The False-Positive Problem: Why Sensitivity Alone Should Not Win an NHS Contract

Diagnostic evaluation has a tendency to reward the headline number. A test that detects 95 per cent of disease sounds impressive, and in a press release it usually is. But sensitivity is only half of a performance claim, and the half that matters most to a patient is rarely the half that appears in the summary.

Two numbers that travel badly

Sensitivity describes how often a test identifies people who genuinely have the condition. Specificity describes how often it correctly clears those who do not. Both are properties of the assay, measured against a reference standard in a defined population. Neither, on its own, tells a clinician what to do with a positive result.

That requires the positive predictive value — the proportion of positive results that are true positives — and PPV depends not only on the test but on how common the condition is in the population being tested. This is not a subtle statistical point. It is the single largest reason well-validated technologies disappoint when deployed at scale.

The arithmetic of a small prior

Take a test with 95 per cent sensitivity and 97 per cent specificity, and apply it to 100,000 people in whom the condition affects 0.5 per cent — a plausible figure for several rare but serious conditions that UK services screen for.

Of the 500 people with the condition, 475 are correctly identified. Of the 99,500 without it, 97 per cent are correctly cleared, which leaves 2,985 false positives. The PPV is therefore 475 divided by 3,460: roughly 14 per cent. Six out of seven positive results are wrong.

Now move the same test into a population with 5 per cent prevalence — a symptomatic clinic, for example. True positives rise to 4,750 and false positives fall to 2,850. The PPV climbs above 60 per cent. The assay has not changed. Only the prior has.

Lessons from lateral flow

England's experience of mass asymptomatic testing during the COVID-19 pandemic made this arithmetic public in an unusually direct way. Lateral flow devices performed respectably against their intended use, but in settings where prevalence was very low, the proportion of positive results that were false rose sharply — a point that was widely reported and frequently misread as a failure of the devices rather than a predictable consequence of the setting.

The episode left a useful legacy: a broader appreciation among NHS staff and the public that a test result is an estimate, not a verdict. It also exposed how poorly most communication frameworks handle conditional probability.

Biomarker panels and the worried well

Outside infectious disease, the same trap opens wherever a test is applied to people with a low probability of disease. Prostate-specific antigen testing in asymptomatic men, CA125 for ovarian cancer in the general population, high-sensitivity troponin in patients with atypical symptoms, D-dimer in low-risk presentations, faecal immunochemical testing in symptomatic primary care — each carries a different evidence base and a different balance of harms.

The common thread is downstream. A false positive is not a harmless statistical artefact; it produces repeat testing, imaging, biopsy, anxiety and, occasionally, incidental findings that trigger further investigation. In a system with constrained endoscopy, radiology and outpatient capacity, that cascade is a real cost.

Specificity is a system property

Laboratories are required to verify manufacturer claims in their own setting before introducing an assay, and this is where UK practice is stronger than it is often given credit for. But verification typically confirms analytical performance, not clinical utility in the local population.

Operator technique, sample quality, reading conditions and the chosen cut-off all shift the effective specificity. So does spectrum bias: a test validated in secondary care may behave differently when deployed in community settings where the case mix is milder. A cut-off optimised for one pathway can be actively harmful in another.

What commissioners should be asking

Before adoption, several questions deserve a documented answer.

What is the expected prevalence in the exact population that will be tested, and what PPV does that imply at the proposed cut-off? What confirmatory pathway exists, and does it have capacity to absorb the false positives the test will generate? Has the test been evaluated in a UK population, or extrapolated from elsewhere? What happens to patients who test positive but cannot be investigated promptly?

Beyond the assay, there are system questions. Will results be returned to a named clinician with a clear action? Is there a registry or audit to capture outcomes in the first year? Does the business case account for the cost of the confirmatory work, not just the test itself?

NICE diagnostics guidance, NHS England's MedTech Innovation Briefings and the UK National Screening Committee all apply variants of this scrutiny, but the rigour is uneven between a nationally commissioned programme and a locally procured pathway.

Communicating uncertainty without undermining confidence

There is a temptation, when false positives are discussed, to conclude that testing should be curtailed. That is the wrong lesson. The right one is that testing should be matched to prevalence, that two-step pathways should be the default where specificity is finite, and that patients should be told what a positive result does and does not mean before they receive it.

A test that finds disease in the right population is one of the most efficient interventions in medicine. A test applied to the wrong population is an expensive way of generating anxiety. The distinction lies not in the sensitivity figure but in the prior — and in whether anyone thought to calculate it before signing the contract.