men at higher risk at every step count with similar absolute differences (9.3 vs 10.8 points).

6. Transparent deviations, broad sensitivity analyses and largely cautious discussion

   Sec 2.13, Table 1; Tables 9–12; Fig 6; Sec 4.3–4.4, 5, 7

   Table 1 lists 18 deviations, Tables 9–12 and Figure 6 report every sensitivity analysis including those that change the classification, and Sec 4.1, 4.3, 5 and the plain-language summary ('links rather than proof') hedge appropriately. Sec 4.4 explicitly warns that a single threshold would overstate precision.

Weaknesses

1. Title and one abstract sentence do not match the results

   major · Title; Abstract (Results); Sec 4.2; Table 11

   The title asserts 'a plateau in all-cause mortality, and differences between women and men'. The primary non-linearity test is not significant after the paper's own Holm correction (P=0.070), and H2 gives P=0.716, so no sex difference was detected (check 11). Separately, the abstract says that 'excluding early deaths or participants in poor health removed the plateau'. This holds in hip cohorts A and B, but in wrist cohort C both exclusions remain P-imp (Table 11: $p_{nonlin}$ <0.001 and 0.020). The same generalisation appears in Sec 4.2. The numbers themselves are correct (43/43 abstract numbers found in the body), and the abstract's Conclusions and Sec 5 are already appropriately hedged. Because this discrepancy is in framing, not in any estimate, I score the paper 5 rather than capping it at 4. Fix: use a neutral title such as 'Daily step count and all-cause mortality in women and men: dose–response and plateau estimation…', and qualify the abstract sentence to 'in the hip-worn cohorts'.

2. Pre-registration is a private hash commitment and cannot be verified

   major · Sec 2.1; Sec 2.13; Table 1; Abstract (Design)

   The plan is identified only by a SHA-256 hash, with no registry, DOI or URL. No supplied file hashes to it, and a web search for the hash returns nothing (check 12). Table 1 shows no timestamps, although Sec 2.1 states that each deviation was logged with one. The claims that the freeze preceded all downloads and that no deviation followed inspection of an association are therefore self-attested. The freeze (9 Nov 2026 13:11 UTC) falls on the same day as the manuscript date. The abstract's 'Design: Pre-registered prospective cohort study' implies more external accountability than is demonstrated. Fix: deposit the frozen plan and the timestamped deviation log in a public, time-stamped repository (OSF or similar) whose file matches the hash, or describe the design as 'analysis plan specified in advance (not publicly registered)'.

3. Headline classification rests on the unadjusted non-linearity P, and many labels flip around P≈0.05

   major · Sec 2.9; Table 3; Table 5; Table 9; Abstract

   The 'present' clause of the rule uses raw $p_{nonlin}<0.05$. With the Holm-adjusted P=0.070 the primary curve would not be classified as present (check 05). Across all analyses, 27 of 79 labelled rows have $0.025\le p_{nonlin}<0.10$, and 44 of 49 'present' rows are P-imp because the 6000-step width threshold is almost always exceeded (check 04). The rule therefore discriminates mainly through whether P crosses 0.05. The sensitivity 'changes' in cohort A mostly reflect loss of power, while $\hat\psi$, $\hat\theta$ and E2 barely move (Table 9). For example, excluding early deaths gives P=0.087 with $\hat\theta=+0.025$, an upper segment that is flatter than the primary one, yet the curve is labelled 'absent'. Reading this as the plateau being 'removed' overinterprets it. Fix: state explicitly whether the rule was meant to use the raw or Holm-adjusted P; report the classification under both; and describe sensitivity results in terms of the estimates ($\hat\psi$, $\hat\theta$, E2), not the labels.

4. Primary model adjusts for probable mediators

   major · Sec 2.6; Table 9

   M2, the primary confounder set, includes BMI, diabetes, CVD, cancer, lung disease, self-rated health and mobility limitation. The authors acknowledge that some of these lie on the causal path from walking to death. Under M1 the non-linearity is stronger (P=0.008, Table 9), so the choice affects both the strength of the evidence and the shape, and the estimand of the headline HRs (a 'direct' association net of health status) is not stated. Fix: justify M2 with a DAG, report M1 alongside M2 in the abstract, or state the estimand.

5. 'Replication' is partly non-independent and judged by a coarse criterion

   minor · Abstract; Sec 2.2, 3.5; Table 8; Fig 5

   Cohort B contains all of cohort A (A is about 48% of B), and its steps for 2003–04 are imputed (CV $R^2$ 81.7%). Its breakpoint (10880) differs from A's (6980) by about 3900 steps on the same hip scale. 'Same classification' is weak evidence of replication when almost every analysis lands in P-imp (check 04). Cohort C is truly independent but uses a different device and scale. Fix: in the abstract, call B a 'larger overlapping cohort', and compare the location estimates and intervals, not only the labels.

