A summary of diagnostic tests principles!
Test Positive or Negative
The definition of normal for continuous variables is a statistical determination
At what point "abnormal" becomes an illness or disease is a judgment based upon the desire to identify those with disease (true positives), but not include a significant portion of patients without the disease (false positives). Furthermore, most tests are not positive in all the patients with a given disease, so there will be patients with the disease who are missed by the test (false negatives). Finally, we want to be sure that a very high proportion of patients who don't have the disease, have a negative test (true negatives).
Probability and Odds
Probability is a ratio or proportion of one part of a population to the population as a whole. A racehorse that wins 1 race in 20 has a probability of winning of 0.05 (1/20 = 0.05).
Odds are the ratio of two probabilities. Because most events are uncommon (otherwise we wouldn't need to make all these calculations), odds are customarily expressed as the odds against an event. For our horse the probability of losing is 0.95 while the probability of winning is 0.05., that is, the odds are 19:1 that it will lose.
Odds and probabilities can be derived from one another:
Odds = Probability/(1 - Probability)
Probability = Odds/(1 + Odds)
Aids in the Selection and Interpretation of Tests
Sensitivity is the number of patients with the disease who have a positive test, divided by the total number with the disease: sensitivity = a/(a + c), a probability. With highly sensitive tests, the vast majority of patients with the disease have a positive test (very few false negatives). Tests with high sensitivity (>0.95) are most useful when negative, thereby making the diagnosis less likely. Note that the sensitivity of a test, because it is calculated only in those with the disease, is independent of the prevalence of the disease. Sensitivity can be increased by changing the cutoff for defining a positive test to a less abnormal value (see Fig. 17-1).
Because sensitivity is independent of prevalence, it is susceptible to overinterpretation when disease prevalence is very low . In this case, the false-positive tests (b) may significantly out number the true positives (a).
Sensitive tests are used when you do not wish to miss a serious disease because of the consequences of a delayed diagnosis. A negative result makes the disease unlikely and helps to reassure the patient and clinician, and serves to narrow the diagnostic possibilities. A positive test needs to be confirmed with more specific tests before a diagnosis can be established.
Specificity is the proportion of patients without the disease who have a negative test: specificity = d/(b + d), a probability. With highly specific tests, the vast majority of patients without the disease have negative tests (very few false positives). However, the test may also be negative in those with the disease. Note that patients with the disease do not enter into the determination of specificity; it, like sensitivity, is independent of the disease prevalence. Specificity can also be improved by changing the cutpoint for defining abnormal to a more abnormal value (see Fig. 17-1).
Because specificity is independent of prevalence, it is susceptible to overinterpretation when disease prevalence (pretest probability) is high (see Example 4 below). In this case, the false-negative tests (c) may significantly out number the true negatives (d).
Highly specific tests are used to confirm a diagnosis. This is especially important when the consequences of the diagnosis are serious for the patient, either for prognosis or therapy.
Setting Your Positive/Negative Cutpoint
For most diagnostic tests, the clinical laboratory supplies a reference range This range is determined by testing hundreds of samples of unselected patients, patients with the disease, and patients known to not have the disease. From this data, graphscan be generated. The data are analyzed to determine the statistical best fit for distinguishing the diseased from the nondiseased populations.
For many clinical tests, such as treadmill exercise tests, interpretation of imaging studies, and application of diagnostic tests, the clinician must decide, based upon the clinical scenario and the type of diagnostic question being asked (screening, case finding, hypothesis testing) what cutpoint will best serve to answer the question. Consultation with specialists in laboratory medicine and with experts in the diseases in your differential diagnosis can assist you in determining what should be regarded as a positive or negative test in each specific clinical situation.
When we do a test, we are not really interested in the test (sensitivity and specificity), but in how it can help us in understanding our patient's problem: does the presence of a positive test predict that the patient has the disease (positive predictive value) and does a negative test predict the absence of the disease (negative predictive value). Predictive values are calculated from 2 Χ 2 tables (see Fig. 17-2). As we shall see, the predictive values for a test are dependent upon the population which was used to generate the data in the 2 Χ 2 table; different populations have different disease prevalence. To generate meaningful predictive values, the patients generating the data must be chosen randomly from a clinical population that is relevant to your question and patient.
POSITIVE PREDICTIVE VALUE (PPV). The PPV is calculated from our 2 Χ 2 table. It is the proportion of patients with a positive test who have the disease: PPV = a/(a + b), a probability. Tests with a high PPV have few false-positive tests, therefore a positive test supports the diagnosis. Note, however, that if the disease is rare in the population (therefore (b + d)>>(a + c), the test will have to be extremely specific (low false positives, b) for the true positives to be greater than the false positives (see examples). Therefore, when the pretest probability of disease is low (low prevalence), even seemingly good tests (sensitivity, specificity) may perform badly for predicting the presence of disease.
NEGATIVE PREDICTIVE VALUE (NPV). The NPV is the proportion of patients with a negative test who do not have the disease: NPV = d/(c + d), a probability. Tests with a high negative predictive value have few false negatives, therefore a negative test argues against the disease. When the condition is very likely in the population to begin with, a negative test may not be very helpful; that is, the NPV may be low and the disease may be present despite a negative test.
Consequently, to use the PPV and NPV, the clinician must know, or have a good estimate of, the prevalence of the condition being tested for in the clinician's population. Most clinicians do not have this data readily available. What we do have is our clinical estimate of the probability of disease that we have generated from our history and physical examination in generating our differential diagnosis.
Likelihood Ratios (LR)
Another way of expressing the usefulness of a test is in likelihood ratios (LR). A positive likelihood ratio (LR+) is the ratio of the probability of a positive test in people with the disease (the sensitivity) to the probability of a positive test in people without the disease: LR+ = [a/(a + c)] χ [b/(b + d)]. A negative likelihood ratio (LR-) is the probability of a negative test in patients with the disease divided by the probability of a negative test in people without the disease (the specificity): LR- = [(c/a + c)] χ [d/(b + d)] (Fig. 17-3). Likelihood ratios, the ratio of two probabilities, are odds.
Likelihood ratios show how well a result more abnormal (LR+) or less abnormal (LR-) than a given value for the test (the cutpoint for "test positive" in the 2 Χ 2 table) discriminates between those with and without the disease. They are a function of the defined parameters of the test and are independent of the prevalence of the disease (see the examples). Likelihood ratios contain all the sensitivity and specificity information and express the relationship between sensitivity and specificity for positive and negative results.
A big advantage of likelihood ratios is that they can be calculated for a range of test values, rather than the single normal/abnormal cutpoint used for sensitivity and specificity. Thus, likelihood ratios allow us to use all the information, rather than the limited information in a single normal/abnormal cutpoint.
As the LR+ becomes larger, the likelihood of the disease increases; as the LR- approaches zero, the disease becomes much less likely. Generally speaking, LR between 0.5 and 2.0 are not useful and those 0.2 or >2.0 but 5 argue strongly for the disease whereas LR- 0.95) are most useful when negative, thereby making the diagnosis less likely.