We conducted a retrospective observational study at Oxford University Hospitals NHS Foundation Trust (OUH) in Oxfordshire, UK. OUH consists of four teaching hospitals with a total of 1000 beds: Hospital A (providing acute care, trauma, and neurosurgery services); Hospital B (elective cancer surgery, transplant, haematology, oncology); Hospital C (district hospital, acute medical services) and Hospital D (elective orthopaedics). OUH acts as a tertiary referral centre for the surrounding region, providing approximately 1 million patient contacts a year and serving a population of around 655,000.


We used individual observations of vital signs conducted at OUH for adult inpatients (≥ 18y) between 01-January-2016 and 30-June-2019. The vital signs observed, with dates and times of collection, included respiratory rate (RR), heart rate (HR), tympanic temperature, systolic and diastolic BP (SBP and DBP) and oxygen saturations. Vital signs were included for all general wards, but those from intensive care units, operating theatre recovery areas, day case units, and OUH’s hospice were not included as these were collected using a separate system or in locations with a different care delivery focus.

Observations were collected by healthcare assistants and registered nurses using a semi-automated vital sign observation system across all 4 hospital sites. HR, SBP, DBP, and oxygen saturations were collected using an observation machine combining an electronic sphygmomanometer and pulse oximeter. RR was manually timed, typically expected to be recorded by counting the number of breaths over 60 s. Temperature was measured with a separate tympanic thermometer. All observations were then manually transcribed into a tablet computer attached to the same stand, this was usually done at the bedside as the tablet computer allowed the patient’s wristband to be scanned to add results to their record. The tablet computer automatically uploaded results into the EHR in real time. Although the tablet computer and observation equipment were co-located on the same mobile stand, there was no automated check that the observations documented had been performed or matched those measured. We do not believe that any of the measurement devices show any intrinsic value preference. All devices produce an error rather than a default reading if measurement is unsuccessful. Supplemental oxygen devices and alertness (alert, responsive to voice, pain or unresponsive, AVPU) were also recorded. However, these non-numerical measurements are not considered further here. Additional data were obtained: hospital-level data (hospital where the observation was made, the specialty managing the patient); and patient data (age, sex, ethnicity, index of multiple deprivation (IMD) score at home address, Charlson comorbidity score).

Statistical analysis

Several approaches have been previously described for identifying and quantifying digit preference25. For example, jointly estimating a flexible, but smooth, underlying distribution and modelling rounding from adjacent values to the nearest number showing digit preference, e.g. from 9 or 11 to 1026,27. Extensions of this approach allow for rounding of groups of adjacent values, e.g. to the nearest 1028. However, here we also wanted to account for a phenomenon in temperature recordings which went beyond simple rounding, where a subset of all observations was set to 36.0 °C. We therefore used a simple maximum likelihood-based estimator to jointly estimate the underlying distribution of temperature, HR, SBP, DBP, and respiratory rate measurements, and the proportion of observations affected by digit preference. Oxygen saturation measurements had only limited dynamic range and no clear evidence of digit preference and so were not studied further. For all other vital signs, we assume that a given vital sign follows an underlying distribution, here we fit both normal and gamma distributions. This leads to the following expression for the statistical likelihood of the observed data, given the parameters governing the underlying distribution and any digit preference (i.e. the probability of digit preference and mean/standard deviation or shape/rate):

Pr(observation was subject to digit preference) * Pr(true value is from the interval of the source distribution leading to rounding) + Pr(observation not subject to digit preference) * Pr(true value given the precision values reported at).

In the case of BP and HR recordings, which are initially reported by the measurement device to the nearest whole number, we estimate the extent of rounding to the nearest 10, for example where the BP reading was 120 mmHg, then the likelihood becomes:

Pr(observation rounded) * Pr(observation from the interval [114.5, 124.5)) + Pr(observation not rounded)*Pr(observation from the interval [119.5, 120.5)).

