Specificity

Specificity refers to a test’s accuracy at identifying those who do not have a condition or characteristic. It is the proportion of truly not at-risk or without condition (e.g., trait, disease, classification, and label) who are correctly identified as such through a diagnostic tool. Specificity describes the characteristic of a test in terms of how well the test correctly identifies true negatives (TNs) or those who do not have the predicted condition. Mathematically, it is expressed as the proportion of TN results to the sum of both true-negative and false-positive results. Mathematically, this can be expressed as:

$$\begin{array}{l}px=\text{number of true negatives}/\\ \left(\text{number of true negatives}+\text{false positives}\right).\end{array}$$

To better understand specificity, imagine describing a test along two dimensions depicting the relation between the predicted conditions. These dimensions can be further divided along four quadrants (see Figure 1). Quadrant 1, true positive (TP), is the number of persons with a disease who test positive. Moving clockwise, Quadrant 2 is the number of false positives (FPs) or number of well persons who test positive. Quadrant 3, TNs, depicts the number of well persons who test negative. Quadrant 4, false negatives, depicts the number of persons with a disease who test negative. Specificity is the sum of TNs (Quadrant 3) divided by the sum of TNs (Quadrant 3) and FPs (Quadrant 4).

Specificity is one of many test indices used to characterize the utility of a diagnostic or screening tool. Other useful indices include sensitivity, classification accuracy, and positive and negative predictive values (PPV and NPV, respectively). Sensitivity is the proportion of truly with or at-risk (TPs) and describes how well a test correctly identifies TPs. Sensitivity and specificity are always reported together. Classification accuracy is the proportion of TPs and TNs to the whole sample. PPV and NPV are the chance proportions that diagnostic results will be correct. Unlike specificity and sensitivity, which are characteristic of the diagnostic test and are not influenced by the population, both PPV and NPV are influenced by the [Page 1566]proportion of a population found to have a condition. These are estimated using data from cross-sectional or other population-based studies in which valid prevalence estimates can be obtained. That is, specificity will remain unchanged as prevalence of the disease changes, whereas PPV and NPV will change as prevalence rate varies.

Figure 1 Relation between true conditions and test results

Sensitivity and specificity of a diagnostic test are determined by comparing test results in a representative sample of individuals against a gold standard diagnostic where true rate of both negative test results and positive test results is known. Although the ideal test would be 100% sensitive and 100% specific in its classification, in practice, context matters. For almost any condition, there are two distributions: one for the population without condition and one for the population with condition. In most circumstances, these two distributions have overlapping scores. Unless there is perfect separation between two distributions on a particular diagnostic measure, a trade-off will have to be made in terms of improved sensitivity or specificity. In medicine, a test result indicating no disease when in fact the person carries a disease (false negative) are of primary concern. Conversely, in law the opposite is true and the primary concern is preventing false convictions (false negatives) as opposed to false acquittals (FPs). In prevention research, we tend to favor FPs, as the intervention is assumed to carry no or low risk (e.g., no harm is done to a student who receives extra math tutoring).

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