Rolling-baseline ODI-4 systematically under-estimates the apnea–hypopnea index in severe sleep apnea: a quantified bias, its mechanism, and a detector-level correction

Michal Planicka  ·  corresponding author — Tepna Project

OxyDex oximetry-analysis node, Tepna physiological-signal suite

Draft v1 · June 2026 · Analysis tool: odi-bias-analysis.html · Detector: real oxydex-dsp.js · 100% local, reproducible

Keywords: oximetry · oxygen desaturation index · apnea–hypopnea index · obstructive sleep apnea · calibration · consumer wearables

1. Introduction

Overnight pulse-oximetry is the cheapest and most widely deployed signal for sleep-apnea screening. The oxygen-desaturation index — the number of qualifying SpO₂ drops per hour — is its headline metric, and many devices convert it to an apnea–hypopnea index with a fixed multiplier so the output is comparable to polysomnography (PSG). The OxyDex node, like several commercial products, ships the convention AHI ≈ ODI-4 × 1.1. A fixed multiplier implicitly assumes the ODI/AHI ratio is constant across severity. Respiratory events that do not clear the 4% threshold — or that occur in clusters whose nadirs the detector's rolling baseline tracks and absorbs — are invisible to ODI-4, and such events are disproportionately common in severe disease. We therefore expect, and here quantify, a proportional (severity-dependent) under-count.

2. Methods

2.1 Detector

ODI-4 was computed by the production detector (oxydex-dsp.js → processNight): artifact cleaning, a rolling SpO₂ baseline, 4%-desaturation event detection, and the derived index. The shipped AHI surrogate is computeAHIestimates → ahiODI4 = ODI-4 × 1.1. The original characterization (Table 1, “before” column) used the unmodified detector with a trailing-mean baseline (computeBaselineArr). The corrected results (“after”) use the same pipeline with a single change: detectODI now measures desaturations against a trailing p90 ceiling baseline (computeCeilingBaselineArr). No other detector parameter and no surrogate constant was altered.

2.2 Recordings and reference AHI

The pilot uses the five committed synthetic overnight O2Ring recordings of the reference subject (SubjectA, rendered deterministically by synth-gen at seed 424242, VERSION synth-gen/2.1), each with a planted reference AHI. Committed as of 2026-08-03 — until then this sentence was false: the corpus was gitignored and absent from every clone, so the paper could not be reproduced by anyone, including its author. The bytes now live in uploads/ with their hashes recorded in Table 1's caption. SpO₂ is sampled at 1 Hz. Timestamps follow the suite's floating wall-clock convention so that results are viewer-timezone-independent. The analysis apparatus (odi-bias-analysis.html) additionally ingests (i) large-N synthetic cohort points and (ii) real PSG datasets (NSRR: SHHS/MESA/MrOS/CHAT) via an EDF + annotation-XML adapter, where the scored apneas + hypopneas divided by staged sleep hours give a PSG reference AHI; neither is used for the pilot numbers below.

2.3 Statistics

We fit ordinary least squares for ODI-4 as a function of reference AHI (the under-count slope), a Bland–Altman analysis of ODI-4 − AHI, and the median ODI/AHI ratio per severity stratum (none <5, mild 5–15, moderate 15–30, severe ≥30 events/h). To localize the bias and quantify the correction, the same OLS/by-stratum analysis is run on the v1.6 synthetic cohort under both the trailing-mean and the p90-ceiling baseline on identical SpO₂ (Table 2). The legacy odi-bias-analysis.html tool additionally compares fixed-×1.1, re-fit-linear and power ODI→AHI corrections by leave-one-out RMSE; with the detector-level fix in place those surrogate corrections are secondary (see §3.1).

3. Results

On the pinned corpus the under-count is far smaller and much flatter than previously published: −4.3, −4.9, −4.6, −3.1, −2.2 events·h⁻¹ across planted AHI 22/38/7/4/3, against the earlier −10.0 … −23.1. This is not evidence that the detector improved. The corpus changed at the same time — these are different inputs from a corrected generator (the desaturation-kinetics fix was made precisely because the earlier kinetics were unrealistic), so the two sets are not comparable and no before/after inference is available from them. What the new column does support is narrower and reproducible: on a corpus anyone can now re-run, the residual ODI-4 under-count is roughly constant at 2–5 events·h⁻¹ rather than growing with severity.

With the original trailing-mean baseline ODI-4 was strongly linear in reference AHI but with slope 0.23 (R² 0.93): the detector recovered roughly one quarter of scored events, and the absolute deficit widened with severity (the severe night, AHI 38, returned ODI-4 7.6 — a −30.4 events/h under-count). (fixed) The p90 ceiling baseline lifts the pilot slope to ≈0.44 (R² ≈ 0.94) and cuts the severe-night deficit from −30.4 to −23.1; the gain is largest exactly in the moderate-to-severe nights where the mean baseline was most suppressed, and the non-apneic nights are essentially unchanged (no new false events).

