Estimation of Normal Ranges and Cumulative Proportions by Transforming Observed Distributions to Gaussian Form

Abstract

Abstract A sequence of transforming functions is proposed to convert nongaussian distributions often seen in laboratory data to gaussian form. These transforms are chosen to eliminate or substantially reduce nongaussian characteristics of positive skewness and peakedness that result from two factors: (a) increases in variance with increasing mean values, and (b) general heterogeneity among intrapersonal variances. Use of these transforms, demonstrated on many sets of clinical laboratory data, enables smooth curves to be drawn through observed cumulative distributions plotted on arithmetic or gaussian probability scales. From such curves, normal ranges or proportions below a specified measurement may be estimated easily and with greater precision than possible through nonparametric methods. Formulas are given for obtaining confidence limits corresponding to these estimates. The entire process of transforming the original variable to gaussian form and graphing the cumulative distribution curve has been computerized. Programs are available to others interested in applying these methods.