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Sensitivity, specificity, predictive value

For clinical purposes observations are classified into compatible (positive) or not compatible (negative) with disease. Let us assume, for the sake of argument, that it is possible to clinically allocate subjects to the group with or without disease without any errors (clinical diagnosis). We can then study how frequently the test we applied gives rise to true positive (TP), false positive (FP), true negative (TN) and false negative (FN) results. This leads to the following matrix:

Clinical diagnosis Test result  
  Positive Negative Total
Sick TP FN TP+FN
Not sick FP TN FP+TN
Totals TP+FP FN+TN TP+FN+FP+TN

From this we can derive the following entities:
Sensitivity the percentage of patients recognized by the test
In mathematical form: 100·TP/(TP+FN)
Specificity the percentage of healthy subjects recognized by the test
In mathematical form: 100·TN/(TN+FP)
Predictive value of a positive test result the percentage of patients among subjects correctly classified on the basis of the test result as positive (‘sick’)
In mathematical form: 100·TP/(TP+FP)
Predictive value of a negative test result: the percentage of subjects correctly classified on the basis of the test result as negative (‘not sick’)
In mathematical form: 100·TN/(TN+FN)
Efficiency of the test the percentage of patients and healthy subjects correctly classified on the basis of test results
In mathematical form: 100·(TN+TP)/(TP+FP+TN+FN)
Disease prevalence the percentage of sick subjects in the population
In mathematical form: 100·(TP+FN)/(TP+FN+FP+TN)
False positive percentage 100 – predictive value of a positive test result
False negative percentage 100 – predictive value of a negative test result

It is desirable that tests lead to both a high sensitivity and high specificity. In practice it is impossible to make a clinical diagnosis with 100% accuracy; therefore a ‘gold standard’ for establishing sensitivity, specificity etc. is not available. In lung disease, as with so many other clinical problems (hypertension, hypercalcemia, etc.) the system is even turned upside down: whether somebody with chronic cough, phlegm, dyspnea and other symptoms has COPD is not decided on the basis of clinical symptoms but on the basis of spirometric test results. De facto the result of the test provides the quasi ‘gold standard’.

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