Review: Daily step count, a plateau in all-cause mortality, and differences between women and men: prospective cohort study using NHANES accelerometry · CheckPaper
Review by CheckPaper · Reviewed 10 Nov 2026
Daily step count, a plateau in all-cause mortality, and differences between women and men: prospective cohort study using NHANES accelerometry
The core cohort, counts and dose–response numbers rebuild exactly from public NHANES files and the conclusions section is appropriately cautious, but the title and one abstract sentence overstate the findings, the pre-registration cannot be verified, and the plateau classification hinges on an unadjusted P=0.035 in a model that adjusts for likely mediators.
Soundness
3/4
Presentation
3/4
Contribution
2/4
Confidence
4/5
✓ 12 confirmed✕ 1 discrepancy○ 2 not checkable
Summary
The paper links NHANES 2005–06 hip-worn accelerometer step counts in 2373 adults aged 40 or older to the 2019 public-use Linked Mortality Files (702 deaths, median 13.6 years) and fits design-based Cox models with a 4-knot restricted cubic spline. Its stated contribution is to formally estimate where the step–mortality curve levels off, using a hinge breakpoint (E1) and a 90%-of-maximal-risk-reduction point (E2), both with bootstrap intervals that re-profile the breakpoint, and to classify the curve with a pre-specified decision rule. It also tests sex differences in curve shape, using an equivalence margin of ±1500 steps/day for the plateau location, and reports standardised 10-year absolute risks.
Main results: HRs vs 4000 steps/day of 0.52 at 8000, 0.43 at 10000 and 0.39 at 12000; non-linearity P=0.035 (Holm 0.070); classification 'present but imprecisely located' with E1 = 6980 (4900–13400) and E2 = 9920 (6910–18380); no sex-by-spline interaction (P=0.72), but equivalence not shown. The analysis is repeated in an overlapping 2003–06 hip cohort (B, 2003–04 steps imputed from counts) and a 2011–14 wrist cohort (C), and in many sensitivity analyses, several of which change the classification. The authors present the work as pre-registered, with 18 logged deviations.
Strengths
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.
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).
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).
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.
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).
Transparent deviations, broad sensitivity analyses and largely cautious discussion
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: pnonlin <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'.
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. 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)'.
Questions for the authors
Did the frozen plan specify the raw or the Holm-adjusted pnonlin in the decision rule's 'present' clause? Under the adjusted P (0.070), would the abstract still describe the plateau as 'present'?
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?
Was the A versus A-DR split implemented with a sign condition on θ (as the pattern in Tables 3 and 8–11 suggests), and what are and the linear-slope test for each absent/NI row?
Verification
15 checks. No code was supplied, so I rebuilt the provenance independently. All Figure 1 flow numbers, the design df, cohort A's n, deaths, person-years, weighted step distribution and spline knots were reproduced exactly from the public NHANES DEMO/PAXRAW and 2019 LMF files. An approximate Cox re-fit reproduced the shape of the Table 4 curve within 0.05 in HR. Internal-consistency checks (spline reconstruction of Table 4, CI symmetry, F→P conversions and Holm, Table 6 differences, Table 7 absolute risks, 153 count identities, hinge vs spline, 79 decision-rule labels) all passed, with only small reporting inconsistencies (N 4918 vs 4917; weighted vs unweighted missingness). One discrepancy is between the text and the results: the title and the abstract's sentence on reverse-causation analyses overstate what Tables 5 and 11 show. The pre-registration and the code-availability claim could not be checked because neither the plan nor the code was available.
[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.
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 (ψ^, θ^, 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.
Ethics and integrity
No ethical concerns about data use: NHANES and the public-use Linked Mortality Files are de-identified public data collected with NCHS ethics approval and consent. Integrity notes: (1) The study is presented as produced end to end by an AI research system (author 'IterSCI'), with no named human accountable for the analysis. The journal should require a responsible human author or guarantor. (2) The 'pre-registered' label rests on a private hash that cannot be matched to any public document, and the plan freeze and the manuscript are dated the same day. This is not evidence of misconduct, but the label should not be used without a verifiable public record. No fabricated or duplicated results were found: every number that could be checked against public data or internally reproduced was correct. Neither the paper nor the requester notes contained instructions aimed at the reviewer.
