A multi-stage Gaussian transformation algorithm for clinical laboratory data

We have developed a multi-stage computer algorithm to transform non-normally distributed data to a normal distribution. This transformation is of value for calculation of laboratory reference intervals and for normalization of clinical laboratory variates before applying statistical procedures in which underlying data normality is assumed. The algorithm is able to normalize most laboratory data distributions with either negative or positive coefficients of skewness or kurtosis. Stepwise, a logarithmic transform removes asymmetry (skewness), then a Z-score transform and power function transform remove residual peakedness or flatness (kurtosis). Powerful statistical tests of data normality in the procedure help the user evaluate both the necessity for and the success of the data transformation. Erroneous assessments of data normality caused by rounded laboratory test values have been minimized by introducing computer-generated random noise into the data values. Reference interval endpoints that were estimated parametrically (mean +/- 2 SD) by using successfully transformed data were found to have a smaller root-mean-squared error than those estimated by the non-parametric percentile technique.