Discussion on several statistical problems in establishing quality standards of standard decoctions.

Since 2016, a number of studies have been published on standard decoctions used in Chinese medicine. However, there is little research on statistical issues related to establishing the quality standards for standard decoctions. In view of the currently established quality standard methods for standard decoctions, an improvement scheme is proposed from a statistical perspective. This review explores the requirements for dry matter yield rate data and index component transfer data for the application of two methods specified in "Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules," which include the average value plus or minus three times the standard deviation ( X - ± 3 S D ) or 70% to 130% of the average value ( X - ± 30 % X - ). The square-root arcsine transformation method is used as an approach to solve the problem of unreasonable standard ranges of standard decoctions. This review also proposes the use of merged data to establish a standard. A method to judge whether multiple sets of standard decoction data can be merged is also provided. When multiple sets of data have a similar central tendency and a similar discrete tendency, they can be merged to establish a more reliable quality standard. Assuming that the dry matter yield rate and transfer rate conform to a binomial distribution, the number of batches of prepared slices that are needed to establish the standard decoction quality standard is estimated. It is recommended that no less than 30 batches of prepared slices should be used for the establishment of standard decoction quality standards.

Background

The concept of “standard decoction” was first put forward by the Ministry of Health, Labour and Welfare of Japan in 1985 (Yu, Tian, Sumida, Yang, & Zeng, 2018). “Standard decoction” is used as the quality reference of Han medicine in Japan (Yu et al., 2018). In Taiwan Province in China, the term “standard decoction” has been used for a concentrate of Chinese medicine extract for decades (Chen et al., 2016).

In 2016, Liu et al. suggested that standard decoctions are used as core samples to determine the Q-Markers of traditional Chinese medicines (Liu et al., 2016). Chen et al. proposed research strategies for standard decoctions of prepared slices at approximately the same time (Chen et al., 2016).

In August 2016, the Chinese Pharmacopoeia Commission issued the “Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules” (Draft For Comments) (Commission, 2016). In this document, standard decoctions are used as the standard reference to determine whether Chinese medicine formula granules are essentially consistent with clinical decoctions. A standard decoction needs to be prepared with standardized technology, including water extraction according to the clinical decoction method, solid–liquid separation, and an appropriate concentration or drying.

After the second consultation in November 2019 (Administration, 2019), the National Medical Products Administration issued “Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules” in January 2021 (Administration, 2021).

Chinese medicine formula granules are a new type of prepared slices, with many advantages. As the quality reference for Chinese medicine formula granules, standard decoctions have been studied by many researchers in recent years. Since 2016, the number of research papers on the topic of standard decoctions has rapidly increased. As of December 31, 2020, a total of 302 research papers were found on www.cnki.net. The distribution is shown in Fig. 1. It can be seen that the standard decoction research is increasing.

Fig. 1

Number of papers on topic of “standard decoction” on www.cnki.net.

As of March 31, 2020, more than 140 kinds of prepared slices have been discussed in the research literature on standard decoctions (Table S1). As there are 616 kinds of medicinal materials and prepared slices included in the 2020 edition of Chinese Pharmacopoeia, it is expected that many studies on standard decoctions will be published over time. Most of the published studies determined the quality indices of standard decoctions. However, very few studies focused on statistical methods for the establishment of quality standards.

The newly issued “Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules” presented research requirements on the quality standards for standard decoctions, recommending that no less than 15 batches of representative prepared slices should be used. After water extraction, solid–liquid separation and concentration (or drying), indices of the dry matter yield rate, index component contents, and the index component transfer rate should be determined. The acceptable ranges of these indices should be specified. For the dry matter yield rate or transfer rate, the acceptable range is the mean value plus or minus three times the standard deviation () or 70% to 130% of the mean (). Although the methods for establishing quality standards of standard decoctions have been provided, the statistical basis of these methods is still unclear.

Analysis of the literature revealed some statistical problems in the establishment of quality standards for standard decoctions. First, the data requirements are unknown for establishing the standards in accordance with the method or the method. Second, some varieties have values greater than 100% or less than 0% in the standards established according to the method or method, which are collectively referred to as the “phenomenon of an unreasonable standard range” in this article. Third, different studies have given different standard ranges for the same prepared slices, which are collectively referred to as the “phenomenon of nonuniform standard range” in this article. Fourth, it is uncertain whether 15 batches of prepared slices are sufficient. The following will analyze and discuss the above issues.

