2025 – PAGE 388 – STATISTICS

SENSITIVITY = TP/(TP+FN)

Numerically, sensitivity is defined as TP/(TP+FN). Note that (TP+FN) represents everyone with the disease; some of them tested positive (TP) and the rest were false negatives (FN). So, TP/(TP+FN) is just the proportion of cases that tested positive.

A high sensitivity is needed for SCREENING tests in order to rule out the presence of disease in a healthy patient. These are tests that are being done to RULE OUT a disease. So a screening test should have a high sensitivity, which will mean that a negative result rules out the disease in that patient. Note that TP/(TP+FN) is just another way to say “the proportion of all actual positives (TP+FN) with positive test results (TP). If you forget or get mixed up on the formulas, just key on the word “sensitive” and calculate what percent of people with the condition were detected with positive results by the test.

MNEMONIC: spIN & snOUT. snOUT should remind you that SeNsitivity (SNout) is related to ruling OUT a disease.

SPECIFICITY = TN/(TN+FP)

Specificity is defined as TN/(TN+FP), where (TN+FP) represents everyone without the disease. So specificity is the probability of a negative test among all the people without the disease.

A high specificity [TN/(TN+FP)] is needed for CONFIRMATORY tests. These are tests that are done to RULE IN (CONFIRM) a disease. So a confirmatory test should have a high specificity, which will mean that a positive result rules in the disease in that patient.

Since the specificity is the probability of a negative test among people without the disease, (1-specificity) is the probability of a false positive. A highly specific test has few false positives.

MNEMONIC: spIN & snOUT. spIN should remind you that SPecificity (SPin) is related to ruling IN a disease.

LIKELIHOOD RATIO = SENSITIVITY/(1–SPECIFICITY)

The likelihood ratio is defined as sensitivity/(1–specificity). Remembering that (1–specificity) is the probability of a false positive, the likelihood ratio is the ratio of (probability of a positive test among people with the disease)/(probability of a positive test among people without the disease).

The likelihood ratio incorporates both sensitivity and specificity to describe how effectively the test detects both the presence and absence of disease. A test which is very sensitive (sensitivity near 1.0) and very specific (specificity near 1.0) will have a high likelihood ratio. For example, a test with a sensitivity of 0.9 and specificity of 0.6 would have a likelihood ratio of 0.9/(1–0.6) = 2.25. A perfectly useless test would be just as likely to be positive in people with and without the disease, so the likelihood ratio would be 1. Remember that a useless test has a LR of 1, not zero, and that higher LR values represent more informative tests.

Sensitivity and specificity are characteristics of the test itself and do not depend on the frequency of the disease in the population. Their interpretation for predicting the disease or condition, however, depends on how prevalent it is. For example, the rarer a disease, the more likely a positive result will be a false positive. The following two measures, positive and negative predictive value, take into account the prevalence.