Multichannel 18-test panels: are 60% of panels abnormal by chance?

Current teaching concerning the frequency of abnormal results secondary to chance alone in a multichannel panel is theoretically based on the binomial distribution. However, this distribution can be used only when the probability of an abnormal result (pi) is the same for each test in the panel. In modern-day multichannel testing, pi varies from test to test and most often is less than the usually reported 0.05. On the other hand, a test such as cholesterol may have a pi level as high as 0.55. Theoretically the only distribution that can take this variability into consideration is the Lexis distribution, a form of the binomial distribution that allows for varying pi s. Since no formula is available to calculate this distribution, we wrote a computer program to generate it. We arranged 18-test panels from 203 normal patients in a frequency distribution. This was then compared with the theoretical Lexis and binomial distributions. This analysis showed that although there was a 50% chance of having one abnormality per panel and a 16% chance of having two abnormalities per panel, there was less than 4% chance of having three or more abnormalities per 18-test panel. In addition, most of the abnormalities noted were minor and were thought to be clinically unimportant.