Letters to the Editor

Abstract

To the Editor: —McGee1 does a service for us by focusing on the likelihood ratio as one of—if not the most important—operating characteristic of a diagnostic test. He suggests that its lack of use is due to the burdensome calculations necessary for conversion between odds and probabilities. Although this may be true, we offer an alternative explanation. Probabilities differ from likelihoods in important ways.2 With probabilities, the data are random and hypotheses are fixed, allowing one to develop conditional probabilities. Conversely, with likelihoods, the data are fixed and the hypotheses are random, as seen in a differential diagnosis. Likelihoods do not follow the rules of probability theory. Odds have made intuitive sense to the man on the street who bets on categorical events like winning a horserace. Odds also apply to such things as whether a solitary pulmonary nodule is malignant or benign or if a woman is pregnant or not. That we in medicine have chosen to remain with probabilities and dismiss odds shows that we have yet to grasp this subtle but important distinction. With respect to an interpretation of likelihood ratios such as that given in McGee's Table 2, Jaeschke et al. 3 from the Evidence-Based Medicine Working Group note the following: “Likelihood ratios greater than 10 or less than 0.1 generate large and often conclusive changes from pretest to post-test probability. Likelihood ratios of 5 to 10 and 0.1 to 0.2 generate moderate shifts in pretest to posttest probability. Likelihood ratios of 2 to 5 and 0.2 to 0.5 generate small (but sometimes important) changes in probability. Likelihood ratios of 1 to 2 and 0.5 to 1 alter probability to a small (and rarely important) degree.” The divergent relationship between odds and probabilities is important in decision-making involving probabilities less than 10% and greater than 90%. If a man has a solitary pulmonary nodule with a 50% probability (odds of 1) of malignancy, would his doctor and he want a hypothetical test that had a likelihood ratio of 13 or one with 101 to rule it in? If the first test was positive, the probability would be 93%, compared with a probability of 99% with a positive second test—a mere difference of 6%. Using odds, after a positive first test, he would have 13 chances of having the malignancy to 1 chance of its being benign, whereas with the second test positive, his odds increase to 101 chances of having a cancer to 1 not. This example involves probability ranges beyond the formula proposed by McGee. Dreyfus and Dreyfus4 have shown that the novice makes decisions in a protracted and laborious manner, using context-free rules, with no base of experience, having no responsibility for the problem, and using conscious analysis. Conversely, the expert gathers information fluently and expeditiously by focusing on the situation at hand, using his or her base of experience, having a strong sense of responsibility that drives an intuitive decision. The range suggested by McGee limits us to probabilities between 10% (odds 1 to 9) and 90% (odds 9 to 1), in which an intuitive sense is meager. While this is sufficient for decisions regarding appendicitis or streptococcal pharyngitis, it is inadequate in dealing with problems such as malignancy.—John C. Peirce, MD, MA, MS, Richard D. Gerkin, MD, MS,Good Samaritan Regional Medical Center, Phoenix, Ariz.