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Sensitivity and Specificity

Like incidence and prevalence, sensitivity and specificity are twin sons of different mothers. And there is no Fogleberg fallout here. These guys stick together. Knowing their similarities and differences is vital to understanding diagnostic testing and the associated biostatistics.

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The 2x2 Table for Sensitivity and Specificity

The above table is a basic diagnostic 2x2 table. The left side represents the diagnostic test results, those that are positive and those that are negative. The top of the table depicts the real status of the individuals, those that actually have or do not have the disease. In harlequin fashion, the upper left and bottom right show the subjects that the test correctly identified. The True Positives (TP) in the top left and the True Negatives (TN) on the bottom right. The remaining upper right and bottom left squares show the number of individuals that the test failed to properly identify: the False Positives (FP) and the False Negatives (FN).

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What Sensitivity and Specificity mean and how to calculate them

Sensitivity is all about the positive cases and is thus known as True Positive Rate. As this topic is deceptively recondite and occasionally confusing, I remember that Sensitivity is about the positives because there is no letter “p” in the word. On the flip side, Specificity has no “N” it is and is all about the negative cases. Makes sense right?

Sensitivity is the ability to identify those with the disease, the True Positives accurately. If there are a 100 people with the disease and the test result is positive for 95 of them, then the test’s Sensitivity is 95%. Specificity is the other side of this coin. Specificity is the ability to identify those without the disease. If there are a 100 healthy people and the test result is negative for 95 of them, then the test’s Specificity is 95%.

If you need to calculate these on your own, first let me extend my congratulations because statistics is fun. Secondly, remember that these numbers run vertically. Sensitivity defines how well the test identifies the True Positives. So your TP is your numerator and all of the patients with the disease, the entire left column is your denominator. Run a parallel calculation for Specificity on the right side of the column.

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Just like people, diagnostic tests have their strengths

The perfect diagnostic test has 100% sensitivity and 100% specificity. As in love, if you are holding out for the perfection in all areas, you will be vapidly waiting for Godot. Luckily, the balance of these characteristics is more exciting, thought-provoking and fulfilling. At least that is true for statistics.

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When do I want a Sensitive test or a Specific one?

Highly sensitive tests leave few false negatives, those who actually have the disease but test negative. Since you do not want to miss anyone, the threshold for positivity is low. This means that in order to accomplish this, the cost may be a few more false positives. No problem though as these false positives can be ruled out later with highly specific tests. For sensitivity, it is better to have anyone that might be positive included in the group. As you have surmised, highly sensitive tests are best used for screening and ruling out a disease. If you test negative under a highly sensitive test, it is unlikely that you have disease.

Highly specific tests are then used to rule in the disease. They will leave few false positives. It is common to start with highly sensitive tests and then confirm with highly specific tests. While being different, these two walk the same path. They accomplish more than the could alone and compliment each other’s strengths. They fulfill each other. I am not sure why I was trying to tie in an analogy of love here.

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