In the case when the HR or BP is not a multiple of ten, then the probability of rounding is set to zero, and only the second term of the likelihood applies. As this term includes the probability that the observation is not rounded it accounts for the fact that rounding leads to depletion in the frequency of observed values relative to the underlying distribution at values that are rounded up/down. The most common way rounding occurs in the RR is by only timing the number of breaths over 15 or 30 s (rather than 60 s), and then multiplying by 4 or 2 respectively to report breaths per minute. We therefore simultaneously estimated the extent of rounding leading to multiples of 4 and 2 for RR. The formula used for the likelihood means that the estimated proportion of observations subject to rounding includes observations where the true value is a multiple of 4 or 2; as such we estimate the total proportion of respiratory rate observations that might have been measured by timing breaths over 15 or 30 s respectively. Similarly, the form of the likelihood for HR and BP rounding means we estimate the total extent of rounding behaviour, including in our calculations the approximately 1 in 10 instances where the true value and the rounded value are the same.

For temperature readings we assume that any true observation can lead to a documented recording of 36.0 °C, as our hypothesis is that an excess of these readings occurs when the temperature is not actually measured but simply documented as 36.0 °C instead, such that the likelihood becomes:

Pr(observation subject to preference for 36.0 °C) + Pr(observation not subject to preference for 36.0 °C) * Pr(observation from the observed interval of the source distribution).

For temperature recordings we make the simplifying assumption that any observation that is not 36.0 °C is not subject to digit preference.

Maximum likelihood estimates were obtained using R, version 4.2 and pnorm, pgamma and optim functions (see Supplement for code). Confidence intervals were estimated by non-parametric bootstrap sampling using 1000 iterations. For computational efficiency only 10,000 observations were included in each iteration. The accuracy of the code was tested through simulation prior to use.

We used multivariable logistic regression to investigate associations between temperature recordings of 36.0 °C and several factors potentially driving value preferences. Analyses were restricted to patients with complete data, and to complete vital sign sets (i.e. all of temperature, HR, RR, SBP, DBP, and oxygen saturations recorded). We used natural cubic splines to account for non-linear relationships for continuous variables (allowing up to five default placed knots, selecting the final number of knots by minimising the Bayesian Information Criterion, BIC). To avoid undue influence of outlying values, continuous variables were truncated at the 1st and 99th percentiles. Pairwise interactions between model main effects were included where this improved model fit based on BIC. We used clustered robust standard errors to account for repeated measurements obtained from the same patient.

To investigate if associations were specific to temperature or applied to vital signs more widely, we also refitted the same model (i.e. with the same spline terms and interactions) with BP digit preference as the outcome, regarding measurements where the SBP and DBP both ended in zero as indicative of possible digit preference. We use this combined measure across both SBP and DBP as it is likely to be most enriched for digit preference. We fitted the same models for HR and RR digit preference regarding readings ending in zero or multiples as two as showing possible digit preference respectively.

We also investigated if the presence of abnormal previous readings affected subsequent digit preference. Temperatures of ≤ 35.5 °C or ≥ 37.5 °C, SBP readings of > 160 or < 90 mmHg, DBP readings of > 100 or < 60 mmHg, HR readings of < 50 or > 120, and RR readings of < 10 and > 24 were arbitrarily considered abnormal. For each observation with a prior observation from the same patient within ≤ 36 h, we selected the most recent prior observation for comparison. A look back period of up to 36 h was allowed to capture vital signs measured just once a day, but at different times. However, where vital signs were measured more frequently only the most recent was considered. We then refitted the regression models above including a term for if the prior vital sign reading (temperature, HR, SBP, DBP, or RR) had been abnormal as a covariate.

Regression analyses were conducted using R, version 4.2.

Ethical approval

Deidentified data were obtained from the Infections in Oxfordshire Research Database which has approvals from the National Research Ethics Service South Central – Oxford C Research Ethics Committee (19/SC/0403), the Health Research Authority and the national Confidentiality Advisory Group (19/CAG/0144), including provision for use of pseudonymised routinely collected data without individual patient consent. Patients who choose to opt out of their data being used in research are not included in the study. The study was carried out in accordance with all relevant guidelines and regulations.

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