First ReSTAGE step under censoring

Stage: REPORT_EN
Report date: 2026-10-25
Classification: reproductive clock and delay of perimenopause
Evidence used: human observational, human endocrine/ultrasonographic, computational, and inferred
Direct animal, in-vitro, or ex-vivo evidence for the endpoint: none
Current Lua data: not used
Overall maturity: H0–H1; not eligible for partnering or clinical use

1. Executive scientific abstract

Answer to the question

With accessible evidence and data, it still cannot be determined whether cumulative incidence of the first recurrent |ΔL|≥7 is explained by Λ(age) plus level lag 3 or retains a reproducible residual. The correct result is neither “the null explains it” nor “there is an ovarian signal”: the primary contrast remains unestimated. The ovarian index exogenous to bleeding therefore is not activated.

This non-identification produced four concrete advances.

1. The endpoint contains an unrecognized algebraic echo. Adjacent differences share one length: ΔL_t=L_t−L_(t−1) and ΔL_(t+1)=L_(t+1)−L_t. A single extreme length, such as 28→42→28, generates two 14-day jumps and confirms ReSTAGE in the next segment without two independent biological perturbations. Under the strict Utah rule, 54/79 confirmations were adjacent, 48/54 reversed sign, and 37/50 first events per woman shared a segment. Utah is young and does not inform the elbow, but demonstrates the metrological problem.
2. The historical null is unspecified. Huang publishes the eight population means of the mean and log-variance model, including CP_σ=42.84 years, but not the diagonals required to reconstruct Ω, the predictive heterogeneity among women. Ecochard publishes P values for lag-3 ACF/PACF, not a common coefficient, sign, or transportable parameter. Bortot obtains a rival random-trend plus ARMA(1,1) dynamic, with higher orders negligible after detrending.
3. Public data fail the identifying gate. Utah exactly reproduces 3,137 segments from 562 women and provides 80–130 closed windows depending on the continuity rule, but no woman can cross 42.84 years. Colombo/Padua extends to age 50 but requires authorized access. Two eligible public cohorts do not exist for development and replication.
4. Ovarian biology is plausible but not incremental. Human studies show HPO branches capable of short and long cycles: accelerated follicular development under high FSH, delayed estrogenic response, LOOP events, and cycles without robust luteal activity. No study combines eleven consecutive segments, individual elbow crossing, censoring adjudication, a frozen hierarchical null, a pre-event ovarian trajectory, and independent replication.

The most likely interpretation today is that any apparent residual will be dominated first by operator echo, selection/censoring, and lack of temporal transport/specification, rather than a new ovarian signal. The surviving ovarian hypothesis is narrower: only a non-overlapping residual (j≥2), absolute magnitude at least 0.10 at age 45, precise, robust, and reproduced, would justify testing a follicular-ovulatory trajectory independent of bleeding. Isolated AMH or FSH do not meet that requirement.

2. Scientific question and relevance

In longitudinal calendars observing women before and after CP_σ=42.84 years and permitting sufficient-window adjudication, is cumulative incidence of the first absolute change of at least seven days that recurs within the following ten segments contained by an age-dependent bleeding process with three-segment level memory, or does a reproducible excess persist that justifies seeking an ovarian measurement independent of bleeding?

ReSTAGE/STRAW+10 uses a persistent change of at least seven days between consecutive lengths to mark entry into early transition. It is clinically descriptive and associated with FSH, but remains an operator on bleeding dates. It does not identify the biological generator, timing of an ovarian lesion, or a lever capable of delaying perimenopause.

M1-4 separates predictive sufficiency—whether the calendar, after modeling age, heterogeneity, temporal dependence, and observation, reproduces the marker—from biological increment—whether an independent ovarian measurement adds out-of-sample information after that null. A fit would establish calendar sufficiency for this classifier, not absence of ovarian contribution. A failure would establish miscalibration, not ovarian origin, until operator effects, heterogeneity, censoring, transport, and uterine/thyroid rivals are excluded.

