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Diagnostic Test Calculator

Q: Why is the PPV only 15 % with a 95 % specific test?

At 1 % prevalence, 990 of 1,000 people are healthy and 5 % of them (49.5) test falsely positive, against only 9 true positives; predictive values depend on prevalence, sensitivity and specificity do not.

Q: How do I use the likelihood ratios?

Post-test odds = pre-test odds × LR. LR+ above 10 or LR− below 0.1 change the probability substantially; values near 1 make the test uninformative.

Computes positive and negative predictive values, likelihood ratios, post-test probabilities, accuracy and the expected numbers of true/false positives and negatives per 1,000 people tested from a test's sensitivity, specificity and the disease prevalence.

When to use

You know a screening or diagnostic test's sensitivity and specificity and the pre-test probability (prevalence) and want to know what a positive or negative result means for an individual.

Do not use when: You need to compute sensitivity and specificity themselves from a 2×2 table of test results (they are TP/(TP+FN) and TN/(TN+FP)), or the inputs are fractions 0–1 (use bayes-theorem). Informational; not medical advice.

Formula

per 1000: TP = 10·prev·sens/100, FN = 10·prev − TP, TN = 10·(100 − prev)·spec/100, FP = 10·(100 − prev) − TN; PPV = TP/(TP + FP); NPV = TN/(TN + FN); LR+ = sens/(100 − spec); LR− = (100 − sens)/spec; accuracy = (TP + TN)/1000

Predictive values depend strongly on prevalence: the same test has a much lower PPV in screening (low prevalence) than in symptomatic patients. Equivalent to Bayes' theorem with prevalence as the prior.

Inputs

Parameter	Type	Unit	Required	Description
`sensitivity_percent`	number	%	yes	Percentage of people with the condition who test positive (true positive rate). Range: ≥ 0, ≤ 100
`specificity_percent`	number	%	yes	Percentage of people without the condition who test negative (true negative rate). Range: ≥ 0, ≤ 100
`prevalence_percent`	number	%	yes	Percentage of the tested population that has the condition. Range: > 0

Outputs

Output	Type	Unit	Description
`ppv_percent`	number	%	Probability of having the condition given a positive result (post-test probability after a positive).
`npv_percent`	number	%	Probability of not having the condition given a negative result.
`post_test_probability_negative_percent`	number	%	100 − NPV: probability of the condition despite a negative result.
`likelihood_ratio_positive`	number		sensitivity / (1 − specificity); > 10 is a strong positive result (omitted when specificity is 100 %).
`likelihood_ratio_negative`	number		(1 − sensitivity) / specificity; < 0.1 is a strong negative result (omitted when specificity is 0 %).
`true_positives_per_1000`	number		People with the condition who test positive, per 1,000 tested.
`false_negatives_per_1000`	number		People with the condition who test negative.
`false_positives_per_1000`	number		People without the condition who test positive.
`true_negatives_per_1000`	number		People without the condition who test negative.
`accuracy_percent`	number	%	(true positives + true negatives) / all tested.

Example

Screening: sensitivity 90 %, specificity 95 %, prevalence 1 %: {"sensitivity_percent":90,"specificity_percent":95,"prevalence_percent":1} → {"ppv_percent":15.38,"npv_percent":99.89,"post_test_probability_negative_percent":0.11,"likelihood_ratio_positive":18,"likelihood_ratio_negative":0.1053,"true_positives_per_1000":9,"false_negatives_per_1000":1,"false_positives_per_1000":49.5,"true_negatives_per_1000":940.5,"accuracy_percent":94.95}

Symptomatic patients: sensitivity 95 %, specificity 90 %, prevalence 30 %: {"sensitivity_percent":95,"specificity_percent":90,"prevalence_percent":30} → {"ppv_percent":80.28,"npv_percent":97.67,"likelihood_ratio_positive":9.5,"likelihood_ratio_negative":0.0556,"true_positives_per_1000":285,"false_positives_per_1000":70,"accuracy_percent":91.5}

GET https://tttkmbb.com/api/v1/calculate/diagnostic-test?sensitivity_percent=90&specificity_percent=95&prevalence_percent=1

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/diagnostic-test (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/diagnostic-test · Markdown: https://tttkmbb.com/statistics/diagnostic-test.md · JSON definition: https://tttkmbb.com/statistics/diagnostic-test.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="diagnostic-test"
OpenAPI operationId: calculate_diagnostic_test_predictive_values
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Altman DG, Bland JM (1994) Diagnostic tests 2: predictive values, BMJ 309:102 (peer_reviewed)
Deeks JJ, Altman DG (2004) Diagnostic tests 4: likelihood ratios, BMJ 329:168-169 (peer_reviewed)
Wikipedia – Sensitivity and specificity (reference)

FAQ

Why is the PPV only 15 % with a 95 % specific test?

At 1 % prevalence, 990 of 1,000 people are healthy and 5 % of them (49.5) test falsely positive, against only 9 true positives; predictive values depend on prevalence, sensitivity and specificity do not.

How do I use the likelihood ratios?

Post-test odds = pre-test odds × LR. LR+ above 10 or LR− below 0.1 change the probability substantially; values near 1 make the test uninformative.

Related calculators

Bayes' Theorem Calculator — Same calculation with probabilities as fractions.
Odds Ratio Calculator — Association measures for a 2×2 exposure table.