GENERAL PAPER Non-parametric estimation of reference intervals in small non-Gaussian sample sets Johan Bjerner Elvar Theodorsson Eivind Hovig Anders Kallner Received: 24 October 2008 / Accepted: 16 January 2009 / Published online: 12 February 2009 Ó Springer-Verlag 2009 Abstract This study aimed at validating common boot- strap algorithms for reference interval calculation.We simulated 1500 random sets of 50–120 results originating from eight different statistical distributions. In total, 97.5 percentile reference limits were estimated from bootstrap- ping 5000 replicates, with confidence limits obtained by: (a) normal, (b) from standard error, (c) bootstrap percentile (as in RefVal) (d) BCa, (e) basic, or (f) student methods. Reference interval estimates obtained with ordinary boot- strapping and confidence intervals by percentile method were accurate for distributions close to normality and devoid of outliers, but not for log-normal distributions with outliers. Outlier removal and transformation to normality improved reference interval estimation, and the basic method was superior in such cases. In conclusions, if the neighborhood of the relevant percentile contains non- normally distributed results, bootstrapping fails. The dis- tribution of bootstrap estimates should be plotted, and a non-normal distribution should warrant transformation or outlier removal. Keywords Reference intervals  Bootstrap  Re-sampling  Algorithm  Non-parametric  Percentile  Confidence intervals  Gaussian  Distribution Introduction In medical biochemistry, a reported level of a biochemical quantity is usually accompanied by a reference interval. Biological reference intervals are conventionally defined in laboratory medicine as covering the central 95% of a reference distribution composed of analyte values obtained by measurement of samples collected from reference individuals selected randomly from the reference popula- tion [1]. The interest in obtaining accurate reference limits for various biochemical quantities seems surging, and is, e.g., reflected in an increasing number of manuscripts on the subject submitted to the Scandinavian Journal of Clinical and Laboratory Investigation, where three of the authors have been involved with the editorial handling of manu- scripts. When the journal during the summer of 2007 received two manuscripts containing relatively few obser- vations, but with conspicuously narrow confidence limits calculated by using the non-parametric bootstrap routine in RefVal, we decided to make a detailed investigation of the Electronic supplementary material The online version of this article (doi:10.1007/s00769-009-0490-2) contains supplementary material, which is available to authorized users. J. Bjerner (&) Department of Medical Biochemistry, Rikshospitalet Medical Center, Oslo, Norway e-mail: johan.bjerner@medisin.uio.no J. Bjerner Dr. Fu ¨rst Medical Laboratory, Søren Bulls vei 25, 1051 Oslo, Norway E. Theodorsson IKE/Clinical Chemistry, Linko ¨ping University Hospital, Linko ¨ping, Sweden E. Hovig Bioinformatics Core Facility, Institute of Cancer Research, Norwegian Radium Hospital, Rikshospitalet University Hospital, Oslo, Norway A. Kallner Department of Clinical Chemistry, Karolinska University Hospital, Stockholm, Sweden 123 Accred Qual Assur (2009) 14:185–192 DOI 10.1007/s00769-009-0490-2