3. Scope, population, and life stage

Target population

The target is adult women undergoing natural reproductive aging, initially menstruating spontaneously, observed from before age 42.21 through after 43.17 and preferably through 46.23. 42.84 is Huang's log-normal estimate; 42.21 comes from the gamma sensitivity analysis, and 42.49–43.17 is the main-estimate interval. Age is continuous. The elbow is a population-support requirement, not an individual biological boundary.

The stage comprises late reproductive −3 and entry into early transition −2. STRAW is not a primary covariate because it contains the bleeding outcome; future FMP is excluded because it would retrospectively condition the analysis.

Inferential unit

The woman is the unit of partitioning, bootstrap, validation, and replication; repeated candidates/windows within a woman are not independent. The former floor of 30 closed windows remains an administrative condition but is replaced inferentially by at least 200 women at risk at age 45, 80 first events per cohort, and adequate simulated precision.

Primary exclusions

Primary exclusions are pregnancy, lactation, gonadal suppression, hormonal contraception or hormone therapy preventing interpretation of spontaneous bleeding, hysterectomy, oophorectomy, gonadotoxic chemotherapy/radiotherapy, and established POI. PCOS, fibroids/adenomyosis, and thyroid dysfunction must be stratified when measured or declared as limitations. Archive end, gap, or treatment is never a non-event.

Out of scope

The project does not estimate fertility, pregnancy probability, symptoms, FMP, healthspan, or longevity; validate AMH as a primordial-follicle census or the −2 bit as clinical benefit; propose an intervention, compound, dose, or recruitment; or use current Lua data.

4. Baseline knowledge and mechanistic map

4.1 From ovary to menstrual segment

reserve/growing cohort
  → granulosa inhibin B/AMH and FSH feedback
  → dominant-follicle selection and growth
  → E1G/E2, LH surge, and ovulation
  → corpus luteum, P4/PdG, and luteal duration
  → endometrial withdrawal or breakthrough
  → observed bleeding onset
  → L_t

Each arrow has different evidential strength. FSHR–cAMP/PKA, aromatase, inhibins, and luteal steroidogenesis are established molecular/cellular physiology; the joint chain around the first M1-4 event has not been measured.

4.2 HPO states that can widen the distribution

• Compensated ovulatory: lengths near 26–29 days despite aging.
• Accelerated: high FSH with a responsive follicle, early selection, and short follicular phase.
• Delayed: delayed estrogenic response, late selection, and long cycle.
• LOOP: dominant follicular development during the luteal phase, out-of-phase E2, lower P4, and an extreme subsequent cycle.
• Without robust luteal activity: low or absent P4/PdG and greater segment dispersion.

Klein observed accelerated follicular development in women aged 40–45 versus younger women. FREEDOM linked delayed E1G takeoff to long cycles. Hale described LOOP, higher FSH, lower inhibin B/P4, and cycles <21 or >40 days. SWAN DHS showed cycles with evidence of luteal activity remain about 26–27 days, whereas non-ELA cycles are more variable and ELA falls from 87.9% five years before FMP to 22.8% one year before it. These human findings support generators of short or long L, not residual information above Λ+lag 3.

4.3 How Λ(age) compresses the mixture

S_it ∈ {compensated, accelerated, delayed, LOOP, non-ELA}
L_it = FP(S_it) + LP(S_it) + UTERUS_it + error_it

Var(L | age) = E[Var(L | S, age)]
             + Var(E[L | S, age]).

Variance can rise through within-state noise, separation among states, switching rate, stable between-woman heterogeneity, or continuity selection. Huang estimates a population mean/log-variance trajectory, but that compression does not identify which component changed.

4.4 Lag 3: predictive signal, not localized mechanism

Ecochard detects significant lag-3 ACF/PACF in Europe and North America. The table contains P=0.0084 and P=0.0030 for North America, not coefficients. Bortot, after random-trend and outlier modeling, favors ARMA(1,1), with higher orders negligible. The approximate match of three cycles to about 85 days of human follicular growth establishes only time-scale compatibility. Without a t−3 map from selection, AFC/inhibin B, or LH state to L_t, lag 3 remains phenomenological.

4.5 Observational state machine

no candidate
  -- |ΔL_t|≥7 --> open candidate
  -- another jump within ≤10 --> confirmed
  -- 10 without recurrence --> expired
  -- end before decision --> open/censored

The age of the first jump is adjudicated only after the second. Confirmation time is prospectively observable; backdated onset requires a multistate model. Neither innocuously substitutes for the other.