Applicable conditions for establishment of current quality standard methods

Conditions of use of method

The premise of the method is that the indexes of the componenttransfer rate or dry matter yield rate data follow a normal distribution. For normally distributed data, the standard obtained by the method can cover 99.7% of the transfer rate or dry matter yield rate data. When selecting the method to establish the standard, the standard range should include the measured index values of the standard decoction, as follows:

In the formulas, and are the measured maximum and minimum values of multiple batches of standard decoctions. Formula (1) and formula (2) are added and transformed to obtain:

In this formula, is the range. Therefore, a necessary but insufficient condition for adopting the method to establish standards is obtained. In other words, the range of the quality indices of multiple batches of standard decoctions must be less than or equal to six times the standard deviation of the data.

Since the evaluation indicators of standard decoctions are all positive numbers, the corresponding standards should also be positive numbers, so the following should hold:

Formula (4) is transformed to obtain

That is, another necessary but insufficient condition for using the method to establish standards is that for the overall data, the .

Conditions for use of method

If the method is selected to establish the standard, the standard should include the measured index values of the standard decoction, as follows:

Formulas (6), (7) are added and transformed to obtain

Therefore, a necessary but insufficient condition is obtained for the selection of the method to establish a standard. That is, the maximum value of multiple batches of the standard decoction should be less than or equal to the minimum value times . When the method is used to establish the quality standard for a standard decoction, intuitively, only the average value is used, but the application conditions imply a certain quantitative relationship between the maximum and minimum data. These relationships can be used to test whether the data are applicable for the use of the method.

Width of standard range calculated with two methods

In many cases, both the method and method are available for the index component transfer rate or dry matter yield rate data. Considering that the number of batches of prepared slices is generally small, it is more likely that the obtained index range for the evaluation of the standard decoction is narrow. Therefore, researchers tend to prefer the standard calculation method that provides a wider standard range. Below, the authors compare the range widths obtained by the two methods.

When the method and method providethe same range, then

Therefore,

When the for the overall data, the method produces a larger range for the standard than that of the method. When the for the overall data, the method produces a smaller range for the standard than that of the method.

Phenomenon of an unreasonable standard range and a potential solution method

As of March 31, 2020, a total of 201 sets of standard decoction data suitable for calculating the dry matter yield rate or transfer rate have been compiled. Fifty-five sets of data were found to produce an unreasonable standard range of the transfer rate obtained according to the method proposed in the “Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules, ”accounting for 27.4% of the total. Eleven sets of data produced an unreasonable standard range of the dry matter yield rate, accounting for 5.47% of the total. Therefore, this phenomenon does not occur only in isolated cases. The following sections will focus on its cause and solution method.

Cause of “phenomenon of an unreasonable standard range”

The dry matter yield rate reflects the transfer of total solids during the standard decoction preparation process, and its value should be in the range 0%−100%. However, like the rate data, the dry matter yield rate does not actually obey the normal distribution. Therefore, strictly speaking, it does not meet the prerequisites for the method.

The transfer rate reflects the transfer of an index component during the preparation of a standard decoction, and its value is generally between 0% and 100%. However, it has been found that there are often chemical reactions during the decoction process that lead to the degradation or synthesis of index components. For example, during the preparation of the standard decoctions of Corni Fructus pieces, 7-β-O-methyl morroniside is degraded to produce morroniside. As a result, the transfer rate of morroniside in a standard decoction prepared from 15 batches of prepared slices was between 105.5% and 145.8% (Guo et al., 2019). Moreover, in the preparation of the standard decoction of Lonicerae Japonicae Flos, the index component of chlorogenic acid may degrade to produce cryptochlorogenic acid and neochlorogenic acid, decreasing the transfer rate (Zhu, Miao, & Chen, 2016). Due to the existence of the abovementioned complex conditions, it is difficult to judge whether the normal distribution can be used to approximate the transfer rate data.

