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Sensitivity and specificity

Author: Rongrong Huang, Ph.D.

Board of reviewers: Jieli (Shirley) Li, M.D., Ph.D.

Last staff update: 9 April 2025 (update in progress)

Copyright: 2022-2025, PathologyOutlines.com, Inc.

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Cite this page: Huang R. Sensitivity and specificity. PathologyOutlines.com website. https://www.pathologyoutlines.com/topic/chemistrysensitivityspecificity.html. Accessed April 29th, 2025.

Definition / general

Diagnostic (or clinical) sensitivity and specificity are measures of diagnostic accuracy of a test, which are essential indicators to assess clinical test performance; analytical sensitivity and specificity are out of the scope of this chapter
Understanding test sensitivity and specificity and how they apply to various patient populations with different disease prevalence is important for result interpretation and test selection

Essential features

Sensitivity and specificity represent a summary of the diagnostic accuracy of a test; they are indicators of clinical test performance and independent of disease status or disease prevalence
Receiver operating characteristic (ROC) curve and area under the curve (AUC) score are useful tools for assessing sensitivity and specificity, selecting optimal cutoff points and comparing diagnostic accuracy among different methods
Predictive value is influenced by both diagnostic accuracy and disease prevalence; it is useful information to aid in result interpretation and clinical decision making
2 x 2 truth table is a useful tool for calculation of sensitivity, specificity, false positive rate, false negative rate, positive predictive value (PPV), negative predictive value (NPV) and likelihood ratio

Terminology

Diagnostic accuracy (clinical accuracy): the ability of a diagnostic test to discriminate between diseased and nondiseased subjects or between 2 or more clinical states
Sensitivity (diagnostic / clinical): the ability of a test to give a positive result for subjects who have the disease or condition for which they are being tested
Specificity (diagnostic / clinical): the ability of a test to give a negative result for subjects who do not have the disease or condition for which they are being tested
True positive (TP): positive test result in a subject in whom the disease or condition of interest is present
True positive rate: equivalent to sensitivity
True negative (TN): negative test result in a subject in whom the disease or condition of interest is absent
True negative rate: equivalent to specificity
False positive (FP): positive test result for a subject in whom the disease or condition of interest is absent
False positive rate: equivalent to 1 - specificity
False negative (FN): negative test result in a subject in whom the disease or condition of interest is present
False negative rate: equivalent to 1 - sensitivity
Receiver operating characteristic (ROC) curve: a graphical description of test performance representing the relationship between the true positive rate (sensitivity) and the false positive rate (1 - specificity)
Likelihood ratio (LR): calculated by dividing the probability of test result in persons with disease by the probability of same result in persons with no disease
Prevalence: the probability of a particular clinical state in a specified population or subpopulation at a given point in time, also known as pretest probability
Positive predictive value (PPV): the probability that a positive test indicates presence of disease
Negative predictive value (NPV): the probability that a negative test indicates absence of disease
Reference: CLSI: CLSI EP24 [Accessed 17 February 2025]

Diagrams / tables

Contributed by Rongrong Huang, Ph.D.

Example of ROC curve

Truth table format

Result	Disease	Nondisease	Total
Positive	TP	FP	TP+FP
Negative	FN	TN	FN+TN
Total	TP+FN	FP+TN	TP+FP+FN+TN

PPV = TP/(TP+FP); NPV = TN/(TN+FN); sensitivity = TP/(TP + FN); specificity = TN/(TN+FP)

Example truth table

Result	Disease	Nondisease	Total
Positive	190	30	220
Negative	10	170	180
Total	200	200	400

PPV = 86%; NPV = 94%; sensitivity = 95%; specificity = 85%

Assessing sensitivity and specificity

Sensitivity and specificity are indicators of a test's ability to distinguish between disease / condition and absence of disease / condition at a chosen cutoff
They are calculated based on the observed results and the status determined by a diagnostic gold standard (i.e., truth)
2 x 2 truth table as illustrated in the first table in Diagrams / tables is commonly used to guide the calculation; a calculation example is given in the second table (see Terminology for definitions) (McPherson: Henry's Clinical Diagnosis and Management by Laboratory Methods, 23rd Edition, 2016)
Altering a cutoff changes a test's sensitivity and specificity and there is a trade off between sensitivity and specificity (or FP and FN rates)
Clinical utility of a test (e.g., screening versus confirmatory) is a critical consideration for assay / method selection; for example, high sensitivity is preferred for screening tests to minimize false negative results, while high specificity is needed for confirmatory tests to reduce false positive results