5. Evidence method

All M1-4 artifacts were integrated: scoping, evidence map and verification, mechanism, computational decision and execution, hypotheses, adversarial review, and experimental design. Nulls and contradictions were preserved rather than restarting from general literature.

Decisive sources were checked in primary originals for design, population, age/stage, size, matrix, estimand, effect, uncertainty, and transport limit. Evidence classes were:

• human observational: calendars, age, bleeding, follow-up, stopping reasons;
• human endocrine/ultrasonographic: E1G, LH, PdG, FSH, inhibin B, AMH, AFC, follicular dynamics;
• computational: change points, ACF/PACF, temporal models, PFGA simulation, Utah reanalysis;
• inferred: HPO switching or PFGA as an incremental explanation of the residual.

No animal, in-vitro, or ex-vivo evidence directly measures the first ReSTAGE step. Recent verification confirmed that Lawley et al. fitted a seven-day PFGA threshold to the population onset distribution, excluded simulated onset before age 42 to match the empirical set, and acknowledged the need for prospective validation. This supports a generative rival, not individual prediction or residual causality.

6. Evidence map

7. Contradictory evidence and null results

7.1 Λ versus temporal memory

Huang shows that age and heterogeneity model much of the trajectories, but its serial predictive check does not refute a specific lag. Ecochard finds lag-3 significance; Bortot finds a rival structure where higher orders cease to matter. The contradiction requires separate locked-replication votes for M0-L3 and M0-A11.

7.2 ReSTAGE as a specific onset

FSH association and precedence over later markers support reproductive relevance. High frequency before age 40 and adjacent-difference echo reduce mechanistic specificity. The criterion remains descriptively useful but cannot mean two persistent HPO episodes without decomposing j=1.

7.3 Endocrine indices

FSH, AMH, inhibin B, and ELA associate with stage, phase, or FMP proximity. None has shown external gain over M0-H/M0-L3. AMH does not beat FSH at 12 months for FMP in SWAN and has only modest later advantage. Inhibin B was null for total length in the TTC cohort. A hormone distinct from L is not exogenous if sampling or definition depends on future bleeding.

7.4 Censoring and continuity

Stricter Utah rules reduce confirmations, but nested filters always remove observation; 129→79 alone does not prove informative censoring. The valid contrast standardizes risk sets and stopping causes. IPCW helps only with observed predictors and positivity, not MNAR or absent causes.

7.5 PFGA

PFGA simulation produces a notable population match, but the seven-day threshold was identified against a seven-day outcome, onsets <42 were excluded, and individual longitudinal primordial activation is unobserved. Evidence is computational H2 for distribution fit and H0 for individual validation.

8. Multiscale mechanistic synthesis

Molecular and cellular scale

At molecular/cellular scale, lower small-follicle granulosa mass can reduce inhibin B/AMH and raise FSH. Response is nonuniform: a competent follicle can accelerate selection, while a temporarily poor cohort delays E1G. FSHR, cAMP/PKA, CYP19A1, inhibins, and luteal steroidogenesis make the bifurcation plausible but do not identify its frequency around the first step.

Follicular and ovarian scale

At follicular/ovarian scale, accelerated, delayed, LOOP, and non-ELA branches provide human generators of extremes. HPO switching may cluster them beyond marginals; the PFGA rival invokes stochastic gaps in immature follicle supply. Both may coexist; neither has shown increment over the null.

HPO scale

At HPO scale, KNDy/GnRH and pituitary gonadotropins interact with ovarian inhibins/steroids. HPA, thyroid, metabolism, and circadian rhythms may modify the system. Lifetime memory supports plausibility, not temporal resolution for inclusion in M1-4; these remain prespecified confounders/modifiers, not post-hoc explanations.

Uterine scale

At uterine scale, the calendar observes the endometrial efferent. Ovulation, anovulation, steroid withdrawal, breakthrough, fibroids, adenomyosis, polyps, and thyroid disease can shift the date. Bleeding duration is not interval between onsets; Paramsothy supports a uterine rival but does not quantify this operator.

