Worked examples¶

Common analyses worked through with and without the atlas's corrections, with code to reproduce them: where clock alignment or rounding changes the answer.

Each worked example takes an analysis people commonly run on VitalDB and does it twice: once on the stored numbers, and once with the atlas's corrections, timing on the time side, the rounding models on the value side. Each page states the question, why the atlas changes the answer, the steps, and the code to rerun it, so the same corrections can be carried into your own work. The time-side examples show what misaligned clocks do to derived signals; the value-side examples show results as distributions instead of single numbers.

Time side: when clocks are misaligned¶

Example	Side	Status	Summary
A cerebral autoregulation index from arterial pressure and cerebral oxygenation	time	planned	A moving correlation between mean arterial pressure and INVOS cerebral oxygenation, and how lag between the two devices changes it.
End-tidal to arterial CO₂, and pulse oximetry against blood gas, at the right moment	time	draft	For 4,281 blood gases, reading the monitor when the blood was drawn rather than at the lab stamp makes changes in end-tidal CO₂ track changes in arterial CO₂ far better (within-patient correlation 0.74 against 0.54), and agreement peaks exactly at the estimated draw. Oximetry shows the same timing (agreement peaks at the draw), but the 100% ceiling hides the size of the oximetry gradient for three gases in four.
Post-induction hypotension, from the charted start and from the devices	time	draft	The charted anaesthesia start comes a median 14 minutes before the patient is induced; measured from it, "hypotension within 20 minutes of induction" is found in 27% of 2,913 patients, against 51% from the devices' induction, and the label changes for a quarter of patients.
Pulse arrival time against blood pressure, before and after synchronisation	time	draft	In 3,270 recordings, PAT tracks systolic pressure only once each pulse is paired with its own beat: the hourly correlation moves from a mean of −0.04 to −0.21 (88% of recordings negative), reproducing Ruffolo et al. 2025 in a second dataset; paired naively, PAT is a heart-rate signal.
Pulse arrival time in two correction steps	time	draft	The time from the ECG R wave to the pulse at the finger, as stored, after the PLETH's sawtooth is removed, and after its device offset is removed, smoothed by maximum likelihood, with the arterial line as the reference.
Pulse pressure variation gated by ventilator breaths	time	draft	Pulse pressure variation per ventilator breath, in 3,448 recordings: the ventilator's clock sits a median 1.8 s off the arterial line's, which moves half of all breaths' values by a point or more and scatters where in the breath the pulse pressure peaks; a recording's median PPV hardly changes.

Value side: when inputs are rounded¶

Example	Side	Status	Summary
A regression that carries rounding uncertainty through	value	draft	Acute kidney injury after surgery against intraoperative urine output (mL/kg/h), fitted once on the recorded numbers and once per draw from the true-value distributions: the rounding moves 14% of cases across the oliguria threshold, but widens the confidence interval of the cohort's regression by at most 4%.
Charted propofol dose against the infusion pump	value	planned	The charted propofol bolus total against the volume the Orchestra pump records, as a check of the propofol heaping model and as a dose in mg/kg with its uncertainty.
Intraoperative fluid balance as a distribution	value	draft	Fluids in minus fluids out, each a heaped charted volume, as a distribution per case: the recording alone makes a balance uncertain by about ±60 mL, and by ±190 mL when the blood loss was written as a round 500 mL.
Oliguria labels for a prediction model	value	draft	One label per patient, oliguric or not, from three rounded numbers: 10% of labels are uncertain and 2.6% are expected to be wrong, which sets a floor under the error any model can be measured to have. A typical model is barely affected; a good one is.
Urine output in mL/kg/h as a distribution	value	draft	Intraoperative urine output per kilogram per hour, from three rounded inputs, as a probability distribution per case: one case in ten cannot be placed confidently on either side of 0.5 mL/kg/h.

