---
title: "Risk and statistics"
description: "Absolute risk before relative risk, natural frequencies before percentages, and no probability without the population it came from and the window it covers."
url: "https://opsinjs.pensievelabs.org/health/risk-and-statistics"
source: "https://opsinjs.pensievelabs.org/health/risk-and-statistics.md"
section: "Health"
kind: "health"
evidence: "opinion"
reviewed: "2026-09-02"
reviewer: "design"
aliases: ["absolute risk", "relative risk", "natural frequencies", "probability", "odds", "percentage"]
implements: ["score-dial", "result-card", "care-card", "value", "disclaimer-note"]
---
> Elements written as `` below are opsinjs documentation
> components. Their attributes are the content: the values they render are
> generated from `tokens/*.json` and `registry/catalogue.ts` and are
> published separately at https://opsinjs.pensievelabs.org/r/index.json and under the Reference
> section.
> Nothing is missing from this page. The data simply does not live in
> the prose.
## What this means [#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 [#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.**
| # | Requirement | What must appear alongside the figure | Basis | Failure it prevents |
| -- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------- |
| 1 | **Absolute, 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. |
| 2 | **Natural 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. |
| 3 | **The 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. |
| 4 | **The 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. |
| 5 | **The 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. |
| 6 | **Both 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. |
| 7 | **No 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. |
| 8 | **No 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. |
| 9 | **A 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. |
| 10 | **A 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](./data-provenance-and-device-accuracy.mdx). | 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) [#why-evidence]
This page is marked `opinion` because it names a literature without citing a
paper from it.
The substance of rules 1, 2 and 6 is not original to us. There is a substantial
and long-established literature on risk communication, most closely associated
with work on natural frequencies and on the distinction between absolute and
relative risk, and it is reflected in the editorial policies of several major
medical journals, which require absolute figures alongside relative ones.
Guidance bodies producing patient-facing material have followed the same line
for years.
We name the school of thought rather than a specific paper because this
documentation's rule is that a citation must be a source we have read and can
point you at, rather than a reference reconstructed from memory. The primary
material is findable under the search terms "natural frequencies risk
communication" and "absolute versus relative risk reporting".
Rules 3, 4, 5, 7 and 8 are our design judgement about how the literature's
conclusions should constrain a component. Rule 8 in particular is a graphical
claim we have not tested: small angular and areal encodings are known to be
read poorly in general, and we extend that to risk visualisation on judgement.
What would change our mind: no observation we can construct would revise rule
1, because a relative figure shown without its absolute pair withholds the
information a reader needs to size the change rather than presenting that
information badly. Rule 2's preference for frequencies over percentages is
worth revisiting for numerate readers, and a comparison in a numerate
population showing equal comprehension of percentages and frequencies would
revise it, because a product that knows its audience might then reasonably
offer both.
Replace the described literature above with specific, read, dated citations
on
[Evidence and references](./evidence-and-references.mdx)
, and change this page
to
`evidence: mixed`
when that is done.
## Applying it [#applying-it]
"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."
"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.
"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.
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.
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.
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.
"This score is based on readings from people of a similar age and sex. It
describes a group, not you."
"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 [#components-that-implement-this]
{/* Generated from `implements`. Do not restate the list by hand. */}
`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 [#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](./delivering-difficult-results.mdx).
* **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](../foundations/data-visualisation/index.mdx).
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 [#updates-to-this-page]