Statistical scale

Statistically, the same age mean/variance can arise from independent extremes or clustered switches. Λ may reproduce the first; the second may leave a residual. Analysis must first discount j=1 echo, Ω heterogeneity, temporal form, and observation.

Integrated inference

age heteroscedasticity
  + between-woman heterogeneity
  + algebraic echo of adjacent differences
  + continuity/censoring
  + model-dependent temporal memory
  + true HPO states
  → observed first ReSTAGE step.

The empirical question is which layer contributes incremental, transportable incidence—not which exists, because several do.

9. Computational layer

Question and input

Public computation was chosen to audit support and recompute lag 3, not BioNeMo; protein, DNA, and single-cell models do not accept censored calendars as valid biological input.

Utah was the executable CC BY-NC 3.0 input. Filtering conception_cycle == "No" exactly reproduced 3,137 rows from 562 women. Maximum continuous age at segment onset was 40.82685; even adding one year for baseline integer-age uncertainty left <41.82685, so no woman could cross 42.84.

Output

Outputs were:

• 141/562 women had simultaneous cycle-number/date gaps;
• 32 segments >60 d occurred in 25 women despite a published stopping rule stopping before that event;
• rules retained 130, 110, and 80 closed windows;
• confirmations fell from 129 to 79 between permissive and strict readings;
• 119–164 candidates remained open depending on rule;
• Q1-LAG-TRANSPORT and Q2-PASSAGE-DIAGNOSTIC stopped by design.

What decision changed

The computation ruled out “too few Utah windows” as the dominant explanation and localized failure to stage and adjudication. It strengthened the observation/transport hypothesis and prevented invalid residual estimation. It produced no lag-3 coefficient, M0-F, residual, or ovarian signal.

Derived adversarial result

The later confirmation-distance audit showed j=1 predominance, so D0-OPERATOR-ECHO must precede any biological contrast.

10. Primary hypothesis — M1-4-REPORT-H1 v1

Role: calendar sufficiency; descendant of M1-4-AR-H1 v2.
Falsifiable statement: in two independent cohorts crossing the elbow, M0-OP→M0-H→M0-L3 will calibrate candidate and confirmation times for original ReSTAGE and non-overlapping j≥2 recurrences within prespecified margins.

Mechanism: age marginals generate extremes; the operator converts one extreme into adjacent recurrence; between-woman heterogeneity widens tails; short dependence adds clustering. Causal ovarian information may already be embedded in bleeding.

Evidence for: Huang supports age/heterogeneity; ReSTAGE is frequent before 40; algebraic echo is a strong memory-free generator; hormonal association may be redundant. Evidence against: Ω is unavailable; lag 3 lacks a transportable coefficient; ARMA(1,1) is a plausible challenger; two eligible cohorts do not exist; external HPO states could retain information.

Predictions: M0-OP reproduces much of j=1; M0-H reduces tail residual; M0-L3 adds external calibration over M0-H; both coprimary outcomes lie within ±0.10 at age 45 and IACE≤0.05.

Kill criterion: absolute j≥2 residual ≥0.10 at age 45, same sign, IC95% excluding zero, IACE>0.05, reproduced in two cohorts under frozen M0-L3, harmonized censoring, and separate temporal challenger.

Status/maturity: weakened/proposed; H0 overall, H1 for components. Confidence 0.25.

11. Competing hypothesis — M1-4-REPORT-H2 v1

Role: structural-observational-transport family, integrating without merging votes from M1-4-AR-H2E v1, H2C v1, and H2T v1.
Falsifiable statement: most apparent residual is absorbed by adjacent-recurrence echo, continuity/censoring harmonization, and lag-3 nontransport; no precise, reproducible non-overlapping excess remains requiring an ovarian measurement.

Internal mechanisms receive separate votes: H2E, one shared extreme produces two jumps and confirms j=1; H2C, long-series selection, gaps, stopping reasons, and look-ahead alter risk sets; H2T, lag 3 attenuates after age/woman effects or loses to ARMA(1,1).

