At a recent social gathering, I learned from a friend in his mid-forties that he was frightened because his doctor informed him, after he’d undergone a colon screening test (Cologuard), his result was “positive”—meaning to him that he likely had cancer of the colon. When I questioned him further, he stated that this test was ordered as part of a routine checkup, and he’d never had symptoms suggesting such a disorder, and none of his family members had ever suffered from this condition. Since I was not familiar with all his medical information, I was unable to provide much reassurance, but I could inform him that a positive result in this context likely did not indicate the presence of cancer. After further reflection, I realized how the average individual could benefit from learning about the meaning of positive and negative test results, especially when applied to individuals with a low likelihood of disease, in this case, cancer. In this instance, the result of the screening triggered the need for more complex and expensive testing that included colonoscopy and possibly additional X-ray scanning techniques. During the whole process, he and his family became anxious and fearful. Subsequently, none of the additional tests disclosed evidence of cancer, and he was relieved that there was no evidence of this fearful disease.
HOW DOES THIS EXAMPLE APPLY GENERALLY TO DISEASE SCREENING TESTS?
Most methods of detection employ tests that are not 100% accurate, meaning that any given test—may or not—detect all those harboring a given condition. But when presented with a positive or negative report, we must assess the likelihood whether a given disease is present.
To answer this type of question, we first turn to Reverend Thomas Bayes (1702–1761), an English clergyman who happened to be a fine mathematician, which was undoubtedly his first love. He formulated a theorem bearing his name, which allows the mathematical calculation of probabilities of outcomes given certain baseline population characteristics. Bayes’ formula remains pertinent and is used by contemporary health professionals, psychologists, economists, physicists, and engineers. The idea that Bayes introduced was conditional probability, i.e., the likelihood of an event occurring, given that another event has already occurred. In medical issues, Bayes’ Theorem usually provides a mathematical means to derive the actual probability of a disease after a test is applied.
Air flight may be used for one example. Worldwide statistics show that this form of commercial travel is approximately 60 times safer than car travel. So why are so many of us afraid of airplanes? The answer can be described in terms of conditional probabilities. The probability of dying in an air fatality is the product of two different probabilities—the probability the airplane will crash, and the probability that, in the event of a crash,the passenger will die. The first probability is extremely low—virtually zero. The second probability is one (100%)—that the individual person will die if there is a crash—and that’s the probability that scares people. But according to Bayes’ concept, the chance of mortality is a result of the product of these two variables—the chance of a crash times the chance of death. So, when the multiple is calculated—nearly 0 times 1—the answer is nearly zero. That is conditional probability.
When used in the medical field, we test for the likelihood that a given individual will—or will not—have a disease in question, and the results depend upon two characteristics of the test used, i.e., its “sensitivity”, and “specificity.” “Sensitivity” denotes the percentage of cases testing positive when the given disease is present. For example, Cologuard stool tests positive in about 90-95% (sensitivity) of those with colon cancer, and “Shield,” a recently introduced blood test, shows similar sensitivities. Both testing methods appear to show a low rate of “false positives” (specificities) ranging around 85-90% in cases without cancer, meaning that about 10-15% of normals will be incorrectly labeled as falsely as “positives”. In this instance specificity is the most important factor, because it shows the percentage of positives that occur in the absence of disease, which are labeled the “false positives.” In a mixed population possessing mostly normal subjects, despite a high test specificity, “positive” designations will cause such a group to contain a disproportionately high percentage of “false positives”. This is why, when we use tests for screening asymptomatic subjects containing a high percentage of normals, the combined results will skew the number testing “positive” to misleadingly high results, potentially inducing much anxiety and often the need for expensive and possibly risky additional tests.
HOW IMPORTANT IS THE POPULATION TO BE TESTED?
As discussed, if the baseline group composition of the suspected disease is low, this will result in many “false” positives. For example, let’s consider treadmill stress testing. If we test a group of asymptomatic individuals with few known cardiovascular risk factors, it will contain a very low likelihood (baseline probability) of heart disease—perhaps in the range of 1%. According to the Bayesian formula (its detailed mathematical description is unnecessary for this discussion) a positive test result will still carry a low likelihood of actual disease, possibly to only 4% to 8%. This minimizes the practical value of this test, and under these circumstances, such a test may not even be recommended. On the other hand, if we test an individual who has lots of cardiovascular risk factors, especially combined with symptoms that suggest the presence of heart disease, we’ve raised the pre-test probability of disease to a high or intermediate level—possibly 50% or more. A calculated positive test outcome in this type of individual has greater practical value, for it may raise the odds of disease to a level exceeding 90%. This then allows us to evaluate further on a much more selective basis, which is more efficient and cost-effective. Thus, Bayesian principles, used daily in medical practice, allow us to better select which tests to use and how to better interpret the results.
In conclusion, this description is by no means presented to prevent the use of all screening tests for diseases such as breast cancer. But it may help to interpret test results and to understand which tests to most effectively use in which subjects, and how to reduce some of the anxiety and fear that may result from results deemed as “positive”.
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