Rounding and heaping of height¶

Recorded height is a mixture of 5 rounding modes (tens, whole_cm, half_cm, round_up_from_x9, measured_0.1); the model gives the true value's distribution for each record.

Background¶

• Height is stored to 0.1 cm, so it looks measured. But some heights were written as whole centimetres, probably when the patient was not measured.
• It is the first variable whose resolution is mixed at the finest digit.
• Height changes by a centimetre or two over the day, which is handled separately as measurement variability.

Data¶

• 6,388 values, none missing or zero. One value is off the 0.1 cm grid (157.36).
• 57 cases are children (42 patients), down to 42 cm. They get native resolution only (flag child_native_resolution).
• Repeat cases copy the height: of 237 patients with more than one case, 158 have the same height every time.
• The fit uses adults, first case per patient (6,041). Later cases with the same height get the same posterior.
• Within each sex, height is close to normal (women 156.5 ± 6.1 cm, men 168.3 ± 6.4 cm).

Method¶

• Screened the last digit by emergency status, department, age, sex and calendar position.
• Latent: normal regression on sex and age (quadratic), with SD by sex.
• Candidate modes: whole cm, round tens, a half-centimetre mode, and a one-sided round-up from .9 with a ceiling anchor.
• Tested a rounding propensity that depends on emergency status, a first for the engine.
• Compared by BIC: no emergency effect, emergency on whole cm, plus the half-cm mode, plus round-up, and both.
• A 1 cm resolution override was fitted and then dropped (see discussion).

Results¶

• After removing the 10% expected by chance, about 11% of elective and 21% of emergency heights were written as whole centimetres. Thoracic surgery is also higher (26% against 20% overall).
• The .9 digit is depleted (7.3% of elective heights, against about 9% for .1 to .4): a height just under a whole centimetre is often written as the centimetre above.
• There is a small excess at .5 (10.3%).
• Among whole-centimetre heights, 150, 160 and 170 are about 1.5 times their neighbours, but 155 and 165 are not.
• Each added component improved BIC: from 64,888 with no emergency effect to 64,852.5 with all of them.
• Emergency status on the 10 cm mode, department, and a heavy-tailed residual did not help.
• The engine reproduces the log-likelihood exactly (−32,378.3).

Discussion¶

• The 1 cm override worked as a fit, but it threw away the decimal digit, which is the best clue to whether a height was measured. The emergency effect vanished and the 160 heap could no longer be told apart from measured heights near 160.
• So the rounding model answers "what was written down?", and a separate measurement-variability field answers "how far is that from the patient's true height today?".
• The posterior weight of the non-measured modes is reported as possibly_written_in. It is zero for any height whose last digit is not 0 or 5.
• Measured heights get SD 0.5 cm (diurnal loss of about 14–17 mm plus stadiometer reproducibility; Leatt, Reilly & Troup 1986; Voss & Bailey 1997).
• Written-in heights are treated as self-reported, with bias by sex and age band from the 2018 Korea Community Health Survey (171,384 adults) and an SD of about 2.6 cm.
• The API needs sex, age and emergency status.

Limitations¶

• Measurement variability comes from the literature, not from this dataset, and is marked provisional.
• Children are not modelled.

Model¶

Model file: …/models/height.model.json. Read from the pinned snapshot of vitaldb-resolution at commit bb03ddfc8a (2026-10-18).

How a true value becomes the recorded one. The rules are tried in order: a record not taken by an earlier rule is taken by this one with the probability shown (where its condition holds); the last rule takes the rest. Shares of all records depend on the conditions and the true value, so the model must be evaluated for them; the probabilities below are the fitted ones.

• Rounding model kept at the native 0.1 cm so that the decimal digit can separate measured from written-in heights; diurnal height change is handled by measurement_variability, not by coarsening.
• Measurement variability (beyond rounding): SD 0.5 cm; for written-in values, SD 2.6 cm (from literature, not fitted).

Sources the model cites:

• Leatt P, Reilly T, Troup JG. Spinal loading during circuit weight-training and running. Br J Sports Med. 1986;20(3):119-124. doi:10.1136/bjsm.20.3.119
• Healey EL, Burden AM, McEwan IM, Fowler NE. Diurnal variation in stature: do those with chronic low-back pain differ from asymptomatic controls? Clin Biomech. 2011;26(4):331-336. doi:10.1016/j.clinbiomech.2010.11.017
• Voss LD, Bailey BJR. Diurnal variation in stature: is stretching the answer? Arch Dis Child. 1997;77(4):319-322. doi:10.1136/adc.77.4.319
• Ko Y, Choi S, Won J, Lee YK, Kim DH, Lee SK. Differences in accuracy of height, weight, and body mass index between self-reported and measured using the 2018 Korea Community Health Survey data. Epidemiol Health. 2022;44:e2022024. doi:10.4178/epih.e2022024

Code¶

• vitaldb-resolution: vitaldb_resolution/engine.py

References¶

• Leatt P, Reilly T, Troup JG. Spinal loading during circuit weight-training and running. Br J Sports Med. 1986;20(3):119-124. ↗
• Voss LD, Bailey BJR. Diurnal variation in stature: is stretching the answer? Arch Dis Child. 1997;77(4):319-322. ↗
• Healey EL, Burden AM, McEwan IM, Fowler NE. Diurnal variation in stature: do those with chronic low-back pain differ from asymptomatic controls? Clin Biomech. 2011;26(4):331-336. ↗

Tags: generated, vitaldb-resolution