Evidence for: algebraic identity; 54/79 strict-Utah j=1; 48/54 sign reversals; discontinuity in 141/562; conflicting stopping rule; P values without coefficient; Bortot's rival. Evidence against: ReSTAGE retains hierarchy and FSH association across four cohorts; Utah misses the elbow; residual may survive j≥2 and harmonized observation.

Predictions: M0-OP covers j=1; F_nonoverlap falls materially; harmonized risk sets move D(45) by at least 0.05 or reverse sign; φ3 changes sign/magnitude or fails to improve IACE≥0.02 in replication.

Kill criterion: j=1 is a minority in two target cohorts, residual displacement is <0.05 under every rule, stopping causes are observed, and φ3 transports with external advantage over ARMA(1,1).

Status/maturity: strengthened. H2E H2 computational/algebraic; H2C H1–H2; H2T H1. Overall qualitative confidence high, not a single probability.

12. Translational hypothesis — M1-4-REPORT-HT1 v1

Role: conditional translation of M1-4-AR-H3S v2 and M1-4-AR-HT1 v2.
Falsifiable statement: only if a robust j≥2 residual persists, a pre-event follicular-ovulatory trajectory—E1G/LH/PdG calibrated against ultrasound—will improve out-of-sample event calibration and, after metrology, anticipate months with orthogonal ovulation and robust luteal exposure better than age, calendar, AMH/AFC, or static FSH/inhibin B.

Mechanism: switching among accelerated, delayed, LOOP, compensated ovulatory, and non-ELA states contains cycle-to-cycle information absent from an age marginal or slow reserve index.

Evidence for: human endocrine/US states generate extreme lengths; ELA separates stable from variable cycles; a trajectory is closer to the generator than FMP or one AMH visit. Evidence against: no activating residual, frozen index, reliability, consecutive cohort, or replication; ELA/PdG is not ovulatory rupture; PFGA is a rival; prediction does not prove causality.

Predictions: IACE improvement ≥0.02, relative Brier improvement ≥10%, and ≥50% reduction in j≥2 residual in the replication center; dynamic index beats static comparators; signal precedes the candidate without depending on next menstruation.

Kill criteria: metrological failure, temporal leakage, in-sample-only gain, no external gain, absorption by censoring/uterus/thyroid, or equivalence/superiority of static comparators.

Status/maturity: parked, H0, confidence 0.05. HUMAN_QA_REQUIRED before any new study. Neither biomarker nor target.

13. Falsifiable predictions and kill criteria

The uncertain link is pre-event ovarian state → non-overlapping residual over M0. Ranked explanations are structural echo > observation/censoring > temporal transport > hierarchical sufficiency > HPO/PFGA switching. Only the discriminants above can change the ranking.

14. Discriminating experiment

D0-OPERATOR-ECHO

Question: What fraction of the original first step arises from j=1, and how much is reproduced by a memory-free marginal?

Construct first events per woman in each eligible archive; tabulate j=1…10, signs, and p_echo; repeat at j≥2; simulate M0-OP using observed age, marginals, and follow-up; permute within woman/age bands; inject one missed menstruation as error control. Require ≥60 women with a first event per cohort; Utah is only a young control. Go: reproduced p_echo and valid F_nonoverlap. No-go: crossed gaps, windows counted as n, or post-result j selection.

D1-PASSAGE-NESTED

Question: After discounting echo, what do heterogeneity and lag 3 contribute?

Use independently sourced development and replication; TREMIN may develop but never self-replicate. Each cohort requires ≥200 women at risk at age 45, ≥80 first events, sufficient j≥2, stopping causes, and simulated precision. Fit M0-PUB, M0-OP, M0-H, M0-L3; treat M0-A11 as challenger, not rescue. Use continuous age and sensitivities 42.21/42.84/43.17. Model candidate and confirmation times in a multistate structure with left truncation and open windows.

Coprimary outcomes are D_L3,orig(45) and D_L3,nonoverlap(45). The activation gate is non-overlapping residual ≥0.10, same sign, IC95% excluding zero, IACE>0.05, robust and externally reproduced.

