改良马氏深度函数法建立多元参考值范围的理论与应用

Application of revised Mahalanobis depth function in statistical method for establishing multivariate reference range

目的:提出一种基于改良马氏深度函数的多变量参考值范围统计学建立方法,并以此为基础探讨统计深度函数在解决多变量参考值范围问题方面的实际应用价值.方法:采用计算机模拟试验和实际数据分析相结合的方式,从参考值范围几何特征、参考值范围合法性与有效性等方面对新的和现有的几种多变量参考值范围建立方法进行比较分析.结果:改良马氏深度法建立的二元参考值范围具有典型的中心椭圆特征,对于多元正态分布资料,改良马氏深度法与正态分布法一致性在98.5%以上,实例数据分析结果显示改良马氏深度法建立的参考值范围大小比多元正态分布法更接近理论水平.结论:改良马氏深度法在参考值范围几何特征方面符合要求,在合法性及有效性方面优于现有的成熟方法,可以作为多变量参考值范围的有效统计学建立方法.

AIM： To bring forward a nonparametric multivariate method based on revised Mahalanobis depth function for establishing multivariate reference range and to explore the usefulness of statistical depth function in solving multivariate reference range problems. METHODS： Through computer simulation experiments and analysis of a case dataset, revised Mahalanobis depth method and currently used methods were compared in several aspects such as geometric features of reference ranges, validity and effectiveness of reference ranges, etc. RESULTS： Bivariate reference ranges constructed with revised Mahalanobis depth method appeared to be central ellipses in the scatter plot of data points. For multivariate normal distributed data, reference ranges of revised Mahalanobis depth method had much higher consistency with those of multivariate normal distribution method, i.e. more than 98.5% of cases were classified into same categories in computer simulation experiments. And for the case data, percentages of cases included in the reference range of revised Mahalanobis depth method were closer to the expected levels than those of multivariate normal distribution method did. CONCLUSION： Revised Mahalanobis depth method meets the requirements of multivariate reference range in the aspect of geometric features and has better performances in aspects of validity and effectiveness for multivariate reference ranges. Revised Mahalanobis depth method can be used as a valid statistical method for establishing multivariate reference range.