# Analysis plan: early-warning statistics of beat-to-beat blood pressure on standing, and their dependence on type 2 diabetes

Registered before any statistic named below was computed on the real data or compared between groups.

## Question

When a person stands, the blood-pressure control loop is challenged by gravity. Dynamical-systems theory predicts that a regulated system closer to losing stability shows "critical slowing down": its fluctuations become more autocorrelated and more variable. We ask:

1. Does standing raise the lag-1 autocorrelation (AR1) of beat-to-beat systolic blood pressure (SBP), relative to sitting, within the same person?
2. Is that rise larger in people with type 2 diabetes (a group with reduced autonomic reserve) than in controls?
3. While standing, is postural sway coupled to SBP fluctuations beyond chance?

## Data

PhysioNet "Cerebral Vasoregulation in Diabetes" v1.0.0 (Novak et al.; CC BY 4.0), downloaded from the PhysioNet open-data mirror `https://physionet-open.s3.amazonaws.com/cerebral-vasoreg-diabetes/1.0.0/`, every file checked against the database's `SHA256SUMS.txt`. We use the 31 sit-to-stand recordings (`Data/Labview/Converted/Sit-to-stand/S####DC.{hea,dat}`, 1000 Hz: finger arterial pressure, bilateral middle cerebral artery Doppler, force plate) and `Data_Description/GE-71_Data_Summary_Table.csv` for group (`group2`: Control or DM), age, the original `Group` label and the dizziness item.

Protocol (from the database description): about 5 min sitting, about 3 min standing with eyes open, about 5 min sitting, about 3 min standing with eyes closed, on a force plate.

## What we saw before registering

We read the database description, data dictionary and channel list; counted, without looking at any physiological value by group, that 29 of the 31 sit-to-stand subjects appear in the summary table (16 Control, 13 DM, of whom 2 carry the label DMOH; 4 report dizziness). We ran the feature extraction once on all recordings to set quality rules, inspecting only: posture-detection timing, beat counts, artefact fractions, mean SBP, channel scales and sway magnitudes. We did not inspect AR1, variance, coherence or any between-group or sit-versus-stand comparison of them. Two decisions came from that inspection, blind to group: (a) the Doppler channels are stored uncalibrated (volts), so only scale-free statistics are taken from them; (b) the centre-of-pressure channels (px, py) are corrupted, so sway is measured from horizontal ground-reaction forces instead.

The included `code/features.py` and `code/analyze.py` are the exact code that will be run.

## Feature extraction (`code/features.py`)

- **Posture**: standing bouts are contiguous runs of at least 60 s in which the 1-s median vertical force exceeds the midpoint between the 5th and 95th percentiles of the recording; bout 1 is eyes open, bout 2 eyes closed.
- **Windows**: sitting = the 240 s ending 10 s before standing begins; standing = from 30 s after standing begins to 5 s before it ends. A bout is excluded if the sitting window would start before the recording or the standing window is shorter than 90 s.
- **Beats**: finger pressure low-pass filtered at 10 Hz (4th-order Butterworth, zero phase); systolic peaks at least 0.33 s apart with prominence at least max(0.3 x the 10-90% range, 5 mmHg). A beat is artefactual if SBP is outside 60-250 mmHg or more than 30% from the 9-beat running median. A window fails quality if more than 10% of beats are artefactual or fewer than 100 good beats remain.
- **Early-warning statistics**: on the good-beat SBP series, linearly detrended within the window: AR1 (Pearson correlation of consecutive residuals) and variance. The same AR1 and coefficient of variation for per-beat mean cerebral blood flow velocity (the hemisphere with the larger sitting standard deviation, at least 0.05 V).
- **Sway**: horizontal ground-reaction forces fy (labelled anteroposterior) and fx (mediolateral), divided by mean vertical force, low-pass 1 Hz, sampled at 4 Hz; standard deviation of the detrended series (units of g).
- **Coupling**: magnitude-squared coherence (Welch, 64-s Hann segments, 50% overlap) between anteroposterior sway and SBP interpolated to 4 Hz, averaged over 0.05-0.15 Hz; z-scored against 200 phase-randomised SBP surrogates (seed 20261007).

## Hypotheses and tests (`code/analyze.py`)

Analysis set: bout 1 (eyes open) of subjects with quality-passing windows and a Control or DM `group2` label.

**Primary (Holm-adjusted across the two, family-wise alpha 0.05):**

- **H1**: standing minus sitting SBP AR1 > 0. One-sided Wilcoxon signed-rank; Hodges-Lehmann estimate with bootstrap 95% CI (10,000 resamples), dz.
- **H2**: the rise in SBP AR1 is larger in DM than Control. One-sided Mann-Whitney; AUC (probability a DM rise exceeds a Control rise) with bootstrap 95% CI.

**Secondary (unadjusted, reported in full):** S1/S2 the same for log SBP variance; S3/S4 the same for cerebral blood flow velocity AR1; S5/S6 H1/H2 repeated on bout 2 (eyes closed); H3 coherence z > 0 across subjects (one-sided Wilcoxon signed-rank); S7 coherence DM versus Control (two-sided; a theory of coupled regulation predicts lower coherence with reduced reserve, but we do not register a direction); S8 the H2 group effect adjusted for age by rank regression.

**Exploratory:** E1 leave-one-out AUC of a ridge logistic regression separating DM from Control using each single measure (SBP AR1 rise, SBP fall on standing, anteroposterior sway, blood flow velocity AR1 rise) and all four jointly. The prediction of interest is that the joint measure separates better than the best single one; with this sample it is descriptive only.

**Not tested:** dizziness (4 subjects) and the DMOH label (2 subjects) are too rare; counts are reported only.

## Power

By simulation (normal data, alpha 0.05 one-sided): H1 with about 27 pairs has 78% power at dz = 0.5 and 44% at dz = 0.3. H2 with 13 versus 16 has 80% power only at a standardised difference of 1.0 (AUC about 0.76) and 35% at 0.5 (AUC 0.64). A null H2 therefore rules out only large group differences; the result will be reported with its CI either way.

## Interpretation rules

H1 supports a gravity-induced shift toward slower blood-pressure dynamics on standing only if positive; note that low-frequency (Mayer-wave) SBP oscillations rising on standing would also raise AR1, so H1 alone does not show proximity to a bifurcation. H2 is the more specific test of reserve dependence. Negative or null results will be published as such.