Scope of this review
Only the PDF was supplied: no LaTeX source, no analysis code, no pre-registration document and no machine-readable results, although Sec 6 refers to an 'experiment/code' directory. I rebuilt cohort A's provenance and descriptive statistics from public NCHS files, but I could not rerun the design-based Cox models, the multiple imputation (including the 2003–04 step-imputation model for cohort B), the 500-replicate subbootstrap or any cohort B/C estimate. My Cox re-fit used an approximate M2 covariate set (no diet, alcohol or mobility; no MI; robust rather than linearisation variance), so it checks shape, not exact values. Absent/NI labels that depend on the unreported linear-slope test could not be verified. Content checks of references [4] and [10] relied on abstracts only.
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.
Fix:
Headline classification rests on the unadjusted non-linearity P, and many labels flip around P≈0.05
The 'present' clause of the rule uses raw pnonlin<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≤pnonlin<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 ψ^, θ^ and E2 barely move (Table 9). For example, excluding early deaths gives P=0.087 with θ^=+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 (ψ^, θ^, E2), not the labels.
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.
'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 R2 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.
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 Δψ=−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 θ −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 ψ^ (e.g. as histograms), report profile-likelihood intervals as a comparison, or present E2, which is smoother, as primary.
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, ∣θ∣<∣β1∣/4. However, all 8 A-DR rows have θ^<0 and 15/17 A rows have θ^>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, θ^=+0.046), which is the opposite of continued decline. 27 absent/NI rows depend on an unreported linear-slope test or β^1 and cannot be checked. Fix: report β^1 and the slope test, and state the rule exactly as implemented.
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'.
(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.)
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.
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).
^
β^1
What do the bootstrap distributions of ψ^ look like for men and for the W−M difference? Are they bimodal, and how do profile-likelihood intervals compare?
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?
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?
Counts in Figure 1, Table 2 and Tables 3, 8-11 are internally consistent; covariate data missing for at most 5.7% of cohort A participants
All 153 identities hold exactly (weighted % sums within rounding). Excluding early deaths removes 64/159/164 persons and the same number of deaths in A/B/C; period splits 736+935=1671 (B) and 731+52=783 (C). Implied weighted female share 0.516-0.553 across rows (mean steps 0.540), coherent. Minor issues: (i) 5.7% is the weighted share missing alcohol; unweighted it is 153/2373 = 6.4%, and 6.3% weighted in women, so the at most 5.7% of participants wording is inexact; (ii) cohort B is 4918 (2482 women) in Fig 1/Table 2/Sec 3.1 but 4917 (2481 women) in every analysis table and the abstract, while the Fig 1 caption says 0 to 3 per imputation were excluded, which does not square with a constant N; (iii) the Sec 2.6 rule of at least 100 deaths is stated for sex-by-age strata, but cohort C beyond-7-year strata with 52/24/28 deaths (Table 11) are reported and classified; (iv) the Table 8 footnote omits the unanalysed C 40-59 sex strata (implied 69/64 deaths).
153 arithmetic identities on transcribed counts: sequential Fig 1 exclusions, category sums and weighted % sums (tol 0.35 points) per Table 2 column, women+men=all, age and sex-by-age strata sums of N and deaths, early-death exclusions (N removed = deaths removed), period-specific death splits; implied weighted female share s=(all-men)/(women-men) from every Table 2 row with sex gap >=3
Title and abstract match the results
Abstract numbers: 43/43 appear in the body; the abstract replication N 4917 matches the analysis tables, while Sec 3.1/Fig 1/Table 2 give 4918. Replication: all three cohorts P-imp; sex x spline P 0.716/0.916/0.477, so the claim of the same classification without sex interaction is supported. Discrepancy: the abstract sentence that excluding early deaths or participants in poor health removed the plateau, repeated in Sec 4.2, holds for hip cohorts A (P-imp -> A, A) and B (P-imp -> A, A-DR) but not for wrist cohort C, where both exclusions remain P-imp (Table 11: pnonlin <0.001 and 0.020). The abstract presents this as a general finding immediately after the replication sentence. Title: a plateau in all-cause mortality is asserted although H1 was not significant after Holm adjustment (P=0.070; Sec 4.1 calls the evidence modest), and differences between women and men is in the title although H2 P=0.716 and the conclusions say no difference was detected; the title is worded as a topic, but it reads as a finding.