6. Percentile bootstrap for a grid argmax may not have nominal coverage

   minor · Sec 2.9; Table 3; Table 6; Sec 3.3

   The breakpoint is a non-smooth argmax over a 100-step grid. Point estimates often sit at the edge of their intervals: W−M $\Delta\psi=-5130$ in (−8800, 5950) at relative position 0.25, and the age difference 5530 in (−8900, 6600) at 0.93 (check 06). The men breakpoint appears to jump between about 5000 and about 12000 (CI for $\theta$ −1.572 to 0.179, boundary 14%). Bootstrap percentile intervals are known to be unreliable for change-point locations. Fix: show the bootstrap distributions of $\hat\psi$ (e.g. as histograms), report profile-likelihood intervals as a comparison, or present E2, which is smoother, as primary.

7. Undisclosed sign condition and odd semantics in the 'absent / diminishing returns' rule

   minor · Sec 2.9; Table 1 (D16); Tables 3, 8–11

   Sec 2.9 defines A-DR by a magnitude condition, $|\theta|<|\beta_1|/4$. However, all 8 A-DR rows have $\hat\theta<0$ and 15/17 A rows have $\hat\theta>0$ (check 04), which suggests that a sign condition was implemented. Under deviation D16, 'absent' is assigned to curves whose upper segment bends upward (e.g. Men A, $\hat\theta=+0.046$), which is the opposite of continued decline. 27 absent/NI rows depend on an unreported linear-slope test or $\hat\beta_1$ and cannot be checked. Fix: report $\hat\beta_1$ and the slope test, and state the rule exactly as implemented.

8. Causal connotation in wording

   minor · Abstract; Sec 2.9, 3.2, 4.4, 7; Table 3 footnote

   Most of the text is carefully associational. Exceptions are 'maximal benefit' and '90% of the maximal risk reduction' as names for an associational quantity (Abstract, Sec 2.9, 3.2, Table 3 footnote, Figs 3 and 6); 'no evidence that women and men need different step targets' (Sec 4.4), which is prescriptive; and 'the point where the benefit levels off' (Sec 7). Given the authors' own conclusion that reverse causation shapes the curve, these terms overstate what can be inferred. Fix: use 'maximal difference in log hazard' or 'maximal association', and phrase Sec 4.4 as 'no evidence that the association differs between women and men'.

9. Small count and reporting inconsistencies

   minor · Figure 1; Table 2; Sec 3.1, 3.3; Tables 8, 11

   (i) Cohort B is n=4918 (2482 women) in Fig 1, Table 2 and Sec 3.1, but 4917 (2481) in the abstract and every analysis table. The Fig 1 caption's '0 to 3 participants per imputation excluded' cannot produce a constant N. (ii) 'Covariate data missing for at most 5.7%' is the weighted share for alcohol; unweighted it is 153/2373 = 6.4%. (iii) The rule of at least 100 deaths is stated for sex-by-age strata, yet cohort C sex-specific curves beyond 7 years with 24 and 28 deaths are fitted and classified (Table 11). (iv) The Table 8 footnote omits the unanalysed C 40–59 sex strata. (v) Sec 3.3 gives 8.5% for women at 10000 steps without its CI. (All from check 10 and check 07.)

10. Code and imputation model not available

    minor · Sec 6; Sec 2.4, 2.7; Table 1 (D5)

    Sec 6 states that the complete code and machine-readable results are 'provided with this article in the experiment/code directory', but only the PDF was supplied (check 15). The survey Cox model is the authors' own implementation (D5) and is not validated against survey::svycoxph. The 2003–04 step-imputation model (Sec 2.4) and the 500-replicate bootstrap therefore cannot be rerun. Fix: release the code with a pinned environment, and report a validation of the custom design-based Cox model against a standard implementation.

11. Citation precision

    minor · Sec 1; Sec 2.7, 2.12, 4.2; refs [4], [10], [26], [37]

    The bootstrap is named 'Rao–Wu–Yue–Beaumont', but [26] covers only Rao–Wu–Yue, and no source is given for the Beaumont component. [37] is a cross-sectional MASLD subsample that excluded early deaths and poor self-rated health only, so it is not a precedent for the CVD/cancer and mobility-limitation exclusions it is cited for. The sex P=0.21 attributed to [4] and the 'women level off earlier' direction attributed to [10] could not be verified from the abstracts (check 14).

Questions for the authors

1. Did the frozen plan specify the raw or the Holm-adjusted $p_{nonlin}$ in the decision rule's 'present' clause? Under the adjusted P (0.070), would the abstract still describe the plateau as 'present'?

