Partitioning of Nongaussian-Distributed Biochemical Reference Data into Subgroups Ari Lahti, 1* Per Hyltoft Petersen, 2,3 James C. Boyd, 4 Pål Rustad, 5 Petter Laake, 6 and Helge Erik Solberg 1 Background: The aim of this study was to develop new methods for partitioning biochemical reference data, covering in particular nongaussian distributions. Methods: We recently proposed partitioning criteria for gaussian distributions. These criteria relate to propor- tions of the subgroups outside each of the reference limits of the combined distribution (proportion criteria) and to distances between the subgroup distributions as correlates of these proportions (distance criteria). How- ever, distance criteria do not seem to be ideal for nongaussian distributions because a generally valid relationship between proportions and distances cannot be established for these. Results: Proportion criteria appear preferable to dis- tance criteria for two additional reasons: (a) The preva- lences of the subgroup populations may have a consid- erable effect on stratification, but these are hard to account for by using distance criteria. Two methods to handle prevalences are described, the root method and the multiplication method. (b) Tied reference values, another complication of the partitioning problem, could also be hard to take care of using distance criteria. Some solutions to the problems caused by tied reference values are suggested. Conclusions: Partitioning of biochemical reference data should preferably be based on proportion criteria; this is particularly true for nongaussian distributions. Both of the described complications of the partitioning prob- lem, the prevalences of the subgroups and tied reference values, are hard to deal with using distance criteria, but the proposed methods make it possible to account for them when proportion criteria are applied. © 2004 American Association for Clinical Chemistry We have recently proposed a new method for partitioning biochemical reference data into subgroups (1, 2). This method was developed with gaussian distributions as a starting point because the statistical properties of those distributions are well known. Hence, a partitioning method based on gaussian distributions can be made mathematically accurate. Although the distributions of biochemical reference data are sometimes gaussian or can be converted to gaussian distributions by use of appro- priate mathematical transformations, this is often not the case. Generally valid partitioning criteria that could be used for all types of distributions are therefore required, but such criteria do not seem to exist in the literature. The partitioning criteria presented by Harris and Boyd (3, 4) were developed using gaussian distributions, and although practitioners seem frequently to apply them to nongaussian distributions as well, their applicability to these is questionable. In contrast to what many users of these criteria seem to believe, the basic idea of the Harris–Boyd method is not to perform statistical signifi- cance tests for distances between means, although a modified normal deviate test is part of this method. Rather, Harris and Boyd aimed at correlating these dis- tances to proportions of the subgroup distributions out- side the reference limits of the combined distribution. This correlation, established for gaussian distributions by Har- ris and Boyd, is not automatically valid for nongaussian distributions, however, because the proportions obtained for nongaussian distributions at particular distances be- tween means can be quite different from those obtained for gaussian distributions at the same distances. The conclusions on partitioning made by applying the same 1 Department of Clinical Chemistry, Rikshospitalet University Hospital of Oslo, Oslo, Norway. 2 Department of Clinical Biochemistry, Odense University Hospital, Odense, Denmark. 3 NOKLUS, Norwegian Centre for External Quality Assurance of Primary Care Laboratories, Division for General Practice, University of Bergen, Bergen, Norway. 4 Department of Pathology, University of Virginia Health System, Char- lottesville, VA. 5 Fu ¨ rst Medical Laboratory, Oslo, Norway. 6 Section of Medical Statistics, University of Oslo, Oslo, Norway. *Address correspondence to this author at: Department of Clinical Chem- istry, Rikshospitalet University Hospital of Oslo, N-0027 Oslo, Norway. Fax 47-2307-1080; e-mail ari.lahti@rikshospitalet.no. Received September 30, 2003; accepted February 13, 2004. Previously published online at DOI: 10.1373/clinchem.2003.027953 Clinical Chemistry 50:5 891–900 (2004) Laboratory Management 891 Downloaded from https://academic.oup.com/clinchem/article/50/5/891/5640052 by guest on 04 July 2022