Both sides¶

Example	Side	Status	Summary
Cuff pressure against the arterial line	both	draft	12,238 cuff readings against the arterial line at the cuff's own moment, in 2,283 patients: no bias over the cohort at any pressure, but each patient's cuff reads a constant 10 mmHg (SD) above or below their line, and half the arterial readings below 65 mmHg are not below 65 by cuff.
Minutes of hypotension per patient, from the monitor and from the waveform	both	draft	Minutes with MAP below 65 mmHg in 3,476 recordings, from the monitor's numeric and from the arterial waveform's beats: the two routes to one pressure differ by several mmHg per patient, which moves half of all patients' minutes by 5 or more and a fifth of their labels, and the numeric's averaging hides short dips in every patient.
Time from a vasopressor bolus to the pressure response	both	planned	How quickly arterial pressure responds to a phenylephrine or ephedrine bolus, with the charted dose times' rounding taken into account. Not feasible in VitalDB, which records bolus totals but no bolus times; kept for a dataset that does.

Population and individual¶

The same measurement error can vanish from a cohort's estimate and still decide one patient's value or label. Errors that are independent and symmetric cancel over many patients; systematic ones do not.

Example	Error	The cohort	Each patient
A regression that carries rounding uncertainty through	random	Carried through 200 draws, the rounding is under 8% of the variance at any threshold: the cohort's answer does not change.	14% of patients sit on both sides of 0.5 mL/kg/h between draws, which is what the cohort averages over.
Cuff pressure against the arterial line	both	The mean bias is −0.1 mmHg at every pressure; even so, hypotension is found in 34% of patients by cuff against 38% by arterial line.	Each patient's cuff sits a constant −11 to +13 mmHg from their arterial line, so 45% of patients with arterial readings below 65 have no cuff reading below 65.
End-tidal to arterial CO₂, and pulse oximetry against blood gas, at the right moment	systematic	Pooled over patients, reading the monitor at the lab stamp instead of the draw changes the gradient's distribution little.	Within a patient, the stamp is always about 7 minutes late, a systematic shift: the monitor tracks the blood gas far worse there (CO₂ change correlation 0.54 against 0.74).
Intraoperative fluid balance as a distribution	random	The distributions' medians sit within 1 mL of the recorded balance: the rounding adds no bias to a cohort's mean.	Each balance is uncertain by about ±60 mL, by about ±190 mL with a round 500 mL blood loss; in 95 cases even its sign is unknown.
Minutes of hypotension per patient, from the monitor and from the waveform	both	The cohort mean moves by 5 minutes between the two routes, and by 2.7 minutes from the averaging alone: neither cancels.	A level offset of up to ±6 mmHg per patient moves half of all patients' minutes by 5 or more and a fifth of their 10-minute labels.
Oliguria labels for a prediction model	random	A typical model's AUC moves by less than 0.001; the labels add a third of the sampling noise.	10% of labels are uncertain and 2.6% are expected wrong, a floor under the error any model can be measured to have.
Post-induction hypotension, from the charted start and from the devices	systematic	The incidence is 27% from the charted start and 51% from the device induction: the shift goes the same way in every patient, so it does not cancel.	26% of patients change label, nearly all from "no hypotension" to "hypotension".
Pulse arrival time against blood pressure, before and after synchronisation	systematic	Naive pairing turns a cohort's mean hourly PAT–SBP correlation from −0.21 into −0.04, and its PAT–HR correlation into −0.40: a systematic error that changes what a study concludes.	Each recording's correlation moves by a median −0.16 when pulses are paired with their own beats; for a patient-level PAT–BP calibration, the pairing decides whether there is a signal at all.
Pulse arrival time in two correction steps	systematic	A device delay of about 0.39 s sits in every stored PAT: a cohort mean is wrong by that much until it is removed.	The PLETH sawtooth adds slips of 33 ms within each patient; removing it lowers the spread against the arterial line from 13.0 to 9.8 ms.
Pulse pressure variation gated by ventilator breaths	systematic	Each recording's median PPV hardly moves (3 of 1,061 cross 13%).	The ventilator sits a median 1.8 s off the arterial line: 53% of breaths' PPV changes by a point or more, and the pulse-pressure peak lands anywhere in the breath.
Urine output in mL/kg/h as a distribution	random	The rounding adds spread but almost no bias: the median of the distributions sits within a hair of the recorded rate.	381 of 3,645 patients (10%) cannot be placed confidently on either side of 0.5 mL/kg/h; with a round 50 or 100 mL, many more.