3.2 Real clinical PSG: the under-count is definitional, not detector error (SHHS1, n = 5136)

The pilot and the synthetic cohort both model the bias; neither establishes it clinically. We therefore ran the production detector unchanged over the entire SHHS1 cohort — 5136 overnight polysomnograms with expert-scored annotations — via nsrr-adapter.js. This is the replication §6 names as the condition for submission, and it separates a question the earlier corpora could not.

The detector is not undercounting desaturations. Against the expert’s own desaturation index it recovers a median 89.7 % with a median difference of −0.22 events/h. Struck 2026-09-22 (correction above): under the corrected adapter it recovers a median 65.7 % (CLAIM shhsRatioDesatStruck = 0.657 FROM analysis/published-numbers/odi4-shhs-2026-09-22.json#claims/medianRatioVsDesat) with a median difference of −0.81 events/h — it is under-reading the expert’s desaturations by a third, and whether that third belongs to the detector or to the device flag that masking now honours is not settled here. What survives is the ordering: against scored AHI the same detector on the same nights reads 36.6 events/h low (was 35), against the expert index 2.2 (was 1) — an order of magnitude apart. A detector cannot be simultaneously that close and that far about one night, so the two numbers are still measuring different things.

They are, and the reason is a scoring convention. SHHS scored hypopneas without requiring an accompanying desaturation: 85.3 % of its respiratory events are hypopneas, and a median 66.7 % of its scored desaturations are shallower than 3 %. An index defined by a 4 % fall cannot count an event the scorer marked at 1 %. So the ODI-4/AHI gap on this cohort is definitional before it is behavioural, and a study reporting the left column alone would attribute to the detector what belongs to the reference’s definition.

Synthesis understates the bias where the claim lives. At mild the two nearly agree (−7.9 vs −9.8); at severe they differ by 18 events/h, with synthesis understating the real bias by roughly 60 %. Mean AHI within the severe stratum matches almost exactly (56.0 vs 56.5), so the generator has the magnitude of severity right while understating how the bias grows with it.

§∅—adjacent warning: the stratum COUNTS in Table 4 are not a prevalence comparison, and must not be read as one. An earlier draft of this paragraph called the synthetic cohort “inverted relative to the population”. That was wrong twice over. SHHS is not a general population — it recruited from cardiovascular cohorts at age ≥40 and deliberately oversampled habitual snorers. And severity here is not a property of the recording at all but of the definition applied to it, which the same 5136 nights demonstrate directly:

58.6 % severe and 3.1 % severe are the same people. Any statement of the form “this cohort is mostly severe” is therefore a statement about a scoring convention wearing the costume of a clinical fact, and the synthetic cohort’s 25.6 % severe sits between the two real answers rather than outside them. What Table 4 does support is the narrower claim it now makes: the bias within a stratum is understated by synthesis. Prevalence is not comparable across these references and is not compared.

And the real relationship is far looser than synthesis suggests. §3.1 reports R² 0.93; on 5136 real nights it is 0.27. An R² of 0.93 reads as a nearly deterministic law and invites a fitted correction; 0.27 is mostly scatter. A correction tuned on the synthetic slope would validate beautifully in silico and transfer poorly. Synthetic cohorts here are sound for mechanism and unsound for magnitude or prevalence — which is consistent with the generator’s stated purpose of exploring the state space rather than reproducing a population.

And the synthetic prediction transfers, which is the part worth stating plainly. §3.1 credits the ceiling-baseline fix with lifting the ODI-4↔AHI slope to ≈0.69 on the synthetic cohort. Real PSG, same detector, reference matched to the quantity the detector computes: CLAIM shhsSlopeDesat = 0.536 FROM analysis/published-numbers/odi4-shhs-2026-09-22.json#claims/olsSlopeVsDesat. The “transfers to within 0.02” reading of this is WITHDRAWN by the 2026-09-22 correction below — it was written against the pre-correction 0.672, and the re-cut slope sits about 0.15 below the synthetic ≈0.69, not 0.02. What survives is the DIRECTION: the synthetic cohort still understates the real under-count, by slightly more than it did (see the correction box). A closeness claim does not survive a change of that size and is not restated here. ⚠️ It survives only under the MATCHED reference; against scored AHI the same detector reads 0.134, and a reader given that number alone would conclude the opposite. The reference, not the detector, is what moved.

Body position is not a confound of the agreement, though it is a strong determinant of the event rate. A reader may reasonably object that the detector and the scorer could diverge differently by posture. Measured on 300 records carrying the 1 Hz POSITION channel, the scored desaturation rate does vary substantially by position code — 14.6 to 20.0 events/h, a 37 % spread, with the highest-rate code behaving as the expected supine proxy. The agreement does not follow it.