Extracted all 43 distinct numbers from the abstract and searched the body text (thousands separators removed); tabulated classes of the reverse-causation sensitivity analyses in cohorts A, B and C from Tables 9-11; primary classes and sex-by-spline P from Tables 3, 8 and 5; compared title wording with H1/H2
Analysis plan pre-registered and frozen 9 Nov 2026 13:11:16 UTC (SHA-256 997495c7...d866) before any data download; all 18 deviations logged with timestamps, none after inspecting associations
The hash is a well-formed 64-hex SHA-256, but the plan document is not supplied (inputs/ holds only paper.pdf and request.json; no input file hashes to it). No registry, DOI or URL is given (the only URL is the NCHS data portal), and a web search for the hash finds nothing, so the plan is a private hash commitment rather than a public pre-registration and its content and timing cannot be verified. Table 1 shows no timestamps despite Sec 2.1 saying each deviation was logged with one. The freeze is 13:11:16 UTC on the same day as the paper date, at most 10 h 49 min before it. Internal items are consistent with the rules as reported: period-specific analyses appear exactly where the Schoenfeld p<0.01 (B, C, not A at 0.018); sex-by-age strata with <100 deaths (A 46/60, B 92, C 69/64) are omitted and the others analysed; primary contrasts use 500 pairs and secondary 200 (D8); Holm is applied to H1 and H2 only. D16 (absent rule applied with positive theta) is an interpretive change that affects classifications (cf. check 04).
Hash format check; SHA-256 of every input file; search of paper text for a registry/URL; web search for the hash string (10 Nov 2026, no hit); timeline arithmetic; internal adherence of reported results to rules stated in Sec 2 (Schoenfeld p<0.01 trigger, 100-death rule, 500/200 replicates, Holm family of two)
NHANES 2003-04 accelerometer files contain counts but no steps (so cohort B steps were imputed); 2005-06 files contain steps
PAXRAW_C variables: PAXCAL, PAXDAY, PAXHOUR, PAXINTEN, PAXMINUT, PAXSTAT (no PAXSTEP, no mention of steps); PAXRAW_D additionally has PAXSTEP. Exact match.
Parsed the CDC PAXRAW_C and PAXRAW_D documentation pages and listed variable names
References exist and support what they are cited for (load-bearing: [1] HRs and follow-up; [3] levelling 6000-8000 >=60 y and 8000-10000 <60 y, sex P 0.11; [4] no upper limit up to 20000, sex P 0.21; [5] ~8800 optimal; [6] elbow 5000-7000; [8] nadir 9000-10500; [12] sex difference on absolute scale P=0.03; [14] breakpoint 8250; [26] RWY-Beaumont bootstrap; [35-37] sensitivity precedents)
All 38 references resolve to real works or to plausible non-Crossref documents (NCHS reports, PhysioNet). Year differences for [7] and [9] are online vs print. Content checks: [1] HR 0.49 (8000) and 0.35 (12000) vs 4000, mortality through Dec 2015 (about a third, as stated); [3] levelling 6000-8000 (>=60 y) and 8000-10000 (<60 y), sex interaction p=0.11 in full text; [4] up to 20 000 steps/day, the more the better; [5] optimal 8763; [6] inflection 5000-7000; [8] nadir 9000-10 500; [12] sex P=.03 for interaction (3-7 days); [14] 8250. Issues (work/ref_issues.json): [26] does not cover the Beaumont component of the named bootstrap; [37] is a MASLD subsample with self-described cross-sectional design and does not exclude CVD/cancer or mobility limitation; the sex P=0.21 for [4] and the women-earlier direction for [10] are not verifiable from the abstracts.
tools/check_refs.py on all 38 references (Crossref DOI/bibliographic query) summarised by 14_refs.py; abstracts of 12 load-bearing refs from Europe PMC (14b); open full texts of [12], [35], [36], [37] (14c), [3] (14d, NCBI efetch); PubMed abstract of [4] (14e)
The complete analysis code and machine-readable results are provided in experiment/code and the master script reproduces every estimate
Only the PDF was supplied (inputs/paper.pdf, inputs/request.json; code_url null; no source/ or code/; no experiment directory). The code and machine-readable results referred to in Sec 6 were not available, so the bootstrap, multiple-imputation and design-based Cox estimates could not be rerun. Instead, cohort A descriptives were rebuilt independently from public NCHS files (checks 01, 02).