D2-STATE-SWITCH, only after G-RESIDUAL

Inventory existing archives first. If none exists, a new study needs human/ethical/legal QA. Use two centers, women aged 40.5–44.5, ≥18 segments or 24 months; daily first-void E1G/LH/PdG with creatinine/density/time; ultrasound substudy; quarterly AMH/AFC; prospectively timed inhibin B/FSH. The algorithm may not use the next menstruation.

T0 metrology: 30 women, two cycles, CV≤10%, completeness ≥85%, point sensitivity/specificity ≥0.85 against ultrasound rupture with lower bound ≥0.75, and <15% unclassifiable.

D2: event-driven, 100 first j≥2 events and 200 women with a complete window, cap 600; one center develops and the other replicates. If 600 do not yield 100 events, the hypothesis remains non-estimable and is not degraded to j=1.

Why this is the smallest experiment

This is the smallest experiment because hormone measurement before D0/D1 would spend a cohort explaining an endpoint possibly generated by its own geometry: operator first, nested calendar second, ovary third.

15. Biomarkers and stratification

No measure currently qualifies as a biomarker. Experimental candidates are: (1) E1G/LH/PdG trajectory anchored to ultrasound; (2) serial inhibin B with FSH; (3) AMH/AFC as slow heterogeneity and comparator; (4) stopping cause, continuity, and adherence as observation-process variables; and (5) uterine pathology and TSH/thyroid diagnosis as pre-event rivals.

STRAW, FMP, SD(L), bleeding duration, menstruation-derived SD(FP), and hormones defined with the next menstruation are ineligible. Primary stratification is by age/entry, continuity, stopping cause, uterine/thyroid pathology, and cohort. Race/ethnicity is descriptive only with adequate support and does not replace between-cohort replication.

16. Individual variability

Ω is part of the phenomenon, not disposable noise, and may encode different intercepts, slopes, and change points. AMH/AFC may explain slow heterogeneity without switching. Adiposity, smoking, reproductive history, PCOS, thyroid disease, uterine pathology, treatment, and cohort generation can modify biology and continuity.

TREMIN is historical and predominantly white/educated; Ecochard is dominated by young ages and regularity criteria; SWAN is multiethnic but enters late and several analyses condition on follow-up/FMP; Utah is young. Transporting effect sizes to Mexican/LATAM populations is premature. Any future LATAM validation must follow closure of mechanism and metrology and may not use current Lua data without explicit legal/ethical authority.

17. Pharma relevance and maturity

Potential relevance

Potential relevance is conditional: if D1 validates j≥2, it could qualify an endpoint for natural history or experimental enrichment; if D2 validates an HPO trajectory, it could become a pharmacodynamic assay of pre-bleeding state in a future mechanistic trial; separating slow heterogeneity from switching could define research strata.

What does not yet exist

There is no molecular target, target engagement, causal perturbation, dose–response relationship, compound, safety profile, surrogate endpoint, or external validation. The residual is unestimated. The Pharma opportunity is metrological and conditional, not therapeutic.

Maturity: H0–H1, not H5. HUMAN_QA_REQUIRED before human study, partnering, or biomarker use. No intervention is prescribed or proposed.

18. Limitations

1. Restricted TREMIN, SWAN, SMWHS, MWMHP, or Padua data were not accessed; the primary contrast was not run.
2. Ω cannot be reconstructed from Huang's published correlations.
3. Ecochard does not publish the lag-3 coefficient; significance is not size or sign.
4. Utah reproduces the denominator but not target stage and has conflicting discontinuities/stopping rules.
5. The algebraic echo was demonstrated in a young cohort and needs post-elbow replication.
6. The 0.10 margin, 0.05 IACE, and 0.02 gain are scientific decision thresholds, not validated clinical MCIDs.
7. Proposed power requires multistate simulation on actual grids before outcome access.
8. Endocrine sources are small, selected, or discontinuous; none assembles the endpoint.
9. ELA/PdG is not follicular rupture or reproductive competence.
10. Uterine and thyroid pathology is undermeasured in historical archives.
11. PFGA is a population-calibrated simulation, not an individual observation.
12. No bleeding, AMH, or FMP result establishes fertility, healthspan, or longevity.
13. Absence of identifying data is not evidence of absence of mechanism.

