Hyltoft Petersen Per, Blaabjerg Ole, Andersen Marianne, Jørgensen Lone G M, Schousboe Karoline, Jensen Esther
Department of Clinical Biochemistry, Odense University Hospital, Odense, Denmark.
Clin Chem Lab Med. 2004;42(7):715-24. doi: 10.1515/CCLM.2004.122.
A well-known transformation from the bell-shaped Gaussian (normal) curve to a straight line in the rankit plot is investigated, and a tool for evaluation of the distribution of reference groups is presented. It is based on the confidence intervals for percentiles of the calculated Gaussian distribution and the percentage of cumulative points exceeding these limits. The process is to rank the reference values and plot the cumulative frequency points in a rankit plot with a logarithmic (In=log(e)) transformed abscissa. If the distribution is close to In-Gaussian the cumulative frequency points will fit to the straight line describing the calculated In-Gaussian distribution. The quality of the fit is evaluated by adding confidence intervals (CI) to each point on the line and calculating the percentage of points outside the hyperbola-like CI-curves. The assumption was that the 95% confidence curves for percentiles would show 5% of points outside these limits. However, computer simulations disclosed that approximate 10% of the series would have 5% or more points outside the limits. This is a conservative validation, which is more demanding than the Kolmogorov-Smirnov test. The graphical presentation, however, makes it easy to disclose deviations from In-Gaussianity, and to make other interpretations of the distributions, e.g., comparison to non-Gaussian distributions in the same plot, where the cumulative frequency percentage can be read from the ordinate. A long list of examples of In-Gaussian distributions of subgroups of reference values from healthy individuals is presented. In addition, distributions of values from well-defined diseased individuals may show up as In-Gaussian. It is evident from the examples that the rankit transformation and simple graphical evaluation for non-Gaussianity is a useful tool for the description of sub-groups.
研究了在正态概率图中从钟形高斯（正态）曲线到直线的一种著名变换，并提出了一种评估参考组分布的工具。它基于计算出的高斯分布百分位数的置信区间以及超过这些限值的累积点数的百分比。该过程是对参考值进行排序，并在横坐标进行对数（In = log(e)）变换的正态概率图中绘制累积频率点。如果分布接近对数高斯分布，累积频率点将拟合描述计算出的对数高斯分布的直线。通过给直线上的每个点添加置信区间（CI）并计算双曲线状CI曲线之外的点数百分比来评估拟合质量。假设是百分位数的95%置信曲线将显示5%的点在这些限值之外。然而，计算机模拟表明，大约10%的系列会有5%或更多的点在限值之外。这是一种保守的验证，比柯尔莫哥洛夫-斯米尔诺夫检验要求更高。然而，图形展示使得很容易发现与对数高斯性的偏差，并对分布进行其他解释，例如，在同一图中与非高斯分布进行比较，累积频率百分比可从纵坐标读取。给出了一长串来自健康个体参考值子组的对数高斯分布的例子。此外，来自明确患病个体的值的分布可能表现为对数高斯分布。从这些例子中可以明显看出，正态概率变换和简单的非高斯性图形评估是描述子组的有用工具。
