Trusting numbers: uncertainty and the pathology laboratory

To the Editor: White emphasised problems that can arise if medical decisions are overly reliant on the results of laboratory tests.1 He relates the case of a patient who, because of a peculiarity of her immunology, consistently produced a false-positive test result. In probabilistic language, the issue is are there risks of both random errors and patient-specific errors? It is important to distinguish between them. Suppose a test has a false-positive rate of 10%. If this is truly random error, the probability of two false-positive results in the same person is 1%, and the probability of three false-positive results is tiny. But if it is due to there being 10% of healthy people for whom the test is invalid and who consistently give a positive result, the probability of two false-positive results in the same person is 10%, and the probability of three false-positive results is 10%!