Normal Distribution
nothing is called 95% until it has been counted
Concept

Decision threshold — where it appears

The value of a score at which a positive call is made. It is a choice rather than a property of the test, and the threshold that minimises harm depends on what each kind of error costs and on how common the condition is.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The operating characteristic, and the point that minimises harm at 0.10% prevalence. The published pair — 90% sensitive, 95% specific — is the open mark. With a miss costing 100 times a false alarm and a prevalence of 0.10%, the threshold that minimises expected cost sits at 74.7% sensitivity and 98.81% specificity, with a predictive value of 5.9%.

The test is a point somebody chose

A test reported as 90% sensitive and 95% specific is not two properties of a test. It is one property read at a threshold, and the threshold that minimises harm runs from 3.05 standard deviations of the score at a prevalence of one in ten thousand to −0.12 at one in two — 45% of cases detected at one end and 99.9% at the other.

screening · Baserate The share of healthy people the harm-minimising threshold flags, against the prevalence, for three spreads of the diseased scores. A miss costs a hundred false alarms. With diseased scores as spread as healthy ones the best threshold flags more healthy people smoothly as the prevalence rises. With them twice as spread it flags 81.1% just below a prevalence of 25.7% and everyone just above it; three times as spread, 45.7% and then everyone at 13.0%.

A threshold that jumps

When a test's scores are equally spread in the healthy and the diseased, the harm-minimising threshold slides smoothly as the prevalence changes. Make the diseased scores twice as spread — the ordinary shape of a group that mixes mild and severe cases — and keep the published 90/95 pair, and the best threshold flags 81.1% of healthy people at a prevalence just under 25.7% and every healthy person just above it. At three times the spread it jumps from 45.7% to everyone at 13.0%. A threshold that jumps cannot be given as a formula; it has to be given with the second-best point beside it.

screening · Baserate

Named alongside it

The objects these essays reach for when they reach for this one.

Base rateExpected lossROC curveScreeningSensitivity and specificityLikelihood ratioPredictive valuePrevalenceThreshold

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