Listed inputs/ and request.json (code_url, fetch_log)
Figure 1 upstream flow (cycle n, MEC-examined, aged>=40, pregnant, LMF-ineligible), design df 15/30/32 and cohort C maximum follow-up 111 months match public NHANES files
All 18 flow numbers match exactly: A 10348/9950/2934/3/0, B 20470/19593/6020/5/7, C 19931/19151/7149/6/14; design df 15/30/32 exact; max PERMTH_EXM among eligible cohort-C adults = 111 months (claimed 111).
Recounted from public DEMO_C/D/G/H.xpt and the 2019 public-use LMF .dat files downloaded from CDC; design df = PSUs minus strata per cycle
Cohort A rebuilt from public files reproduces Figure 1 exclusions, n, deaths, person-years, follow-up, weighted step distribution, knots and the Table 4 HR shape
Exact matches: 219 no hip record, 234 unreliable/uncalibrated, 105 no valid day, n=2373 (1187 W/1186 M), deaths 702 (317/385), person-years 28553 (14618/13935), weighted mean steps 9254 (W 8636, M 9980), weighted median 9112, weighted mean age 56.9, age>=60 n=1196. Median follow-up 13.58 y (claimed 13.6). Knots 3014/7521/10458 exact; 95th pct 16149 exact with inverse-CDF definition. Weighted 1st/99th pct 1570/19989, which explains why Table 4 All stops at 18000 and matches the 1st percentile (~1600) implied by E2/50%-point in check 03. Approximate-M2 HRs vs 4000: 0.48 @8000 (claimed 0.52), 0.39 @10000 (0.43), 0.35 @12000 (0.39), 0.35 @14000 (0.37), 0.36 @18000 (0.38): all within the +-0.05 tolerance set for a different covariate set, same flattening above ~12000.
Streamed PAXRAW_D (72M minutes) applying Sec 2.4 rules (Troiano non-wear, >20000 counts/>250 steps missing, >=600 wear min, >=1 valid day); joined DEMO_D and 2019 LMF; weighted percentiles; weighted Cox (lifelines, robust SE, Efron ties) with the same 4-knot RCS and an approximate M2 covariate set (no diet, alcohol, mobility; missing as category; no MI, no design-based variance)
Table 4 HRs are consistent with a 4-knot RCS (knots 3014/7521/10458/16149, ref 4000); nadir 14880, E2 9920, 50%-point 5420 follow from the curve
All: max |fitted - printed HR| = 0.0039 (tolerance 0.005 rounding); Women 0.0035; Men 0.0067 (16000 steps: fitted 0.347 vs printed 0.34, slightly above rounding, plausibly pooling over imputations). Nadir: claimed 14880, obtained 14848 (diff 32 steps/day, below grid/rounding resolution). With a single 1st percentile of 1600 steps/day, E2 = 9923 (claimed 9920) and 50%-point = 5427 (claimed 5420) simultaneously; over p1 500-2000 E2 ranges 9651-10028 and the 50%-point 4837-5648. Women curve is monotone decreasing over 2000-18000 (nadir at upper end), consistent with the A-DR label.
Weighted least-squares fit of the 3 RCS coefficients (Harrell basis) to the printed log-HRs; nadir by dense grid; E2 and 50%-point recomputed while scanning the unreported weighted 1st percentile (500-2000) and 99th percentile (18000-20000)
The pre-specified decision rule (Sec 2.9) was applied correctly to all strata and analyses in Tables 3, 8-12; primary psi interval spans 8500
0/79 violations. Primary CI 4900-13400 spans 8500 (text: 8500). 52 rows are fully determined by printed numbers; 27 absent/NI rows depend on the unreported linear-slope test or beta1, so their A vs A-DR vs NI split cannot be verified. Pattern: all 8 A-DR rows have theta<0 and 15/17 A rows have theta>0, which suggests diminishing returns was implemented with a sign condition, whereas Sec 2.9 states only a magnitude condition (|theta|<|beta1|/4); e.g. B beyond 7 y theta=0.009 labelled A. Of 49 present rows, 44 are P-imp (CI width >6000), so the imprecision threshold rarely discriminates; 27 rows have 0.025<=p_nonlin<0.10, i.e. many labels hinge on p crossing 0.05.
