Determination of reference limits: statistical concepts and tools for sample size calculation

Reference limits are estimators for 'extreme' percentiles of the distribution of a quantitative diagnostic marker in the healthy population. In most cases, interest will be in the 90% or 95% reference intervals. The standard parametric method of determining reference limits consists of computing quantities of the form X̅±c·S. The proportion of covered values in the underlying population coincides with the specificity obtained when a measurement value falling outside the corresponding reference region is classified as diagnostically suspect. Nonparametrically, reference limits are estimated by means of so-called order statistics. In both approaches, the precision of the estimate depends on the sample size. We present computational procedures for calculating minimally required numbers of subjects to be enrolled in a reference study. The much more sophisticated concept of reference bands replacing statistical reference intervals in case of age-dependent diagnostic markers is also discussed.