Sensitivity (tests)
EditorInChief: C. Michael Gibson, M.S., M.D. [1]; Assistant Editor(s)InChief: Kristin Feeney, B.S.
Overview
Sensitivity refers to the statistical measure of how well a binary classification test correctly identifies a condition^{[1]}. In epidemiology, this is referred to as medical screening tests that detect preclinical disease. In quality control, this is referred to as a recall rate, whereby factories decided if a new product is at an acceptable level to be massproduced and sold for distribution.
Critical Considerations
 The results of the screening test are compared to some absolute (Gold standard); for example, for a medical test to determine if a person has a certain disease, the sensitivity to the disease is the probability that if the person has the disease, the test will be positive.
 The sensitivity is the proportion of true positives of all diseased cases in the population. It is a parameter of the test.
 High sensitivity is required when early diagnosis and treatment is beneficial, and when the disease is infectious.
Worked Example
 Relationships among terms
Condition (as determined by "Gold standard")  
True  False  
Test outcome 
Positive  True Positive  False Positive (Type I error, Pvalue) 
→ Positive predictive value 
Negative  False Negative (Type II error) 
True Negative  → Negative predictive value  
↓ Sensitivity 
↓ Specificity 
 A worked example
 the Fecal occult blood (FOB) screen test is used in 203 people to look for bowel cancer:
Patients with bowel cancer (as confirmed on endoscopy)  
True  False  ?  
FOB test 
Positive  TP = 2  FP = 18  = TP / (TP + FP) = 2 / (2 + 18) = 2 / 20 ≡ 10% 
Negative  FN = 1  TN = 182  = TN / (TN + FN) 182 / (1 + 182) = 182 / 183 ≡ 99.5%  
↓ = TP / (TP + FN) = 2 / (2 + 1) = 2 / 3 ≡ 66.67% 
↓ = TN / (FP + TN) = 182 / (18 + 182) = 182 / 200 ≡ 91% 
Related calculations
 False positive rate (α) = FP / (FP + TN) = 18 / (18 + 182) = 9% = 1  specificity
 False negative rate (β) = FN / (TP + FN) = 1 / (2 + 1) = 33% = 1  sensitivity
 Power = 1 − β
Hence with large numbers of false positives and few false negatives, a positive FOB screen test is in itself poor at confirming cancer (PPV=10%) and further investigations must be undertaken, it will though pickup 66.7% of all cancers (the sensitivity). However as a screening test, a negative result is very good at reassuring that a patient does not have cancer (NPV=99.5%) and at this initial screen correctly identifies 91% of those who do not have cancer (the specificity).
Definition
A sensitivity of 100% means that the test recognizes all sick people as such.
Sensitivity alone does not tell us how well the test predicts other classes (that is, about the negative cases). In the binary classification, as illustrated above, this is the corresponding specificity test, or equivalently, the sensitivity for the other classes.
Sensitivity is not the same as the positive predictive value (ratio of true positives to combined true and false positives), which is as much a statement about the proportion of actual positives in the population being tested as it is about the test.
The calculation of sensitivity does not take into account indeterminate test results. If a test cannot be repeated, the options are to exclude indeterminate samples from analyses (but the number of exclusions should be stated when quoting sensitivity), or, alternatively, indeterminate samples can be treated as false negatives (which gives the worstcase value for sensitivity and may therefore underestimate it).
SPPIN and SNNOUT
SPPIN  SNNOUT  Neither  Nearperfect  

Proposed definition  Sp > 95%  SN > 95%  Both < 95%  Both > 99% 
Example  Many physical dx findings  Ottawa fracture rules^{[2]}  Exercise treadmill test^{[3]}  HIV1/HIV2 4th gen test^{[4]} 
Predictive values:  
10% pretest prob  PPV= 35%
NPV = 99% 
PPV = 64%
NPV = 98% 
PPV = 31%
NPV = 97% 
PPV = 92%
NPV > 99% 
50% pretest prob  PPV = 94%
NPV = 83% 
PPV = 83%
NPV = 94% 
PPV = 80%
NPV = 80% 
PPV = 99%
NPV = 99% 
90% pretest prob  PPV = 98%
NPV = 64% 
PPV = 99%
NPV = 35% 
PPV = 97%
NPV = 31% 
PPV > 99%
NPV = 92% 
Clinical messages  Accept test result when:

Accept test result when:

Accept test result unless:
 
Notes: Green font indicates when results are more likely to be trustable 
Terminology in Information Retrieval
In information retrieval, positive predictive value is called precision, and sensitivity is called recall.
Fmeasure: can be used as a single measure of performance of the test. The Fmeasure is the harmonic mean of precision and recall:
In the traditional language of statistical hypothesis testing, the sensitivity of a test is called the statistical power of the test, although the word power in that context has a more general usage that is not applicable in the present context. A sensitive test will have fewer Type II errors.
Related Chapters
 binary classification
 receiver operating characteristic
 specificity (tests)
 statistical significance
 Type I and type II errors
 Selectivity
Online Calculators
References
 ↑ Altman DG, Bland JM (1994). "Diagnostic tests. 1: Sensitivity and specificity". BMJ. 308 (6943): 1552. PMID 8019315.
 ↑ Stiell, Ian. "The Ottawa Rules". University of Ottawa. Retrieved January 5, 2020.
 ↑ Banerjee A, Newman DR, Van den Bruel A, Heneghan C (2012). "Diagnostic accuracy of exercise stress testing for coronary artery disease: a systematic review and metaanalysis of prospective studies". Int J Clin Pract. 66 (5): 477–92. doi:10.1111/j.17421241.2012.02900.x. PMID 22512607. Note that 80% is a rough estimate of sensitivity and specificity.
 ↑ Malloch L, Kadivar K, Putz J, Levett PN, Tang J, Hatchette TF; et al. (2013). "Comparative evaluation of the BioRad Geenius HIV1/2 Confirmatory Assay and the BioRad Multispot HIV1/2 Rapid Test as an alternative differentiation assay for CLSI M53 algorithmI". J Clin Virol. 58 Suppl 1: e85–91. doi:10.1016/j.jcv.2013.08.008. PMID 24342484.
External links
 Sensitivity and Specificity Medical University of South Carolina