19. Conclusions

The current scientific answer is strict: Λ(age)+lag 3 has not been validly tested against the first ReSTAGE step in two eligible cohorts, and no reproducible residual activates an exogenous ovarian index.

The principal advance is conceptual and quantitative. Original recurrence may arise largely from one extreme length because adjacent differences share a segment. This echo precedes any discussion of HPO memory/persistence. The historical null must be layered into published marginal, operator/observation, heterogeneity, lag 3, and temporal challenger. A flexible fitting model does not retrospectively rehabilitate Λ+lag 3.

The surviving ovarian hypothesis is narrow and falsifiable: after discounting echo, observation, heterogeneity, and transport, a pre-event follicular-ovulatory trajectory should explain a precise, reproduced j≥2 residual better than static AMH or FSH. Until D0 and D1 pass, measuring it is premature.

Final scientific delta of M1-4/REPORT_EN

M1-4 redefines the decisive object as the non-overlapping residual of the first step, not raw ReSTAGE recurrence: public evidence shows the original endpoint is strongly exposed to algebraic echo and observation process, while the Λ+lag 3 null remains unspecified and untested. The ovarian index therefore stays off, but a quantitatively gated sequence—j≥2 residual ≥0.10 at age 45, precise, robust, and replicated—can activate or eliminate it without confusing missing data with biology.