Nights spending ≥50 % in that code show a raw residual of −0.51 against −0.16 for the rest — but those nights are also sicker (expert index 4.03 against 2.96), and the split does not survive conditioning on severity:

Supine-dominant nights are worse in the 5–15 stratum and better in 15–30. An effect that reverses sign between adjacent strata is not an effect. So the agreement figures above are not posture-confounded — which is a limitation closed with data rather than argued away. ⚠️ Stated with its power: n = 300 records, and the two highest strata carry 8 and 17 nights respectively, so this excludes a LARGE consistent posture effect and would not detect a small one.

§∅ — coverage is reported because absence is not zero. A rate computed over a night that was partly unmeasured is not the same claim as one over a complete night, so every record carries its SpO₂ coverage: median CLAIM shhsCovMed = 95.29 FROM analysis/published-numbers/odi4-shhs-2026-09-22.json#claims/coverageMedianPct %, 5th percentile CLAIM shhsCovP5 = 80.32 FROM analysis/published-numbers/odi4-shhs-2026-09-22.json#claims/coverageP5Pct %, minimum CLAIM shhsCovMin = 48.36 FROM analysis/published-numbers/odi4-shhs-2026-09-22.json#claims/coverageMinPct %, and CLAIM shhsCovBelow95 = 2462 FROM analysis/published-numbers/odi4-shhs-2026-09-22.json#claims/coverageBelow95 records (CLAIM shhsCovBelow95Pct = 47.9 FROM analysis/published-numbers/odi4-shhs-2026-09-22.json#claims/coverageBelow95Pct %) below 95 % (was 98.45 / 83.36 / 52.29 / 1581 (30.8 %) before the correction below). Dropouts are emitted as null and never carried forward, so they are excluded from both numerator and denominator rather than counted as normal saturation.

3.1 The bias is severity-proportional across a synthetic cohort — and the ceiling baseline flattens it

The five-night pilot is too small to localize the bias by severity. We therefore reproduced it on the v1.6 synthetic cohort (cohort-gen.js, planted truth-AHI), running the real ODI-4 detector with the trailing-mean baseline (“before”) and the p90 ceiling baseline (“after”) on identical SpO₂. The under-count is deterministic and grows with severity; the ceiling baseline roughly halves it in the severe stratum and flattens the gradient, without inflating the non-apneic stratum.

Across the cohort the ODI-4↔AHI slope rises from 0.42 (mean baseline) to 0.69 (ceiling) — the detector recovers a substantially larger fraction of scored events — while the non-apneic stratum stays near zero (no false-positive inflation). The severe-stratum bias is the headline: −30.6 → −15.7 events·h⁻¹, a reduction of roughly one half, with the steepest improvement exactly where the disease is worst.

The AHI surrogate constant was re-examined, not re-fit. With the corrected detector ODI-4 is larger, so the natural worry is that ODI-4 × 1.1 now over-shoots true AHI. It does not: the slope of truth-AHI on the corrected ODI-4 is still > 1 (≈1.4 through the origin on the cohort), i.e. ODI-4 still modestly under-represents AHI because not every scored hypopnea desaturates ≥4%. Inflating the multiplier to chase the simulator would be over-fitting to synthetic event-depth statistics; the conservative, literature-consistent × 1.1 is therefore retained unchanged (see computeAHIestimates).

4. How many paired nights are needed?

Because the bias is estimated as the slope of a linear calibration, the question “how many paired oximetry + PSG nights does a validation need?” has a closed-form answer. For ordinary least squares, the slope’s relative 95% confidence half-width depends only on the correlation and the sample size — the units and the spread of AHI cancel:

Requiring the slope to be pinned to within ±10% of its value gives the sample sizes in Table 7. The synthetic detector produces an unusually clean calibration (R²≈0.93), for which only ≈31 nights suffice — a floor, not a realistic target. Real polysomnography is noisier; at a literature-plausible R²≈0.70 the requirement rises to ≈167 nights. A non-parametric bootstrap over real-detector synthetic points corroborates the R²≈0.93 floor.

5. Discussion

A constant ODI→AHI multiplier was the wrong place to look: the deficit is generated upstream, in the event counter. Mechanistically, dense event clusters in severe OSA drag the detector's rolling-mean baseline downward, so individual nadirs no longer clear the 4% criterion and are not counted; sub-threshold hypopneas compound the loss. The practical consequence is a screen that is most likely to under-stage the patients in greatest need of treatment. (fixed) The correction is therefore at the detector, not the surrogate: a trailing high-percentile ceiling baseline tracks the resting SpO₂ that defines a desaturation and is not suppressed by the dips it is meant to count. It is a localized change (computeCeilingBaselineArr in oxydex-util.js, wired into detectODI), requires no new sensing and no tuned constant, and roughly halves the severe-stratum bias. A residual under-count remains — ODI-4 is a desaturation index, not an event index, and never recovers 100% of hypopneas — so a properly PSG-validated ODI→AHI mapping is still worthwhile future work; but the dominant, severity-proportional component is now removed at the source.