Prescription patterns are rules or regularities used to generate, recognize, or judge a prescription. Most of existing studies focused on the specific prescription patterns for diverse diseases or syndromes, while little attention was paid to the common patterns, which reflect the global view of the regularities of prescriptions. In this paper, we designed a method CPPM to find the common prescription patterns. The CPPM is based on the hierarchical clustering of herb-pair efficacies (HPEs). Firstly, HPEs were hierarchically clustered; secondly, the individual herbs are labeled by the HPE
The processes of diagnosing syndrome and prescribing prescriptions in TCM (traditional Chinese medicine) are empirical. It is essential to minimize the uncertainty caused by human factors by finding the unchangeable TCM patterns, syndrome pattern, and prescriptions pattern.
As far as the first kind of TCM patterns, syndrome pattern, is concerned, several syndrome patterns had been proposed, such as SEM (structure equation modeling) to explore the diagnosis of the suboptimal health status [
Here we studied the second kind of TCM patterns, prescription patterns, which are rules or regularities used to generate, recognize, or judge prescriptions. In TCM, the herbs in one prescription are not organized randomly, but according to a set of principles for the therapeutic purposes of mutual enhancement, mutual assistance, mutual restraint, or mutual antagonism [
Before discussing the prescription patterns in further detail, the TCM data relationships used in this paper were described firstly. There are three forms of TCM data, individual herbs (herbs), herb-pairs, and prescriptions. An herb-pair is composed of two herbs for the purposes of mutual enhancement, mutual assistance, mutual restraint, or mutual antagonism [
The existing prescription patterns vary from methods to methods. By clustering algorithms, the patterns are in the form of specific groups of herbs for stroke [
Up to now, too much attention has been paid to the specific patterns for diverse diseases or syndromes, while little attention is paid to the common patterns of all prescriptions. A particular pattern is suitable to generate or recognize a specific prescription for a certain disease, while the common patterns are also important when judging the feasibility of a prescription at a high overall level. Common features of complex systems are ubiquitous, such as small world [
To explore the common prescription patterns, there are some questions: are prescriptions characterized by any common features? Is it possible to extract some mathematical expressions of the common features for all prescriptions? We discussed the possibility of solving the problems from two aspects.
In this paper, we dug the common prescription patterns from the herb-pair data by hierarchical clustering methods and summarized a mathematic expression of the common patterns.
An herb-pair is composed of two herbs and provides some synergistic efficacy in vivo. In this study, 697 herb-pairs were directly collected from two reputable TCM literatures [
HPEs and some statistics.
ID | Efficacy | Size | Candidate | HPE |
The number of herb-pairs composed of herbs in HPE | |
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HPE |
HPE | |||||
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Expelling wind and dispersing cold | 35 | ||||
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Dispelling wind and clearing hot | 24 | √ | HPE |
20 | 0 |
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Warming Zang-fu organs | 17 | √ | HPE |
17 | 0 |
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Warming meridians | 9 | ||||
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Clearing hot and purging fire | 46 | √ | HPE |
42 | 1 |
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Clearing hot and cooling blood | 17 | √ | HPE |
17 | 0 |
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Clearing hot and detoxicating | 19 | √ | HPE |
17 | 2 |
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Clearing deficient hot | 12 | √ | HPE |
4 | 7 |
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Resolving and drying dampness | 19 | √ | HPE |
5 | 14 |
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Promoting urination and dehumidification | 34 | √ | HPE |
31 | 1 |
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Clearing wind and damp | 14 | ||||
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Cold purgation | 6 | ||||
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Warm purgation | 4 | ||||
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Moistened cathartic | 5 | ||||
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Dispelling retained water | 7 | ||||
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Regulating Qi | 24 | √ | HPE |
2 | 20 |
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Promoting Qi | 18 | √ | HPE |
3 | 15 |
|
Depressing Qi | 12 | √ | HPE |
0 | 12 |
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Activating blood | 40 | √ | HPE |
37 | 2 |
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Hemostasis | 26 | √ | HPE |
26 | 0 |
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Relieving cough and asthma | 33 | √ | HPE |
7 | 22 |
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Elimination | 22 | √ | HPE |
4 | 18 |
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Supplying Qi and blood | 135 | √ | HPE |
131 | 1 |
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Astringing | 29 | √ | HPE |
28 | 1 |
|
Extinguishing wind | 21 | √ | HPE |
3 | 18 |
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Tranquilization | 16 | √ | HPE |
3 | 13 |
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Resuscitation | 11 | ||||
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Expelling parasite | 4 | ||||
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Emetics | 3 | ||||
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External application | 16 | √ | HPE |
15 | 1 |
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Clearing hot and drying dampness | 6 | ||||
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Eliminating phlegm | 13 | √ | HPE |
0 | 12 |
Summary | 697 | 412 | 160 |
332 prescriptions were collected from two popular books:
The symbols used in this paper are as follows. Let
Jaccard similarity coefficient is a statistic metric used for comparing the similarity and diversity of finite sample sets. It is defined as the size of the intersection divided by the size of the union of the sample sets. Given two sets
Jaccard coefficient was used to compare the similarity of any two HPEs. An HPE is denoted by a set of individual herbs which make up the herb-pairs with the HPE. The number of HPEs is 32, and the similarities between these efficacies can be represented as a similarity matrix,
For example, given a number of herb-pairs which are
In this section, a method of finding the common prescription patterns (CPPM) was proposed. The basic idea of CPPM was to use the clusters of HPEs to represent the common patterns of prescriptions. The methodological possibility had been elaborated in Section
Hierarchical clustering structure reflects both individual and common features of complex systems. The hierarchical clustering of HPEs could be used to study the individual problem or the common problem. The higher clustering of HPEs reflects commonality and the lower clustering reflects individuality.
