Sensitivity and specificity

Sensitivity and specificity are statistical indicators of the effectiveness of a diagnostic test to identify cases (patients) and non-cases (not patients). Both indicators are intensive relative, expressed in fractions of a unit or percent: non-negative values ​​[0; 1] or [0; 100%].

• Sensitivity (a truly positive proportion) reflects the proportion of positive results that are correctly identified as such (in other words, the sensitivity of a diagnostic test indicates the likelihood that a patient will be classified as a patient). ^[one]
• Specificity (a truly negative proportion) reflects the proportion of negative results that are correctly identified as such (i.e., the likelihood that non-sick subjects will be classified as non-sick). ^[one]

For example, we can consider a group, some members of which suffer from a certain disease, while others do not. Suppose that there is a method for distinguishing between these two lobes, but some of the healthy are classified as sick, and some of the patients are classified as healthy. By “healthy” and “sick” we mean the absence or presence of the disease in question. This is illustrated in the figure below “General model of sensitivity and specificity”.

${\displaystyle \text{<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;">Sensitivity</span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">=</span></span>\frac{\text{number of patients classified as sick}}{\text{total number of patients}}}${\ displaystyle {\ text {Sensitivity}} = {\ frac {\ color {Green} {\ text {number of patients classified as patients}}} {\ color {navy} {\ text {total number of patients}}}} }

${\displaystyle \text{<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;">Specificity</span></span>}<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">=</span></span>\frac{\text{<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;">number of healthy people classified as healthy</span></span>}}{\text{<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;">total healthy</span></span>}}}${\ displaystyle {\ text {Specificity}} = {\ frac {\ color {fuchsia} {\ text {number of healthy, classified as healthy}}} {\ color {teal} {\ text {total healthy}}}} }