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Understanding Medical Tests and Test Results
Defining a Positive Test Result
Among the most common tests are those that provide results along a continuous, quantitative scale (eg, blood glucose, white blood cell count). Such tests may provide useful clinical information throughout their ranges, but clinicians often use them to diagnose a condition by requiring that the result be classified as positive or negative (ie, disease present or absent) based on comparison to some established criterion or cutoff point. Such cutoff points are usually selected based on statistical and conceptual analysis that attempts to balance the rate of false-positive results (prompting unnecessary, expensive, and possibly dangerous tests or treatments) and false-negative results (failing to diagnose a treatable disease). Identifying a cutoff point also depends on having a gold standard to identify the disease in question. Typically, such quantitative test results (eg, white blood cell count in cases of suspected bacterial pneumonia) follow some type of distribution curve (not necessarily a normal curve, although commonly depicted as such). The distribution of test results for patients with disease is centered on a different point than that for patients without disease. Some patients with disease will have a very high or very low result, but most have a result centered on a mean. Conversely, some disease-free patients have a very high or very low result, but most have a result centered on a different mean from that for patients with disease. For most tests, the distributions overlap such that many of the possible test results occur in patients with and without disease; such results are more clearly illustrated when the curves are depicted on the same graph (see figure Distributions of test results ). Some patients above and below the selected cutoff point will be incorrectly characterized. Adjusting a cutoff point to identify more patients with disease (increase test sensitivity) also increases the number of false positives (poor specificity), and moving the cutoff point the other way to avoid falsely diagnosing patients as having disease increases the number of false negatives. Each cutoff point is associated with a specific probability of true-positive and false-positive results. Patients with disease are shown in the upper distribution; patients without disease are shown in the lower distribution. For patients with disease, the region beneath the distribution of results that lies to the right of (above) the cutoff criterion corresponds to the test’s true-positive rate (ie, its sensitivity); the region that lies to the left of (below) the criterion corresponds to the false-negative rate. For patients without disease, the region to the right of the cut-off criterion corresponds to the false-positive rate, and the region to the left corresponds to the true-negative rate (ie, its specificity). For 2 overlapping distributions (eg, patients with and without disease), moving the cutoff criterion line affects sensitivity and specificity, but in opposite directions; changing the cutoff criterion from 1 to 2 decreases the number of false negatives (increases sensitivity) but also increases the number of false positives (decreases specificity). Graphing the fraction of true-positive results (number of true positives/number with disease) against the fraction of false-positive results (number of false positives/number without disease) for a series of cutoff points generates what is known as an ROC curve. The ROC curve graphically depicts the tradeoff between the sensitivity and specificity when the cut off point is adjusted (see figure Typical receiver operating characteristic (ROC) curve ). By convention, the true-positive fraction is placed on the y-axis, and the false-positive fraction is placed on the x-axis. The greater the area under the ROC curve, the better the test discriminates between patients with or without disease. ROC curves allow tests to be compared over a variety of cutoff points. In the example, Test A performs better than Test B over all ranges. ROC curves also assist in the selection of the cutoff point designed to maximize a test’s utility. If a test is designed to confirm a disease, a cutoff point with greater specificity and lower sensitivity is selected. If a test is designed to screen for occult disease, a cutoff point with greater sensitivity and lower specificity is selected. 