A diagnostic test is judged against a reference standard (gold standard): the best available way of knowing who truly has the disease
Validity (accuracy) is whether the test measures what it should. Reliability (repeatability) is whether it gives the same result when repeated. A test can be reliable but not valid

## The 2 × 2 table

Measure	Formula	Question answered
Sensitivity	a ÷ (a + c)	Of those with the disease, what proportion test positive?
Specificity	d ÷ (b + d)	Of those without the disease, what proportion test negative?
Positive predictive value (PPV)	a ÷ (a + b)	Of those who test positive, what proportion have the disease?
Negative predictive value (NPV)	d ÷ (c + d)	Of those who test negative, what proportion are disease-free?
Accuracy	(a + d) ÷ total	What proportion are classified correctly?
Likelihood ratio positive (LR+)	sensitivity ÷ (1 − specificity)	How much a positive result raises the odds of disease
Likelihood ratio negative (LR−)	(1 − sensitivity) ÷ specificity	How much a negative result lowers the odds of disease

Sensitivity and specificity are read down the columns (by true disease status); predictive values are read across the rows (by test result)
SnNout: a highly sensitive test, when negative, rules the disease out
SpPin: a highly specific test, when positive, rules the disease in
Sensitivity and specificity are properties of the test and change little with prevalence. Predictive values depend on prevalence

## Worked example: the effect of prevalence

A glaucoma test has a sensitivity of 90% and a specificity of 95%. It is used on 10,000 people in two settings

Step	Community screening (prevalence 2%)	Glaucoma clinic (prevalence 30%)
With disease	200	3000
True positives (90%)	180 (false negatives 20)	2700 (false negatives 300)
Without disease	9800	7000
True negatives (95%)	9310 (false positives 490)	6650 (false positives 350)
PPV	180 ÷ (180 + 490) = 27%	2700 ÷ (2700 + 350) = 89%
NPV	9310 ÷ (9310 + 20) = 99.8%	6650 ÷ (6650 + 300) = 96%

In the community, almost three in four positive results are false positives, even with a good test. This is why screening for an uncommon disease produces many unnecessary referrals
As prevalence rises, PPV rises and NPV falls

## Likelihood ratios

Likelihood ratios do not depend on prevalence and can be applied to an individual patient
Pre-test odds × LR = post-test odds, where odds = probability ÷ (1 − probability), and probability = odds ÷ (1 + odds)
Worked example, using the test above: LR+ = 0.90 ÷ 0.05 = 18; LR− = 0.10 ÷ 0.95 = 0.105

Community, positive test: pre-test odds = 0.02 ÷ 0.98 = 0.0204. Post-test odds = 0.0204 × 18 = 0.367. Post-test probability = 0.367 ÷ 1.367 = 27%, the same as the PPV
Clinic, negative test: pre-test odds = 0.3 ÷ 0.7 = 0.43. Post-test odds = 0.43 × 0.105 = 0.045, a probability of 4% (1 − NPV)

An LR+ above 10 or an LR− below 0.1 changes the probability a lot; values near 1 hardly change it. A Fagan nomogram does the conversion graphically

## Cut-offs and ROC curves

For a continuous result, the cut-off sets the trade-off: lowering the threshold for a positive result (e.g. calling IOP above 18 rather than 24 mmHg abnormal) raises sensitivity and lowers specificity
The receiver operating characteristic (ROC) curve plots sensitivity (true positive rate) against 1 − specificity (false positive rate) at each cut-off

The area under the curve (AUC) summarises overall accuracy: 0.5 is no better than chance (the diagonal) and 1.0 is perfect
The point nearest the top left corner, or with the highest Youden index (sensitivity + specificity − 1), is often chosen as the cut-off

Combining tests: in series (positive only if both are positive) increases specificity; in parallel (positive if either is positive) increases sensitivity

## Screening

Screening is the systematic testing of people without symptoms to find disease (or its risk) early, so that treatment improves the outcome. A positive screening test is followed by a diagnostic test
The Wilson and Jungner criteria (WHO, 1968):

The condition is an important health problem
There is an accepted treatment
Facilities for diagnosis and treatment are available
There is a recognisable latent or early symptomatic stage
There is a suitable test
The test is acceptable to the population
The natural history is adequately understood
There is an agreed policy on whom to treat
The cost of case-finding is economically balanced against overall medical spending
Case-finding is a continuing process, not a one-off project

Screening bias	Effect
Lead-time bias	Earlier diagnosis lengthens the apparent survival from diagnosis even if the time of death or blindness is unchanged
Length-time bias	Screening preferentially finds slowly progressing disease, which has a better prognosis anyway
Overdiagnosis	Detecting disease that would never have caused harm in the person's lifetime
Selection (volunteer) bias	People who attend screening are healthier than those who do not

Diabetic retinopathy meets the criteria well: common, a long asymptomatic stage, an accurate photographic test, and effective treatment (laser, anti-VEGF). Many countries run systematic retinal photography programmes, increasingly with automated (AI) grading
Retinopathy of prematurity screening of at-risk preterm infants is another established programme
Population screening for glaucoma is generally not recommended: the prevalence is low, and no single test (IOP, disc assessment or field) has enough sensitivity and specificity. IOP alone misses normal-tension glaucoma and labels many ocular hypertensives. Targeted case-finding in high-risk groups is used instead
Childhood vision screening aims to detect amblyopia and refractive error while treatment is still effective

Diagnostic accuracy studies are reported to the STARD standard. Agreement between two instruments is assessed with a Bland–Altman plot (see Hypothesis Testing)