Here is an example to show how to extract the common patterns and the specific patterns of prescriptions at the different levels of the HPE hierarchical clustering.
The hierarchical clustering structure of the five HPEs.
Prescription patterns at different levels of granularity.
Prescriptions | Prescription patterns | ||
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5-clustering | 2-clustering | 1-clustering | |
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Results | Core-set: |
Common patterns: |
Common pattern: |
The inputs and outputs of CPPM were shown as follows.
Inputs are as follows: Similarity matrix of HPEs. Candidate prescriptions = The granularity level of hierarchical clustering
Outputs are as follows:
Common prescription patterns:
combination of HPE OO.
The metrics PO and OO were used to evaluate the support of the results, which would be stated in Section
A hierarchical clustering algorithm, such as Ward algorithm or BIRCH algorithm, was applied on the similarity matrix of HPEs. Then the
There are two substeps: an herb may make up some herb-pairs with different HPEs. (1) The frequent HPE is its dominating HPE. (2) According to the dominating HPE, the corresponding HPE
For a prescription, replace its herbs by the corresponding HPE
The metric PO of each pattern is calculated and the frequent patterns with higher value of PO are selected as the common prescription patterns.
By inputting different parameter
At the top level (
It is not easy to determine the level of granularity. A good granularity level should be a meaningful clustering, which should be coincident with a certain biological action of mechanism or a TCM theory. Here we performed the process in the manual way which would be stated in Section
There are two different datasets with different data sources in CPPM, herb-pairs and prescriptions. Through the mapping technique, herb-pairs and prescriptions established a certain connection. The size of the intersection of the two sets reflects their consistency and completeness. Let
To identify the commonality of the prescription patterns, we designed the probability of occurrence (PO). Let
The size of an herb-pair efficacy is the number of herb-pairs with the herb-pair efficacy. The herb-pair efficacy sizes of different efficacies are not the same (in Table
A hierarchical clustering method (average linkage within groups) applied to
The hierarchical tree of HPEs, where the nodes of left are the IDs of HPEs.
Here we counted the number of herb-pairs whose two herbs belong to one cluster,
The number of herbs in the sets
The number of all herbs in all the inputted prescriptions with repeating is 2057, where 1677 herbs could be located in
To get the prescription patterns, we projected the herbs of the prescriptions to the two clusters,
Prescription patterns at level 2, 2-clustering of HPEs.
Four patterns | Number of prescriptions | PO |
---|---|---|
HPE |
209 | 0.63 |
HPE |
110 | 0.33 |
HPE |
8 | 0.02 |
Other | 5 | 0.02 |
Total |
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From the value of PO of each pattern, two common prescription patterns were recognized: Pattern 1: Pattern 2:
The verbal description of the common patterns is as follows: if a prescription contains the herbs of
This section is quite argued and mysterious. But, for the sake of perfect mathematical matching, we found that the common prescription patterns are completely consistent with the Blood-Qi theory in TCM.
The Blood-Regulating efficacies,
In the Blood-Qi theory of TCM, Qi stagnation leads to blood stasis and blood stasis does not always cause Qi stagnation. So the formalization of the theory is
The two formulas
The prescription of TCM is a complex system. Usually, the knowledge of a few entities (prescriptions) of a complex system does not straightforwardly lead to a description of the overall system. So the common prescription patterns can provide us with a global view of the regularities of prescriptions. A method CPPM proposed in this paper is to find the common prescription patterns based on the hierarchical clustering of herb-pairs efficacies. The method was applied on the 697 herb-pairs and the 332 prescriptions. The statistic results showed that when the granularity level of the hierarchical clustering is 2, the common patterns are obvious. The description of the common patterns is that if a prescription contains the herbs of the clusters (
The author declares no competing interests.
The author is grateful to Professor Wang Yun from the Beijing University of Chinese Medicine for providing the conditions for data collections and some important advices for this paper. This paper is supported by Beijing Higher Education Young Elite Teacher Project (YETP0767), the Fundamental Research Funds for the Central Universities (YX2013-29), and the National Natural Science Foundation of China (30973946). The above three funds supported equally this work.