20. References

1. Harlow SD, Mitchell ES, Crawford S, Nan B, Little R, et al. The ReSTAGE Collaboration: Defining Optimal Bleeding Criteria for Onset of Early Menopausal Transition. Fertility and Sterility. 2008;89(1):129–140. DOI: 10.1016/j.fertnstert.2007.02.015. PMID: 17681300. PMCID: PMC2225986.
2. Harlow SD, Gass M, Hall JE, Lobo R, Maki P, Rebar RW, Sherman S, Sluss PM, de Villiers TJ. Executive summary of STRAW+10: Addressing the unfinished agenda of staging reproductive aging. Journal of Clinical Endocrinology & Metabolism. 2012;97(4):1159–1168. DOI: 10.1210/jc.2011-3362. PMID: 22344196. PMCID: PMC3340904.
3. Derry PS, Derry GN. An analysis of the STRAW operational definition of the early menopausal transition. Women's Reproductive Health. 2014. DOI: 10.1080/23293691.2014.901797.
4. Huang X, Elliott MR, Harlow SD. Modeling menstrual cycle length and variability at the approach of menopause using hierarchical change point models. Journal of the Royal Statistical Society: Series C. 2014;63:445–466. DOI: 10.1111/rssc.12044. PMID: 24729638. PMCID: PMC3979630.
5. Ecochard R, Stanford JB, Fehring RJ, Schneider M, Najmabadi S, Gronfier C. Evidence that the woman's ovarian cycle is driven by an internal circamonthly timing system. Science Advances. 2024;10:eadg9646. DOI: 10.1126/sciadv.adg9646. PMID: 38598621. PMCID: PMC11006216.
6. Bortot P, Masarotto G, Scarpa B. Sequential predictions of menstrual cycle lengths. Biostatistics. 2010. DOI: 10.1093/biostatistics/kxq020. PMID: 20400622.
7. Harlow SD, Zeger SL. An application of longitudinal methods to the analysis of menstrual diary data. Journal of Clinical Epidemiology. 1991. DOI: 10.1016/0895-4356(91)90003-r.
8. Ferrell RJ, O'Connor KA, Holman DJ, et al. Monitoring reproductive aging in a 5-year prospective study: aggregate and individual changes in steroid hormones and menstrual cycle lengths with age. Menopause. 2005. DOI: 10.1097/01.gme.0000172265.40196.86. PMID: 16145311.
9. Santoro N, Crawford SL, El Khoudary SR, et al. Menstrual cycle hormone changes in women traversing menopause: study of women's health across the nation. Journal of Clinical Endocrinology & Metabolism. 2017;102:2218–2229. DOI: 10.1210/jc.2016-4017. PMID: 28368525. PMCID: PMC5505186.
10. Santoro N, Crawford SL, Lasley WL, et al. Declining luteal function during the menopausal transition. Journal of Clinical Endocrinology & Metabolism. 2008;93(5):1711–1721. DOI: 10.1210/jc.2007-2165. PMID: 18285413. PMCID: PMC2386686.
11. Klein NA, Battaglia DE, Miller PB, Branigan EF, Giudice LC, Soules MR. Ovarian follicular development and the follicular phase with aging: marked development accelerated by a monotropic FSH rise. Journal of Clinical Endocrinology & Metabolism. 1996;81(3). DOI: 10.1210/jcem.81.3.8772573. PMID: 8772573.
12. Miro F, Parker SW, Aspinall LJ, Coley J, Perry PW, Ellis JE. Origins and consequences of the elongation of the human menstrual cycle during the menopausal transition: the FREEDOM Study. Journal of Clinical Endocrinology & Metabolism. 2004. DOI: 10.1210/jc.2003-031731. PMID: 15472184.
13. Hale GE, Hughes CL, Burger HG, Robertson DM, Fraser IS. Atypical estradiol secretion and ovulation patterns caused by luteal out-of-phase events underlying irregular ovulatory menstrual cycles in the menopausal transition. Menopause. 2009. DOI: 10.1097/GME.0b013e31817ee0c2. PMID: 18978637.
14. Vanden Brink H, Chizen D, Hale G, Baerwald A. Age-related changes in major ovarian follicular wave dynamics during the human menstrual cycle. Journal of Clinical Endocrinology & Metabolism. 2015. DOI: 10.1210/jc.2015-2643.
15. Robertson DM, et al. Interrelationships between FSH, inhibin B, antral follicle count and AMH in women of late reproductive age. Endocrinology, Diabetes & Metabolism. 2021;4:e00172. DOI: 10.1002/edm2.172.
16. Harris BS, Steiner AZ, Jukic AM. Ovarian reserve biomarkers and menstrual cycle length in a prospective cohort study. Journal of Clinical Endocrinology & Metabolism. 2021. DOI: 10.1210/clinem/dgab204. PMID: 33772306. PMCID: PMC8372629.
17. Sowers MR, Eyvazzadeh AD, McConnell D, et al. Anti-Müllerian hormone and inhibin B in the definition of ovarian aging and the menopause transition. Journal of Clinical Endocrinology & Metabolism. 2008. PMCID: PMC2567855.
18. Finkelstein JS, Lee H, Karlamangla A, et al. Antimüllerian hormone and impending menopause in late reproductive age: the Study of Women's Health Across the Nation. Journal of Clinical Endocrinology & Metabolism. 2020;105:e1862–e1871. DOI: 10.1210/clinem/dgz283. PMID: 31965189. PMCID: PMC7067546.
19. Paramsothy P, Harlow SD, Greendale GA, et al. Bleeding patterns during the menopausal transition in the multi-ethnic Study of Women's Health Across the Nation. BJOG. 2014. DOI: 10.1111/1471-0528.12768. PMID: 24735184. PMCID: PMC4199918.
20. Paramsothy P, Harlow SD, Nan B, et al. Duration of the menopausal transition is longer in women with young age at onset: the multi-ethnic Study of Women's Health Across the Nation. Menopause. 2017. DOI: 10.1097/GME.0000000000000736. PMCID: PMC5266650.
21. Lawley SD, Sammel MD, Santoro NF, Johnson J. Mathematical recapitulation of the end stages of human ovarian aging. Science Advances. 2024;10:eadj4490. DOI: 10.1126/sciadv.adj4490. PMID: 38215196. PMCID: PMC10786411.
22. Li K, Urteaga I, Wiggins CH, et al. Characterizing physiological and symptomatic variation in menstrual cycles using self-tracked mobile-health data. npj Digital Medicine. 2020;3:79. DOI: 10.1038/s41746-020-0269-8.
23. Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Statistics in Medicine. 2007;26:2389–2430. DOI: 10.1002/sim.2712. PMCID: PMC2692556.
24. Stanford J, Najmabadi S. Menstrual Cycles Length of Women in the USA and Canada, 1990–2013. The Hive, University of Utah Research Data Repository. DOI: 10.7278/S50d-4gxs-s4hj. CC BY-NC 3.0 license.