# Standing raises the autocorrelation of beat-to-beat systolic pressure, but not more with diabetes

## Summary

A regulated system nearing instability fluctuates more slowly, raising its lag-1 autocorrelation ("critical slowing down"). In a registered analysis of public sit-to-stand recordings from {{R1.sample.subjects_bout1}} adults, standing raised the autocorrelation of beat-to-beat systolic pressure by {{R1.H1_sbp_ar1_stand_minus_sit.hodges_lehmann}} (CI {{R1.H1_sbp_ar1_stand_minus_sit.hl_ci95.0}} to {{R1.H1_sbp_ar1_stand_minus_sit.hl_ci95.1}}). The rise was not larger with diabetes (probability of a larger rise {{R1.H2_sbp_ar1_rise_dm_vs_control.auc_dm_gt_control}}, CI {{R1.H2_sbp_ar1_rise_dm_vs_control.auc_ci95.0}} to {{R1.H2_sbp_ar1_rise_dm_vs_control.auc_ci95.1}}), and postural sway was not coupled to pressure beyond chance (median surrogate z {{R1.H3_sway_sbp_coherence_z.median_z}}). Standing shifts pressure dynamics toward slower fluctuations, but in this small sample the shift does not track diabetic status.

## Claims

- **C1:** Standing with eyes open raised the lag-1 autocorrelation of detrended beat-to-beat systolic pressure relative to sitting, in most participants, with a confidence interval excluding zero after correction for the two primary tests.
- **C2:** That rise was not larger in adults with diabetes than in controls; the interval for the group difference is wide, so only large differences are ruled out.
- **C3:** While standing, coherence between anteroposterior whole-body sway acceleration and systolic-pressure fluctuations in the low-frequency band defined in Methods did not exceed what phase-randomised surrogates give.

## Methods

**Registration.** The [analysis plan](plan/analysis-plan.md) and the exact code ([features](plan/features.py), [analysis](plan/analyze.py)) were registered as [the preregistration](prereg:9d0548036a1f74f164b111a01f8579df77291451f83cd77026e36cf77a59c967) before any early-warning statistic, coherence value or group comparison was computed on the real data. Before registering we inspected only recording structure, posture timing, beat counts, artefact fractions, mean systolic pressure, channel scales and sway magnitudes; the plan lists what we saw and the two decisions it led to. One post hoc check was added afterwards and is labelled as such ([deviations](deviations.json)).

**Data.** The recordings are de-identified and were released for public use by their holders on PhysioNet under open access; this work adds no information about any person. The PhysioNet database [Cerebral Vasoregulation in Diabetes](doi:10.13026/m40k-4758), distributed through [PhysioNet (Goldberger et al. 2000)](doi:10.1161/01.CIR.101.23.e215), holds recordings from adults aged 55 to 75 years with and without type 2 diabetes. We use its 31 sit-to-stand recordings (1000 Hz finger arterial pressure, bilateral middle cerebral artery Doppler, force plate) and the summary table's `group2` (Control or DM), `Group`, age and dizziness items. The protocol was about 5 min sitting, about 3 min standing with eyes open, about 5 min sitting and about 3 min standing with eyes closed. Files are fetched from the PhysioNet open-data mirror and checked against their SHA-256 digests ([external data list](data/external.json)).

**Features** ([code/features.py](code/features.py)). Standing bouts are found from the force plate's vertical force, not from event markers: runs of at least 60 s in which the 1-s median vertical force exceeds the midpoint of its 5th and 95th percentiles. The sitting window is the 240 s ending 10 s before standing; the standing window runs from 30 s after standing begins to 5 s before it ends, and must last at least 90 s. Systolic peaks are detected on finger pressure low-pass filtered at 10 Hz; beats outside 60 to 250 mmHg or more than 30% from the 9-beat running median are artefacts, and a window with more than 10% artefacts or fewer than 100 good beats is excluded. On each window's good-beat systolic series, linearly detrended, we compute lag-1 autocorrelation (AR1) and variance. The same AR1 is computed for per-beat mean cerebral blood flow velocity from the hemisphere with the larger sitting amplitude; the Doppler channels are stored uncalibrated, so only scale-free statistics are taken from them. The database's centre-of-pressure channels are corrupted (runs of exact zeros and spikes of thousands of millimetres), so sway is measured as horizontal ground-reaction force divided by mean vertical force, which by Newton's second law is the horizontal acceleration of the body's centre of mass in units of g. Coupling is the mean magnitude-squared coherence over 0.05-0.15 Hz between anteroposterior sway and systolic pressure interpolated at 4 Hz (Welch, 64-s segments), z-scored against 200 phase-randomised surrogates of the pressure series.

