Copula index for detecting dependence and monotonicity between stochastic signals

Herb pairs containing Curcumae Rhizoma (Ezhu): A review of bio-active constituents, compatibility effects and t-copula function analysis

ETHNOPHARMACOLOGICAL RELEVANCE

An herbal pair is a classic form of clinical dispensing in Traditional Chinese Medicine (TCM), often used in prescriptions to enhance the effect or reduce potential side effects. It is the smallest component unit of Chinese medicine prescription and an essential bridge between Chinese medicine and prescription. Curcumae Rhizoma (called Ezhu in Chinese) is a representative TCM herb that promotes blood circulation and removes blood stasis. It has been used in Chinese medicine for thousands of years. Ezhu is generally used in clinical applications as a part of a "drug pair" to treat heartburn, stomach pain, tumour, amenorrhea and abdominal pain caused by blood stasis, qi stagnation and injury.

AIMS OF THE REVIEW

This review aims to summarize the latest and comprehensive situation of the biological activity and clinical application of drug pairs containing Ezhu, find the law of Ezhu compatibility application, and discuss the rationalization of Ezhu drug compatibility. For Ezhu, herb pairs to provide a theoretical basis for clinical research in TCM and serve as a research foundation for developing new drugs.

MATERIALS AND METHODS

Using a self-built prescription database and Apriori algorithm for association rule mining. A systematic search for studies on herb pairs containing Ezhu was carried out by using the internet databases of PubMed, CNKI, Baidu Scholar, Google Scholar and Web of Science, as well as other relevant textbooks, reviews and documents (e.g. Chinese Pharmacopoeia, 2020 edition, Chinese herbal classic books and PhD and MSc theses, etc.). Among them with keywords including "Curcumae Rhizoma", "Ezhu", "herb pairs", "clinical application", etc. and their combinations. Moreover, the t-copula function was used to analyse the dose-coupling effect of five drug pairs, including Ezhu.

RESULTS

The preliminary statistical analysis retrieved Ezhu prescriptions from self-built prescription database and internet databases. The results showed that the compatibility frequency of Ezhu with the other five Chinese medicines was high. Most of these selected herbal combinations are used to treat internal diseases. In this paper, the progress of the ethnopharmacology of Ezhu was reviewed, emphasizing the changes in bioactive components and compatibility of Chinese traditional medicine combinations such as Ezhu and Astragalus Curcuma (Sparganium stoloniferum Buch. -Ham; called Sanleng in Chinese), Ezhu and Astragali Radix (Astragalus membranaceus (Fisch.) Bge. var. mongholicus (Bge.) Hsiao, Astragalus membranaceus (Fisch.) Bge.; called Huangqi in Chinese). Some other varieties, such as Ezhu and Rhizoma Chuanxiong (Ligusticum chuanxiong Hort.; called Chuanxiong in Chinese), Trionycis Carapax (Trionyx sinensis Wiegmann; called Biejia in Chinese), and Coptidis Rhizoma (Coptis chinensis Franch., Coptis deltoidea C. Y. Cheng et Hsiao, Coptis teeta Wall.; called Huanglian in Chinese), are also recorded in ancient books but rarely researched. The dose of Ezhu is strongly correlated with the amount of Sanleng, Huangqi, Biejia, Chuanxiong and Huanglian, respectively. Furthermore, there was a positive correlation between them.

CONCLUSIONS

The bioactive components and compatibility effects of Ezhu herb pairs were studied in detail using data mining and t-copula function analysis. Ezhu and Astragalus Curcuma (Sanleng) mainly treat gynecological disorders by activating blood circulation and relieving congestion. Ezhu and Astragali Radix (Huangqi) drug pair and Ezhu and Trionycis Carapax (Biejia) drug pair are all commonly used in the clinical treatment of tumors, the former is mainly used clinically for the treatment of digestive tract-related inflammation and tumors, liver cancer and gynecological tumors, and the latter is commonly used for the treatment of malignant tumors, such as liver cancer and mammary cancer.

Dose Correlation of Panax ginseng and Atractylodes macrocephala Koidz. Drug Pairs in the Chinese Medicine Prescription Based on the Copula Function

Objective

Panax ginseng and Atractylodes macrocephala Koidz. (AMK) are widely used in treating various diseases; however, research is insufficient on measuring the relationship that exists by combining this drug pair using the copula function.

Methods

In this study, 279 traditional Chinese medicine prescriptions containing the Panax ginseng and AMK drug pair were extracted from the prescription database for three types of screened indications, namely, diabetes mellitus, diarrhea, and insomnia. Following the principle of dose conversion, each dynasty unit was uniformly converted into a modern unit. Then, the kernel density distribution of Panax ginseng and AMK was fitted with their empirical distribution functions. Finally, the optimal copula function was selected from the copula function family as a t-copula function.

Results

The empirical distribution and probability density functions of Panax ginseng and AMK were obtained. From the results, their Kendall rank correlation coefficients with indications of diabetes mellitus, insomnia, and diarrhea were 0.8689, 0.7858, and 0.7403, whereas their Spearman rank correlation coefficients were 0.9563, 0.9276, and 0.8958. Results also indicated that the use of the t-copula function can better reflect the correlation between Panax ginseng and AMK doses.

Conclusion

From the three indications, the dose between Panax ginseng and AMK was positively correlated. This study, therefore, confirms the medicinal principle of Chinese medicine “combining” from the perspective of mathematical statistics. Results from this study are practical to evaluate the correlation between the drug pair doses, Panax ginseng and AMK, using the copula function model, which provides a new model for the scientific explanation of compatibility for Chinese medicines. This study also provides a methodological basis for more drug measurement studies and clinical medications.

Dose Correlation of Danggui and Chuanxiong Drug Pairs in the Chinese Medicine Prescription Based on the Copula Function

Dosage is essential for studying the compatibility and effectiveness of traditional Chinese medicine. Danggui and Chuanxiong are widely used in traditional Chinese medicine for ailments and treatment of various disorders. 628 traditional Chinese medicine prescriptions containing Danggui and Chuanxiong were extracted from the self-built prescription database and screened for the three groups of prescriptions, i.e., irregular menstruation, sores, and stroke. We processed and tested the dosage of Danggui and Chuanxiong and selected the optimal copula function, Gumbel copula function, from the Archimedes function family and elliptical copula function family to establish the data model. To establish the presence of a correlation between the dose of Danggui and Chuanxiong, a graph of the joint distribution function of rank correlation coefficients, Kendall's rank correlation coefficient and Spearman's rank correlation coefficient, was used. Our results suggest that the model using the Gumbel copula function better reflects the correlation between the dose of Danggui and Chuanxiong. For irregular menstruation, sores, and strokes, Kendall's rank correlation coefficients were 0.6724, 0.5930, and 0.7757, respectively, and Spearman's correlation coefficients were 0.8536, 0.7812, and 0.9285, respectively. In all three prescription groups, the dose of Danggui and Chuanxiong was positively correlated, implying that, as the dosage of one drug increases, the dosage of the other increases as well. From the perspective of data mining and mathematical statistics, the use of the copula function model to evaluate the correlation between the prescribed dosage of the two drugs was innovative and provided a new model for the scientific interpretation of the compatibility of traditional drugs. This might also serve to guide the clinical use of traditional Chinese medicine.