Reference range: Which statistical intervals to use?

Reference ranges, which are data-based intervals aiming to contain a pre-specified large proportion of the population values, are powerful tools to analyse observations in clinical laboratories. Their main point is to classify any future observations from the population which fall outside them as atypical and thus may warrant further investigation. As a reference range is constructed from a random sample from the population, the event 'a reference range contains (100 P)% of the population' is also random. Hence, all we can hope for is that such event has a large occurrence probability. In this paper we argue that some intervals, including the P prediction interval, are not suitable as reference ranges since there is a substantial probability that these intervals contain less than (100 P)% of the population, especially when the sample size is large. In contrast, a (P,gamma) tolerance interval is designed to contain (100 P)% of the population with a pre-specified large confidence gamma so it is eminently adequate as a reference range. An example based on real data illustrates the paper's key points.