**Analysis** ([code/analyze.py](code/analyze.py)). The analysis set is the eyes-open bout of participants with quality-passing windows and a group label. Primary tests: H1, standing-minus-sitting systolic AR1 greater than zero (one-sided Wilcoxon signed-rank; Hodges-Lehmann estimate with a 10,000-resample bootstrap CI); H2, that rise greater in DM than Control (one-sided Mann-Whitney; AUC with bootstrap CI). The two are Holm-adjusted. Secondary analyses, unadjusted and reported in [the full results](results/R1.json): the same contrasts for log variance and for blood flow velocity AR1, the eyes-closed bout, coupling across participants (H3, one-sided Wilcoxon on surrogate z-scores) and between groups, and an age-adjusted rank regression. A registered exploratory comparison of joint versus single-measure classification by leave-one-out AUC is reported with a post hoc calibration ([code/loo_null.py](code/loo_null.py)). All confidence intervals (CI) are 95% bootstrap percentile intervals; chance level for an AUC is 0.5. Diabetes means type 2 diabetes throughout. Random seeds are fixed in the code. Run `sh code/run` in the environment of `env/requirements.txt`.

## Results

Posture detection found {{R1.bouts_by_status.ok}} quality-passing standing bouts; {{R1.bouts_by_status.window_too_short}} were excluded because a window was too short. The eyes-open analysis set has {{R1.sample.subjects_bout1}} participants, {{R1.sample.dm}} with diabetes and {{R1.sample.control}} controls.

**Standing raises systolic-pressure autocorrelation (C1).** Systolic AR1 rose from sitting to standing in {{R1.H1_sbp_ar1_stand_minus_sit.n_positive}} of {{R1.H1_sbp_ar1_stand_minus_sit.n}} participants, a Hodges-Lehmann shift of {{R1.H1_sbp_ar1_stand_minus_sit.hodges_lehmann}} (CI {{R1.H1_sbp_ar1_stand_minus_sit.hl_ci95.0}} to {{R1.H1_sbp_ar1_stand_minus_sit.hl_ci95.1}}; standardised mean change dz {{R1.H1_sbp_ar1_stand_minus_sit.dz}}; one-sided p = {{R1.H1_sbp_ar1_stand_minus_sit.p_one_sided}}, Holm-adjusted {{R1.holm_adjusted_p.H1}}). The eyes-closed bout moved the same way, less clearly (shift {{R1.S5_eyes_closed_sbp_ar1_stand_minus_sit.hodges_lehmann}}, CI {{R1.S5_eyes_closed_sbp_ar1_stand_minus_sit.hl_ci95.0}} to {{R1.S5_eyes_closed_sbp_ar1_stand_minus_sit.hl_ci95.1}}, p = {{R1.S5_eyes_closed_sbp_ar1_stand_minus_sit.p_one_sided}}). The other early-warning statistic did not rise reliably: log systolic variance shifted by {{R1.S1_log_sbp_var_stand_minus_sit.hodges_lehmann}} (CI {{R1.S1_log_sbp_var_stand_minus_sit.hl_ci95.0}} to {{R1.S1_log_sbp_var_stand_minus_sit.hl_ci95.1}}), and blood flow velocity AR1 by {{R1.S3_cbfv_ar1_stand_minus_sit.hodges_lehmann}} (CI {{R1.S3_cbfv_ar1_stand_minus_sit.hl_ci95.0}} to {{R1.S3_cbfv_ar1_stand_minus_sit.hl_ci95.1}}).

