基于Copula函数研究柴胡-白芍药对在治疗“肝郁血虚”方剂中的剂量相关性

Study on dose correlation of Bupleuri Radix and Paeoniae Radix Alba pair in treatment of“liver stagnation and blood efficiency”by using Copula function

目的构建Copula函数,研究柴胡Bupleuri Radix-白芍Paeoniae Radix Alba药对在治疗“肝郁血虚”方剂中的剂量相关性。方法从自建方剂数据库中收集治疗“肝郁血虚”证并含柴胡-白芍药对的传统中医方剂,对其中柴胡剂量和白芍剂量进行数据处理和检验,从阿基米德Copula函数族、椭圆Copula函数族中选择出最佳的Copula函数建立数学模型,描绘联合分布函数图,测算Kendal秩相关系数和Spearman秩相关系数,监测柴胡剂量和白芍剂量数据间的相关性。结果筛选出109首方剂。Gaussian Copula函数模型能较好地反映柴胡和白芍剂量之间的相关性,柴胡和白芍的剂量的Kendal秩相关系数为0.3301,Spearman秩相关系数为0.4718,说明柴胡和白芍剂量之间具有较强的非线性关系,且呈正相关,即随着其中一味药剂量增大,另一味药也倾向于增大剂量。结论从数据挖掘和数理统计角度,创新引入Copula函数模型,研究药对剂量的相关性,为传统经典药对相使为用提供证据,以及为传统医学临床用药提供新的研究思路。

Objective To study the dose correlation of Bupleuri Radix and Paeoniae Radix Alba pair in the treatment of“liver stagnation and blood deficiency”by constructing Copula function.Methods The traditional Chinese medicine prescriptions containing Bupleuri Radix and Paeoniae Radix Alba pair for the treatment of"liver stagnation and blood deficiency"syndrome were collected from the self-established prescription database.The data of the dosage of Bupleuri Radix and Paeoniae Radix Alba were processed and tested.The best Copula function was selected from Archimedes function family and elliptic Copula function family to establish the data model,depict the joint distribution function diagram,and calculate the Kendal rank correlation coefficient and Spearman coefficient.A rank correlation coefficient was used to monitor the correlation between the dose data of Bupleuri Radix and Paeoniae Radix Alba.Results A total of 109 cases of traditional Chinese medicine prescriptions containing Bupleuri Radix and Paeoniae Radix Alba were collected from the self-established prescription database.Gaussian Copula function model could better reflect the correlation between Bupleuri Radix and Paeoniae Radix Alba.The Kendall rank correlation coefficient and Spearman correlation coefficient of Bupleuri Radix and Paeoniae Radix Alba were 0.3301 and 0.4718 respectively,which indicated that there is a strong nonlinear correlation between Bupleuri Radix and Paeoniae Radix Alba,and the correlation was positive,with the increase of the dose of one medicine,the other medicine also tended to increase the dose.Conclusion From the perspective of data mining and mathematical statistics,this paper innovatively introduces Copula function model to study the correlation between drug pair and dose,and provides a new research model for the scientific interpretation of traditional classic drug pair compatibility and guiding traditional medical clinical medication.