Chapter adapted and updated, with permission, from Nicoll D et al. Guide to Diagnostic Tests, 7th ed. McGraw-Hill, 2017.
A practical way to calculate the posttest probability of disease is to use the likelihood ratios and odds-probability approach.
Likelihood ratios (LRs) combine both test sensitivity and specificity into a single measure (a mathematical description of the strength of a diagnostic test), which helps evaluate and interpret a diagnostic test. LRs indicate how many times more (or less) a test result is to be found in diseased compared to nondiseased persons. There are two types of LR—LR positive and LR negative, calculated by the following formulas:
When test results are dichotomized using a single cut-off value to divide “positive” from “negative,” every test has two LRs, one corresponding to a positive test (LR+) and one corresponding to a negative test (LR–):
For continuous measures, multiple interval likelihood ratios (iLRs) can be defined to correspond to ranges or intervals of test results. The iLR for a test result interval is the probability of a result in that same interval for a disease-positive patient divided by the probability of a result in the same interval for a disease-negative patient. Given the pretest probability of disease and the test result, the iLR is used to calculate the posttest probability (Table e2–6).
Table e2–6.Interval likelihood ratios for serum ferritin as a test for iron deficiency anemia. ||Download (.pdf) Table e2–6. Interval likelihood ratios for serum ferritin as a test for iron deficiency anemia.
|Serum Ferritin (mcg/L) ||Interval Likelihood Ratios for Iron Deficiency Anemia |
|≥ 100 ||0.08 |
|45–99 ||0.54 |
|35–44 ||1.83 |
|25–34 ||2.54 |
|15–24 ||8.83 |
|≤ 15 ||51.85 |
LRs can be calculated using the above formulas. They can also be found in some textbooks, journal articles, and online programs (such as www.thennt.com) (see Table e2–7 for sample values). LRs provide an estimation of whether there will be significant change in pretest to posttest probability of a disease given the test result, and thus can be used to make quick estimates of the usefulness of contemplated diagnostic tests in particular situations. An LR of 1 implies that there will be no difference between pretest and posttest probabilities. LRs of more than 10 or less than 0.1 indicate large, often clinically significant differences. LRs between 1 and 2 and between 0.5 and 1 indicate small differences (rarely clinically significant).
Table e2–7.Examples of likelihood ratios (LR). ||Download (.pdf) Table e2–7. Examples of likelihood ratios (LR).
|Target Disease ||Test ||LR+ ||LR– |
|Abscess ||Abdominal CT scanning ||9.5 ||0.06 |
|Coronary artery disease ||Exercise electrocardiogram (1 mm depression) ||3.5 ||0.45 |
|Lung cancer ||Chest radiograph ||15...|