Encoded the rule and the printed p_nonlin, CI(psi), theta, CI(theta), boundary share for 79 rows; checked each printed label lies in the set the rule allows
Table 5 p-values follow from F statistics with the stated df; Holm P 0.070/0.716; primary P-imp classification depends on unadjusted H1 P
15/15 F->P conversions match within rounding (e.g. H1 F(2,15)=4.23 -> P=0.0349, reported 0.035; H2 F(3,15)=0.46 -> 0.714, reported 0.716; small 0.001-0.003 differences consistent with D1 adjustment). Holm: 2x0.035 = 0.070 and 0.716 exact. Global Schoenfeld A chi2=54.67, P=0.018 corresponds to 35 df, plausible for the M2 model. With the Holm-adjusted P=0.070 the primary curve would fail the p<0.05 clause of the present rule (Sec 2.9), so the P-imp headline classification rests on the unadjusted P; the paper reports both but the rule as written uses the raw P.
scipy F survival function with numerator 2/3 and denominator design df 15/30/32, allowing +-0.005 rounding on F; Holm recomputed; Schoenfeld chi-square df scanned; decision rule re-applied with Holm P
Table 6 paired differences equal differences of the stratum point estimates and the Claimed/Within +-1500 columns follow Sec 2.10
22/22 differences equal the difference of printed point estimates exactly (e.g. W-M psi 6900-12030 = -5130); claim logic and equivalence column correct in 22/22 rows (no CI lies inside +-1500). Point estimates are often far from the CI centre (A age psi 5530 in (-8900, 6600), relative position 0.93; A W-M psi -5130 at 0.25), consistent with skewed/multimodal bootstrap distributions of a grid argmax.
Recomputed 22 differences from printed stratum psi and E2 (Tables 3, 8, 9); re-derived Claimed from stratum classes and CI; equivalence from CI vs +-1500
Absolute 10-year risk: 17.8% -> 8.5% (women) and 21.8% -> 11.0% (men) from 4000 to 10000 steps/day, i.e. 9.3 and 10.8 points; further 0.6 and 1.1 points to 12000; men higher than women at every step count
17.8-8.5=9.3, 21.8-11.0=10.8, 8.5-7.9=0.6, 11.0-9.9=1.1 exactly as stated; men > women at all 5 step counts in cohorts A and B; all 30 point estimates inside CIs; risk monotone decreasing; All lies between sexes. Risk ratios 10000 vs 4000 (W 0.478, M 0.505) are higher than Table 4 HRs (0.37, 0.40) and than the homogeneous-risk implied HR (0.453, 0.474), consistent with expected attenuation under marginal standardisation over heterogeneous risk; not a contradiction. Minor: Sec 3.3 quotes 8.5% for women at 10000 without its CI (6.0 to 12.5) while giving CIs for the other three numbers; the PLS statement that men were higher at every step count covers cohorts A and B only (Table 7: not estimable in C).
Arithmetic on all 30 Table 7 cells (copied from paper.txt); monotonicity, CI containment, W<All<M ordering; risk ratio vs Table 4 HR compared under homogeneous-risk approximation
Table 4 CIs are log-symmetric Wald intervals around the HRs (no transcription errors)
25/25 intervals symmetric within rounding (largest asymmetry +0.040 at All 14000, rounding range [-0.016, +0.096]). Abstract HRs 0.52 (0.43-0.63), 0.43 (0.35-0.52), 0.39 (0.29-0.52) match Table 4 exactly.
Interval arithmetic: log(U)+log(L)-2log(HR) with +-0.005 rounding on all three printed values
Hinge estimates (lower slope -0.202/1000, psi 6980, theta -0.049) are consistent with the Table 4 spline HRs
Hinge-implied HRs: 1.498/0.668/0.521/0.472/0.428/0.388/0.352/0.319 vs spline 1.47/0.70/0.52/0.43/0.39/0.37/0.37/0.38; within 15% at 7/8 points (max +9.9% between 2000 and 16000); at 18000 the hinge gives 0.319 vs 0.38 (-16%), still inside the spline CI 0.18-0.80. All 8 inside the spline CIs. The tolerance overrun at 18000 is reported transparently; it reflects the hinge continuing to decline (theta<0) where the spline turns up slightly.
Computed exp of the hinge log-HR relative to 4000 at 2000-18000 and compared with Table 4 (pre-set tolerance 15% relative; secondary criterion added after the first run: inside the spline 95% CI)
Show bootstrap histograms of ψ^ (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.