Nonparametric Estimation of Reference Intervals by Simple and Bootstrap-based Procedures

In recent years, increasing interest has arisen in nonparametric estimation of reference intervals. The IFCC recommendation focuses on the nonparametric procedure, and the NCCLS guideline on reference interval estimation deals exclusively with the nonparametric approach (1)(2). The mentioned reports are based on the simple nonparametric approach, taking as a basis the sorted sample values. In addition to this basic approach, modern computer-based procedures have been introduced, which have made it possible to attain slightly increased precision for the nonparametric approach by applying resampling methods, weighted percentile estimation, or smoothing techniques (3)(4). In the present report, both the simple nonparametric reference interval estimation procedure and the resampling (bootstrap) principle were studied using simulations based on distribution types that should be relevant for clinical chemistry, i.e., gaussian and skewed distributions. According to the procedure recommended by the IFCC and NCCLS, the observations are ranked according to size, and the 2.5 and 97.5 percentiles are obtained as the 0.025 (n + 1) and 0.975 (n + 1) ordered observations (1)(2). If the estimated rank values are not integers, then linear interpolation is carried out. In the statistical literature, various modifications of the computation procedure have been considered (5)(6)(7). Here the traditional one used in clinical chemistry as outlined above (called method I) is compared with an alternative (called method II): p /100 × n + 0.5, where p indicates the percentile (6). For the 2.5 and 97.5 percentiles, method II yields the 0.025n + 0.5 and 0.975n + 0.5 ordered values, respectively. In the following, the above-mentioned calculation principles are referred to as “simple” procedures (IS or IIS) as opposed to “bootstrap” modifications described below (IB or IIB). The bootstrap principle consists of repeated random resampling of the original observations with replacement, which …