ROC curve and AUC score

Inverse relationship between sensitivity and specificity across a range of cutoffs can be plotted in an ROC curve as illustrated in Diagrams / tables; the diagnostic accuracy of a test is indicated by the area under the curve (AUC), usually ranging between 0.5 and 1.0
AUC score of 0.5 is indicative of equivalence of random guess, while an AUC score of 1.0 is indicative of a perfect test (no overlapping results between disease and nondisease populations); in general, an AUC score ≥ 0.8 is considered satisfactory
Optimal cutoff is identified by the coordinate that maximizes discriminatory power, which is the point closest to the upper left corner (true positive rate of 1.0 and false positive rate of 0); in the example illustrated in Diagrams / tables, point C is the optimal cutoff, with point A having high sensitivity but low specificity and point B having high specificity but low sensitivity
ROC curve and AUC score can be used to compare the diagnostic accuracy of 2 methods; if one test has an ROC curve with a greater AUC than a comparison test, it has better sensitivity and specificity at all cutoffs and therefore, it has an overall higher diagnostic accuracy
For test developers or clinical laboratories, diagnostic accuracy can be evaluated according to the Clinical and Laboratory Standards Institute (CLSI) guideline EP24A2 (CLSI: CLSI EP24 [Accessed 17 February 2025])

Likelihood ratios

Likelihood ratio (LR) is another assessment of test performance that combines sensitivity and specificity into a single number; like sensitivity and specificity, LR is independent of disease status in the testing patient or disease prevalence in the testing population
Positive LR is calculated as sensitivity / (1 - specificity); negative LR is calculated as (1 - sensitivity) / specificity

Predictive value and prevalence

Clinically, it is useful to know how the test result changes the probability of disease (predictive value), given certain test performance and disease prevalence
Predictive value of a test is influenced by both diagnostic accuracy (sensitivity and specificity) and disease prevalence (pretest probability)
Predictive value of a positive result is highly dependent on the prevalence of the disease being tested and increases with increasing prevalence and improved accuracy
For a disease with low prevalence, even a test with high diagnostic accuracy will yield a low positive predictive value because most positive test results will be false positives
Testing patients with high clinical suspicion increases the positive predictive value of a test
In theory, predictive value (posttest probability) can be calculated as (sensitivity x pretest probability) / ([sensitivity x pretest probability] + [{1 - specificity} x {1 - pretest probability}]) (McPherson: Henry's Clinical Diagnosis and Management by Laboratory Methods, 23rd Edition, 2016)

Practice question #1

Which of the following best describes test specificity?

Probability that someone with a negative test result does not have the disease
Probability that someone with a positive test result has the disease
Proportion of people without the disease who have a negative test result
Proportion of people without the disease who have a positive test result
Proportion of people with the disease who have a positive test result

Practice answer #1

C. Proportion of people without the disease who have a negative test result. Specificity is calculated as TN/(TN+FP), where TN and FP are the true negative and false positive numbers, respectively. Answer E is incorrect because it describes test sensitivity. Answer D is incorrect because it describes false positive rate (1 - specificity). Answer B is incorrect because it describes test positive predictive value (PPV). Answer A is incorrect because it describes test negative predictive value (NPV).

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Reference: Sensitivity and specificity

Practice question #2

Result	Disease	Nondisease	Total
Positive	170	30	200
Negative	10	190	200
Total	180	210	400

The laboratory is validating an assay that detects anti-dsDNA in patients with systemic lupus erythematosus (SLE). The validation study results are shown in the table above. Which of the following represents the sensitivity and specificity of the test?

Sensitivity 85%; specificity 95%
Sensitivity 90%; specificity 85%
Sensitivity 91%; specificity 94%
Sensitivity 94%; specificity 90%
Sensitivity 95%; specificity 90%

Practice answer #2

D. Sensitivity 94%; specificity 90%. Sensitivity is calculated as TP/(TP+FN) where TP and FN are the true positive and false negative numbers, respectively. In this case, sensitivity = 170/(170+10) = 170/180 = 94%. Specificity is calculated as TN/(TN+FP) where TN and FP are the true negative and false positive numbers, respectively. In this case, specificity = 190/(190+30) = 190/210 = 90%. Answers A, B, C and E are incorrect because the values do not match the calculated sensitivity and specificity based on the numbers provided in the table.

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Reference: Sensitivity and specificity

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