The use of box-cox transformations in the development of multivariate tolerance regions with applications to clinical chemistry

Attempts often have been made to transform clinical and laboratory data to approximate normality for the purpose of developing either univariate “normal” ranges or multivariate reference ranges in the “supposedly healthy” population. For many of these transformations to be successful, it has been necessary to arbitrarily delete outlier values with no scientific justification for doing so. In this article, construction principles used in the determination of these ranges are reviewed. In addition, the Box-Cox family of power transformations is proposed as a means of obtaining an approximate multivariate normal distribution without an arbitrary deletion of outlier values. This method will allow for the construction of reference ranges for the clinical and laboratory variables of interest.