2. Can the frozen plan and timestamped deviation log be deposited publicly, so that the SHA-256 hash in Sec 2.1 can be matched and the claim that no deviation followed inspection of an association can be audited?

3. Was the A versus A-DR split implemented with a sign condition on $\hat\theta$ (as the pattern in Tables 3 and 8–11 suggests), and what are $\hat\beta_1$ and the linear-slope test for each absent/NI row?

4. What do the bootstrap distributions of $\hat\psi$ look like for men and for the W−M difference? Are they bimodal, and how do profile-likelihood intervals compare?

5. Why does cohort B have 4918 participants in Figure 1/Table 2 but 4917 in all analyses, and how is a constant N obtained if 0–3 participants are excluded per imputation?

6. Has the custom design-based Cox implementation (D5) been checked against survey::svycoxph on the same data, and how closely did the coefficients and standard errors agree?

Verification

References

38 references checked

• [26] J. N. K. Rao, C. F. J. Wu, K. Yue. Some Recent Work on Resampling Methods for Complex Surveys. Survey Methodology 18(2):209-217, 1992

  Cited (Sec 2.7) as the source of a 'Rao–Wu–Yue–Beaumont rescaled subbootstrap'. [26] is the Rao–Wu–Yue rescaling bootstrap; Beaumont is not an author, and no reference is given for the Beaumont component, so the exact replicate-weight method is not traceable. The work itself exists but is not indexed by Crossref (best match was an unrelated 2005 chapter).

• [37] Peng et al. Association of daily step counts and step intensity with mortality among US adults: a cross-sectional study of NHANES 2005-2006. BMC Gastroenterology 25:21, 2025

  Exists, but it is a study of 1108 NHANES participants with MASLD that labels itself cross-sectional. It is cited (Sec 2.12) as precedent for excluding participants with CVD or cancer and those with fair/poor self-rated health or mobility limitation. Its full text shows exclusions of deaths within 2 years and of fair/poor self-rated health only, not CVD/cancer or mobility limitation. In Sec 4.2 it is grouped with [35, 36] as 'earlier sensitivity analyses'; all three reported robust associations, whereas here the plateau disappeared.

• [4] Banach et al. The association between daily step count and all-cause and cardiovascular mortality: a meta-analysis. Eur J Prev Cardiol 2023

  The abstract (PubMed 37555441) supports 'up to 20 000 steps/day ... the more the better'. The sex-interaction P=0.21 attributed to it in Sec 1 does not appear in the abstract, and the full text was not openly accessible, so it is unverified rather than wrong.

• [10] Umbrella review and meta-analysis, Preventive Medicine 2024

  The abstract says only that the optimal dose 'differed according to age and sex'. The specific direction attributed to it in Sec 1 and Sec 4.2 (levelling at lower step counts in women) is not stated in the abstract, so it is unverified.

• [15] Koffman & Muschelli. Minute level step counts ... NHANES 2011-2014 (version 1.0.2). PhysioNet, 2026

  A PhysioNet dataset, not indexed by Crossref; the Crossref best match was an unrelated CRAN package. The version and year could not be verified by the lookup tool.

Suggestions

• Retitle neutrally (e.g. 'Daily step count and all-cause mortality in women and men: dose–response and plateau estimation in NHANES accelerometry'). Restrict the abstract's reverse-causation sentence to the hip-worn cohorts, and note that cohort C kept the classification.

• Deposit the frozen analysis plan and the timestamped deviation log in a public time-stamped registry, link them from Sec 2.1, and add the timestamps to Table 1.

• Report the decision-rule classification using both the raw and the Holm-adjusted non-linearity P. Describe sensitivity analyses through the estimates ($\hat\psi$, $\hat\theta$, E2 with CIs), not through classification labels.

• Report M1 (minimal adjustment) results next to M2 in the abstract and Table 4, and state the estimand of each.

• Show bootstrap histograms of $\hat\psi$ (overall, women, men, W−M), and add profile-likelihood or smoothed-bootstrap intervals for the breakpoint.

• Describe cohort B as an overlapping extension rather than a replication. Compare breakpoint estimates across cohorts quantitatively.

• Release the analysis code, including the step-imputation model for 2003–04 and the custom survey Cox implementation with a validation against survey::svycoxph.

• Replace 'maximal benefit' / 'need different step targets' with associational wording throughout (Sec 2.9, 3.2, 4.4, 7; Table 3 and figure legends).

• Fix the 4918/4917 inconsistency, report unweighted missingness alongside weighted, and either apply the 100-death rule to the cohort C period-by-sex strata or justify the exception.

Ethics and integrity

Scope of this review