## 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’.