title: Impact of subgroup prevalences on partitioning of Gaussian-distributed reference values.
abstract: BACKGROUND
  The aims of this report were to examine how unequal subgroup prevalences in the source population may affect reference interval partitioning decisions and to develop generally applicable guidelines for partitioning gaussian-distributed data.
  
  
  METHODS
  We recently proposed a new model for partitioning reference intervals when the underlying data distribution is gaussian. This model is based on controlling the proportions of the subgroup distributions that fall outside each of the common reference limits, using the distances between the reference limits of the subgroup distributions as functions to these proportions. We examine the significance of the unequal prevalence effect for the partitioning problem and quantify it for distance partitioning criteria by deriving analytical expressions to express these criteria as a function of the ratio of prevalences. An application example, illustrating various aspects of the importance of the prevalence effect, is also presented.
  
  
  RESULTS
  Dramatic shrinkage of the critical distances between reference limits of the subgroups needed for partitioning was observed as the ratio of prevalences, the larger one divided by the smaller one, was increased from unity. Because of this shrinkage, the same critical distances are not valid for all ratios of prevalences, but specific critical distances should be used for each particular value of this ratio. Although proportion criteria used in determining the need for reference interval partitioning are not dependent on the prevalence effect, this effect should be accounted for when these criteria are being applied by adjusting the sample sizes of the subgroups to make them correspond to the ratio of prevalences.
  
  
  CONCLUSIONS
  The prevalences of subgroups in the reference population should be known and observed in the calculations for every reference interval study, irrespective of whether distance or proportion criteria are being used to determine the need for reference interval partitioning. We present detailed methods to account for the prevalences when applying each of these types of criteria. Analytical expressions for the distance criteria, to be used when high precision is needed, and approximate distances, to be used in practical work, are derived. General guidelines for partitioning gaussian distributed data are presented. Following these guidelines and using the new model, we suggest that partitioning can be performed more reliably than with any of the earlier models because the new model not only offers an improved correspondence between the critical distances and the critical proportions, but also accounts for the prevalence effect.
authors.affiliation: Department of Clinical Chemistry, Rikshospitalet University Hospital of Oslo, N-0027 Oslo, Norway. ari.lahti@rikshospitalet.no
authors.forename: Ari
authors.initials: A
authors.lastname: Lahti
authors.forename: Per
authors.initials: P
authors.lastname: Hyltoft Petersen
authors.forename: James C
authors.initials: JC
authors.lastname: Boyd
mesh_terms: D001699:Biometry; D019411:Clinical Laboratory Techniques / Q000706:statistics & numerical data*; D006801:Humans; D008954:Models, Biological; D016011:Normal Distribution; D012016:Reference Values; D018401:Sample Size