opsinjs
HealthNumbers on a screen

Risk and statistics

Absolute risk before relative risk, natural frequencies before percentages, and no probability without the population it came from and the window it covers.

What this means

A relative risk states the ratio between two probabilities and omits their size. "This raises your risk by 50%." is a relative figure, and a sentence of that shape is arithmetically correct whenever the ratio behind it is, so it passes review on accuracy while carrying nothing about how many people are affected. If the underlying risk was 2 in 10,000, the sentence describes a change to 3 in 10,000, which is one additional person in ten thousand. If the underlying risk was 40 in 100, the same sentence describes a change of an entirely different magnitude. A relative figure is invariant to the baseline, so both readings are covered by the same words, and a reader given the ratio alone cannot recover which of them was meant.

A percentage is a normalised ratio, and normalisation is the operation this page treats as hardest for a lay reader. The risk-communication literature described in "Why (evidence)" below holds that "10% of people" is understood less reliably than "1 in every 10 people", and rule 2 rests on that finding rather than on any measurement of ours. Comparison across percentages with different denominators is the harder case, because a 10% chance of one thing against a 5% chance of another that is ten times worse asks the reader to renormalise both figures and weigh two severities before the comparison can be made at all.

Health interfaces render probabilities on many surfaces, including risk scores, likelihoods, confidence figures and "people like you" comparisons. This page governs the form those figures take on screen, and whether a product should compute or show one at all is set out under "What this does not cover".

The rule

Express risk as an absolute frequency, with a stated population, over a stated time window, alongside the baseline it is being compared to.

#RequirementWhat must appear alongside the figureBasisFailure it prevents
1Absolute, never relative alone. A relative figure is never the only figure given.Both absolute figures, given greater prominence than the ratio.Risk-communication literature. The editorial policies of several major medical journals require absolute figures alongside relative ones.A ratio read as though it were a magnitude.
2Natural frequencies over percentages. "About 3 in every 100 people" rather than "3%".The same denominator on every figure the reader is asked to compare.Risk-communication literature on natural frequencies.A comparison the reader can complete only by renormalising one figure against another.
3The population is always stated. "3 in every 100 people of your age with a similar reading" is a different claim from "3 in every 100 people", and the reader is entitled to know which one is being made about them.The population the figure describes, named at the figure.Design judgement.A rate for people in general read as a rate for people like the reader.
4The time window is always stated. A probability with no window is unbounded, because the same event grows more likely the longer the period considered.The period the probability covers, written inside the figure itself as "In the next 10 years".Design judgement.A probability the reader cannot bound in time and therefore reads as imminent.
5The baseline is given. A risk figure on its own cannot be interpreted, because the comparison it is implicitly making is what gives it a size.The comparable figure for the population the reader is being distinguished from.Design judgement.A figure the reader has nothing to weigh against.
6Both halves of the frequency appear. If 3 in 100 experience something then 97 in 100 do not.The complement of the figure, on the same denominator.Risk-communication literature.A small frequency read as larger than it is because its complement was never shown.
7No bare percentage as a headline. A percentage does not stand alone in a tile, in a notification, or as a dial value with no explanation attached to it.The population, the window and the baseline, on the same surface as the headline figure.Design judgement.A figure carried into a tile or a notification stripped of everything needed to read it.
8No small probability encoded as an area or an angle. A pie slice at 3% is unreadable and an arc at 3% looks like an error.A countable representation such as an array of 100 marks, or a worded statement, with a text equivalent for a reader who cannot see the graphic.Design judgement, extended from the general reading of small angular and areal encodings and untested in risk visualisation.A 3% arc read as a rendering fault rather than as a quantity.
9A population figure describes a group. A risk score is a statement about a group the reader resembles, not a prediction about the reader.A sentence naming the group, at the score.A group rate read as the reader's own outcome.
10A model's confidence and the reader's risk are different quantities. A figure that is a model output is labelled as one. See Data provenance and device accuracy.The model's identity and its known performance, at the figure.A model's internal confidence read as the probability of an outcome for the reader.

The Basis column follows the classification set out in "Why (evidence)" below, which also records rule 8 as an untested extension. Rules 9 and 10 are not classified in that note, and their cells are left empty rather than filled by assumption.

Why (evidence)

Not written yet. Replace the described literature above with specific, read, dated citations on Evidence and references, and change this page to evidence: mixed when that is done.

Applying it

Do

"About 4 in every 100 people with a similar reading have this happen in the next 10 years. For people with a reading in the usual range it is about 2 in every 100."

Don’t

"Your risk is doubled." The statement holds at every baseline, so a reader shown it alone learns the ratio and learns nothing about how many people the change affects.

Do

"About 3 in every 100. That means about 97 in every 100 do not." The example states both halves of the frequency on a single denominator.

Don’t

Use "3% chance" as the headline number on a tile and put the explanation behind a disclosure control, which leaves the population, the window and the baseline readable only to a reader who opens it.

Do

Show a grid of 100 marks with 3 highlighted, with a text summary that states the same figure for anyone who cannot see the grid.

Don’t

Show a donut chart with a 3% arc. The arc reads as a rendering bug, and without the text twin the figure is unavailable to a screen reader.

Do

"This score is based on readings from people of a similar age and sex. It describes a group, not you."

Don’t

"Your heart age is 62." The figure addresses the reader in the second person while describing a population, and it states neither the population it was derived from nor the period it covers.

Components that implement this

ScoreDial is the component this page binds most tightly, because a dial renders one figure at the centre of a bounded arc and so reads as a complete statement even when the population, the window and the baseline are absent. Its specification therefore requires that the band is named in words, that the derivation is disclosed on the same surface, and that no dial may render a bare percentage as its primary value.

What this does not cover

  • Calculating risk. opsinjs ships no risk models and no scores. Where a product computes one, its validity, its population and its performance are the product owner's to establish and to disclose.
  • Whether a risk figure should be shown at all, which is a clinical and ethical decision. See Delivering difficult results.
  • Genetic and hereditary risk, which carries family-disclosure implications well beyond this system.
  • Screening statistics cover sensitivity, specificity and the positive predictive value problem, none of which has a page in this section yet.
  • Chart construction, which is covered in Data visualisation.
Not written yet. Write the screening-statistics page: why a positive result on a good test for a rare condition is usually a false positive, and how to say so.

Updates to this page

Last read through against the system on 2026-09-02. Due for review every 12 months; expiry is reported by pnpm run check:freshness.

On this page