A. Introduction. Diagnoses tend to exist on the following continuum:
Probability of Disease
a. Most diseases listed on an initial differential diagnosis will fall somewhere on a continuum of possibility: from least possible to most probable.
b. The goal of the physician is to explain the patient’s presentation by moving most diagnoses as far to the left of this line as possible (reasonably excluding them), while moving one diagnosis as far to the right as possible.
c. The inappropriate use of diagnostic tests will leave many diagnoses frustratingly close to the midpoint of the continuum.
B. Qualitative Assessment. The degree of certainty required to qualify a diagnosis as “reasonable” depends on:
a. The severity of the condition under consideration
b. The extent to which the condition is treatable
c. The risks associated with diagnostic testing
d. The risks associated with the treatment
C. Quantitative Assessment
a. The pretest probability is the probability of disease before formal testing
i. Consider the following three examples:
1. A 45-year-old man presents to an urgent care clinic with a history of paroxysmal, sharp, left-sided chest pain occurring both at rest and with exercise. He denies chest pressure occurring with exercise. The symptoms have been present for 2 months. A literature search reveals that 50% of 45-year-old men with atypical chest pain have coronary artery disease. Therefore, the pretest probability of coronary artery disease in this patient is 50%.
2. If the patient is a 30-year-old woman with atypical chest pain, the corresponding pretest probability of coronary artery disease would be 5%.
3. If the patient is a 60-year-old man with exertional chest tightness (typical angina), the pretest probability of coronary artery disease is increased to 95%.
ii. Suppose all three of these patients undergo an exercise treadmill test. Is coronary artery disease ruled in if the tests are positive? Is it ruled out if the tests are negative? To answer these questions, it is necessary to consider the likelihood ratio.
i. Sensitivity and specificity are the characteristics used most often to define diagnostic tests.
1. Sensitivity answers the question, “Among patients with the disease, how likely is a positive test?”
2. Specificity answers the question, “Among patients without the disease, how likely is a negative test?”
3. The likelihood ratio helps answer the clinically more important questions:
a. Given a positive test result, how likely is it that the disease is truly present?
b. Given a negative test result, how likely is it that the disease is truly absent?
ii. Mathematically, likelihood ratios indicate the odds of having a disease given a test result versus not having a disease given the same test result.
1. For example:
If the circle represents all patients with a positive test and the shaded portion represents the portion who actually have disease, then the likelihood ratio is 3 (Figure 2.1).
2. Consider another example. The likelihood ratio of a positive treadmill test is 3.5. In a large, heterogeneous population of patients, all of whom have had positive treadmill tests, seven patients will actually have coronary artery disease for every two patients who do not. Therefore, if your patient has a positive treadmill test, the odds of that person having coronary artery disease are 7 to 2, or 3.5 to 1. That is, given a positive treadmill test, it is 3.5 times more likely that coronary artery disease is present.
Likelihood ratio of a positive test = True positive rate / False positive rate = (Sensitivity) / (1 − Specificity)
Likelihood ratio of a negative test = False negative rate / True negative rate = (1 − Sensitivity) / (Specificity)
1. Most diagnostic tests have likelihood ratios in the 2–5 range for positive results and in the 0.5–0.2 range for negative results. These types of tests, therefore, are only very useful if the pretest probability of disease is in the middle (e.g., 30%–70%). In this way, the test can shift probability of disease from present or absent. Conversely, at either end of the probability scale, diagnostic tests with small likelihood ratios do not substantially change the probability of disease and are therefore not as useful for clinical decision-making.
2. Good diagnostic tests have positive likelihood ratios of 10 or more. These powerful tests help rule in a diagnosis across a broader range of pretest probabilities. Unfortunately, these types of tests are often expensive or dangerous—that is, they carry important risks (e.g., contrast nephropathy for computed tomography [CT] scans).
3. For a test to truly rule in disease across the full range of pretest probabilities, it must have a likelihood ratio of 100 or more. Very few tests (e.g., some biopsies, exploratory laparotomy, cardiac catheterization) have likelihood ratios this high. Often, these are invasive procedures with risk to the patient.
c. The posttest probability is the probability that a specific disease is present after a diagnostic test. Once we have determined the pretest probability of disease (using clinical information and disease prevalence data) and the likelihood ratio of the diagnostic test result, we are ready to calculate the posttest probability. First, however, the pretest probability must be converted to odds in order to make the estimates comparable (the likelihood ratio is already expressed in odds).
1. Pretest probability must be converted to pretest odds:
Odds = (Probability) / (1 − Probability)
(For example, a probability of 75% equals odds of 3:1.)
2. Pretest odds are multiplied by the likelihood ratio to give posttest odds.
3. Posttest odds must then be converted back to posttest probability:
Probability = (Odds) / (Odds + 1)
1. In the 45-year-old man with atypical chest pain and a positive treadmill test, the posttest probability of disease would be 78%:
a. The 50% pretest probability is converted to pretest odds: (0.5)/(1 − 0.5) = (0.5)/(0.5) = 1:1.
b. The 1:1 pretest odds are multiplied by the likelihood ratio (3.5) to yield posttest odds of 3.5:1.
1/1 × 3.5/1 = 3.5/1
2. In the 30-year-old woman with atypical chest pain and a positive treadmill test, the posttest probability would be 16%:
1/19 × 3.5/1 = 3.5/19
3. In the 60-year-old man with typical chest pain and a positive treadmill test, the posttest probability would be 98.5%:
19/1 × 3.5/1 = 66.5/1
a. To gain diagnostic strength, several tests may be combined—as long as they are independent tests. The posttest probability after the first test then becomes the pretest probability for the next test.
b. To really learn this approach, you must use it. Try it on your next patient and you’ll be familiar with odds before you know it!
Suggested Further Readings
Graber ML, Franklin N, Gordon R. Diagnostic error in internal medicine. Arch Intern Med 2005;165:1493–9.Find this resource:
Kassirer JP, Kopelman RI. Cognitive errors in diagnosis: instantiation, classification, and consequences. Am J Med 1989;86:433–41. (Classic Article)Find this resource:
McGee S. Evidence-Based Physical Diagnosis: Elsevier Health Sciences; 2016. (Print book, ISBN-13: 978-1437722079)Find this resource:
Saint S, Drazen JM, Solomon CG. Clinical problem-solving: McGraw-Hill Professional; 2006.Find this resource:
Shapiro DE. The interpretation of diagnostic tests. Stat Methods Med Res 1999;8:113–34. (Classic Article)Find this resource: