Background
People unconsciously prefer certain numbers (clean, cultural, prime, zero, five, or two), and those numbers are easier for them to remember and record.
Older analogue machines, such as scales for measuring weight or sphygmomanometers for blood pressure, could be hard to read, leading to errors and prompting people to round readings for simplicity and ballpark accuracy. Some training for practitioners on these machines even stated that the results should be rounded to avoid common misreading, e.g., 0.7 or .2.
Even today, with digital outputs, when recording figures, clinicians still tend to round to specific end digits, usually zero or five. Each end-digit should appear at approximately the same rate (10%), but numerous studies have demonstrated preferences for zero and five across a wide range of variables, including blood pressure measurements [see here and here], body weight, self-reported height, cigarette consumption and vital signs like heart rate, respiratory rate and oxygen saturation. Such results, especially near threshold boundaries, may lead to misclassification of whether a patient has a disease, errors in estimating the proportion of patients meeting a target threshold, and under- or overestimation of disease risk.
This is how end-digit preference bias is referred to in Sackett’s 1979 paper. A specific type of end-digit bias can also occur when there is a treatment threshold, resulting in disproportionately high numbers of patients recorded as just below or just above the threshold, depending on the actions required, or within “normal” ranges, as illustrated in the examples below.
Also known as Terminal Digit Preference and digit bias, threshold end-digit bias.
Example
A trial of the treatment of isolated systolic hypertension, Syst-Eur, demonstrates end-digit preference: 42.4% of the first sitting systolic blood pressure readings taken were recorded as ending with a zero. Over the course of the trial, the proportion of readings ending with a zero declined from 31.5% in the first year to 22.3% after 3 years. The systolic BP readings are therefore more uncertain at the start of the trial.
For this large-scale experimental study, levels of uncertainty could easily be removed, but for individual patients, if their doctors have a higher zero preference, the results will be less certain, and, consequently, there would also be uncertainty about whether the required BP reduction had been achieved.
This trial also demonstrated an end-digit preference bias toward a systolic BP reading of 148 mmHg in the active arm, likely resulting from the target BP < 150 mmHg. Because the number of patients achieving target BP was exaggerated, this could lead to an overestimation of the BP reduction attributable to the treatment.
The end-digit preference noted here was not observed in other corresponding recorded results, such as standing or supine BP, which were not specifically associated with treatment control.
A 2024 study using routinely collected hospital data on vital-sign measurements demonstrated both end-digit preference biases that varied by the vital sign under consideration and a disproportionately large number of values recorded within the “normal” range for heart rate, oxygen saturation, and blood pressure. Heart rate and blood pressure showed a preference for multiples of five, whereas systolic heart rate and respiratory rate showed an even-number preference.
Impact
End-digit preference bias is more likely when readings are recorded manually rather than automatically. Despite sounding trivial, the impacts can be large: for blood pressure readings, an error of up to ±5 mmHg can easily arise from practitioners’ end-digit preference for recording zero or five.
An over- or underestimation of 5 mmHg is large relative to the accuracy required for cardiovascular risk estimation and may lead to substantial misclassification. Estimates suggest that systematically underestimating blood pressure by 5mmHg would misclassify 21 million people as pre-hypertensive instead of hypertensive [see here and here]. These 21 million people might benefit from anti-hypertensive medication, which would not be prescribed as a result of the misclassification. Conversely, systematic overestimation by 5mmHg could lead to 27 million being labelled hypertensive and potentially being prescribed unnecessary treatment.
The impact of misclassification of patient risk or disease status can lead to incorrect medical decisions: patients requiring treatment may not receive it, or, conversely, may receive unnecessary treatment and potentially suffer adverse effects.
Misclassification of patients results in financial costs from unnecessary prescriptions and emergency care when timely prevention was not provided. There are also societal burdens associated with inaccuracies in understanding disease prevalence in the population, evaluating the efficacy of a new medication, or needing or responding to treatment.
Finally, there may be implications for risk scores and machine learning models created or trained on data that contain these biases.
End-digit preference bias is more likely when readings are recorded manually rather than automatically. Despite sounding trivial, the impacts can be large: for blood pressure readings, an error of up to ±5 mmHg can easily arise from practitioners’ end-digit preference for recording zero or five.
An over- or underestimation of 5 mmHg is large relative to the accuracy required for cardiovascular risk estimation and may lead to substantial misclassification. Estimates suggest that systematically underestimating blood pressure by 5mmHg would misclassify 21 million people as pre-hypertensive instead of hypertensive [see here and here]. These 21 million people might benefit from anti-hypertensive medication, which would not be prescribed as a result of the misclassification. Conversely, systematic overestimation by 5mmHg could lead to 27 million being labelled hypertensive and potentially being prescribed unnecessary treatment.
The impact of misclassification of patient risk or disease status can lead to incorrect medical decisions: patients requiring treatment may not receive it, or, conversely, may receive unnecessary treatment and potentially suffer adverse effects.
Misclassification of patients results in financial costs from unnecessary prescriptions and emergency care when timely prevention was not provided. There are also societal burdens associated with inaccuracies in understanding disease prevalence in the population, evaluating the efficacy of a new medication, or needing or responding to treatment.
Finally, there may be implications for risk scores and machine learning models created or trained on data that contain these biases.
Preventive steps
End-digit preference is avoided by using digital measurement devices that eliminate the need for manual rounding. Training should be provided, and standardised protocols should be written for taking measurements and accurately recording the results.
There may be value in regular training to ensure consistency between practitioners and clinicians with different training backgrounds, especially across different roles and organisations.
When analysing the data, graphical methods may further aid the detection of end-digit bias, and several statistical methods exist that aim to reduce or compensate for this bias.