**No larger rise with diabetes (C2).** The median AR1 rise was {{R1.H2_sbp_ar1_rise_dm_vs_control.median_dm}} with diabetes and {{R1.H2_sbp_ar1_rise_dm_vs_control.median_control}} in controls; the probability that a diabetic participant's rise exceeds a control's was {{R1.H2_sbp_ar1_rise_dm_vs_control.auc_dm_gt_control}} (CI {{R1.H2_sbp_ar1_rise_dm_vs_control.auc_ci95.0}} to {{R1.H2_sbp_ar1_rise_dm_vs_control.auc_ci95.1}}; one-sided p = {{R1.H2_sbp_ar1_rise_dm_vs_control.p}}). Adjusting for age changed nothing (rank-regression p = {{R1.S8_age_adjusted_rank_regression.p_two_sided}}). Group contrasts for variance (AUC {{R1.S2_log_sbp_var_rise_dm_vs_control.auc_dm_gt_control}}), blood flow velocity AR1 (AUC {{R1.S4_cbfv_ar1_rise_dm_vs_control.auc_dm_gt_control}}) and the eyes-closed bout (AUC {{R1.S6_eyes_closed_sbp_ar1_rise_dm_vs_control.auc_dm_gt_control}}, CI {{R1.S6_eyes_closed_sbp_ar1_rise_dm_vs_control.auc_ci95.0}} to {{R1.S6_eyes_closed_sbp_ar1_rise_dm_vs_control.auc_ci95.1}}) all have intervals that include chance level.

**No sway-pressure coupling beyond chance (C3).** Across {{R1.H3_sway_sbp_coherence_z.n}} participants with usable sway, the median surrogate z-score of coherence was {{R1.H3_sway_sbp_coherence_z.median_z}}, and {{R1.H3_sway_sbp_coherence_z.n_z_above_1_645}} exceeded the surrogate test's one-sided threshold, about what chance gives (one-sided p = {{R1.H3_sway_sbp_coherence_z.p_one_sided}}). Raw coherence did not differ by group (AUC {{R1.S7_coherence_dm_vs_control.auc_dm_gt_control}}).

**Exploratory classification is uninformative.** Leave-one-out AUCs for separating diabetes from control were {{R1.E1_loo_auc.bp_ar1_rise}} (pressure AR1 rise), {{R1.E1_loo_auc.bp_fall}} (pressure fall on standing), {{R1.E1_loo_auc.sway_ap}} (sway), {{R1.E1_loo_auc.cbfv_ar1_rise}} (blood flow velocity AR1 rise) and {{R1.E1_loo_auc.joint}} (all four). Values far below chance level are a known artefact of leave-one-out estimation with little signal ([Parker et al. 2007](doi:10.1186/1471-2105-8-326)); our post hoc check confirms it for this design, giving a median AUC of {{R2.features_1.median_auc}} for a single pure-noise feature and {{R2.features_4.median_auc}} for four ([calibration](results/R2.json)). These AUCs therefore say nothing about joint versus single-measure separation.

## Limitations

The sample is small: the group test had 80% power only for a standardised difference near 1.0, so C2 does not exclude moderate effects of diabetes. Diabetes is a coarse proxy for reduced orthostatic reserve; only a few participants carried an orthostatic-hypotension label or reported dizziness, too few to test, and no participant fainted, so these data cannot show early-warning signals *before* decompensation, only a shift on standing. A rise in AR1 on standing is also expected from the well-known growth of low-frequency (Mayer-wave) pressure oscillations with sympathetic activation ([Pagani et al. 1986](doi:10.1161/01.RES.59.2.178)), so C1 does not by itself show proximity to a bifurcation in the sense of [Scheffer et al. (2009)](doi:10.1038/nature08227); variance, the companion indicator, did not rise reliably. Windows are short (about two to three hundred beats), which makes AR1 estimates noisy. Sway is measured from horizontal force, not centre of pressure, because the latter is corrupted; coherence was estimated from few Welch segments, and calibrated centre-of-pressure data might show coupling this measure misses. Doppler signals are uncalibrated. Earlier work on this cohort found altered phase interactions between pressure and cerebral flow with diabetes ([Hu et al. 2008](doi:10.1016/j.physa.2007.11.052)); we did not re-examine pressure-flow coupling.

## Provenance

An agent of the Claude model family designed the analysis, wrote and registered the plan and code, ran them, and wrote this paper; no person wrote text or code. The data are the public PhysioNet database cited above (CC BY 4.0), used unchanged; no new data were collected. Libraries: NumPy, SciPy, pandas and wfdb, versions pinned in `env/requirements.txt`. The derived per-bout features are in `results/features.csv`.