Potential solution

The square-root arcsine transformation of the rate data brings the data distribution close to the normal distribution. After data transformation, the use of the two methods, and , to establish the quality standards for standard decoctions can mostly avoid the phenomenon of an unreasonable standard range. The specific method is as follows.

First, square root arcsine transformation is performed on the rate data, as shown in formula (11) (Zeng, Peng, Zhang, & Wang, 2020):where X is the transfer rate or dry matter yield rate before conversion, and X' is the transfer rate or dry matter yield rate after conversion. After obtaining the mean value and standard deviation of the transformed data X', the standard range of the transformed data X' can be calculated with the or method. The inverse transformation is then used to calculate the standard range of data X. For example, if using the method, the upper limit of transformed data X' should be . The upper limit of data X should be .

Table 1, Table 2 provided the results for the standards before and after the square-root arcsine transformation is used on data with unreasonable standard ranges as of March 31, 2020. It can be seen from the tables that the standard ranges established after data transformation are more reasonable. Generally, the arcsine square root transformation is often used when there is value less than 30% or larger than 70% for rate data. If all the transfer rate or dry matter yield rate data are within 30%−70%, the authors also suggest using the arcsine square root transformation, because the standard deviation value of the data might be large and leads to difficulties for the method.

Table 1

Standard range of dry matter yield rate before and after using square root arcsine transformation.

No.	Prepared slices	Transformation parameters	X-±3SD		X-±30%X-		References
			Before conversion / %	After conversion / %	Before conversion / %	After conversion / %
1	Vinegar Cyperi Rhizoma	Dry matter yield rate	−6.77–56.5	8.43–27.4	17.4–32.3	8.50–27.3	(Chen, 2018)
2	Curcuma kwangsiensis	Dry matter yield rate	−2.18–21.8	1.16–24.4	6.85–12.7	4.71–15.6	(Chen, 2018)
3	Coptidis Rhizoma	Dry matter yield rate	−3.59–33.5	1.85–36.1	10.5–19.5	7.29–23.7	(Guo et al., 2019)
4	Alismatis Rhizoma	Dry matter yield rate	−5.1–3.7	3.2–55.4	17.0–31.6	12.2–37.8	(Chen, 2017)
5	Bambusa Tuldoides	Dry matter yield rate	−2.8–11	0.105–12.4	2.8–5.3	1.87–6.35	(Chen, 2017)
6	Perillae Caulis	Dry matter yield rate	−2.25–13.3	0.482–14.7	3.85–7.15	2.60–8.79	(Chen, 2017)
7	Schizonepetae Herba	Dry matter yield rate	−1.8–10.8	1.97–17.1	3.15–5.85	3.89–13.0	(Chen, 2017)
8	Forsythiae Fructus	Dry matter yield rate	−3.3–34.3	7.5–24.3	10.9–20.2	1.2–39.8	(Xu et al., 2018)
9	Albiziae Cortex	Dry matter yield rate	−0.8–16.7	1.3–18.9	5.6–10.4	3.8–12.8	(Chen, 2018)
10	Euryales Semen	Dry matter yield rate	−9.4–39.6	0.9–40.1	10.6–19.6	7.3–23.7	(Chen, 2018)

Table 2

Standard range of transfer rate of index components before and after using square root arcsine transformation.

			X-±3SD		X-±30%X-
No.	Prepared slices	Index component	Before conversion / %	After conversion / %	Before conversion / %	After conversion / %	References
1	Cyathulae Radix	Cyasterone	37.6–109	25.3–100	51.3–95.3	44.8–95.7	(Sun et al., 2019)
2	Paeoniae Radix Alba	Paeoniflorin	53.4–101	50.6–95.8	54.0–100	46.9–97.1	(Chen, 2017)
3	Paeoniae Radix Alba	Paeoniflorin	69.2–99.5	67.5–96.1	59.1–110	53.2–99.7	(Ge, 2018)
4	Paeoniae Radix Rubra	Paeoniflorin	41.2–107	37.0–98.2	51.8–96.2	44.6–95.5	(Zhu et al., 2016)
5	Astragali Radix	Calycosin	16.1–103	16.8–95.1	41.5–77.1	33.7–83.3	(Wang, Zhao, Dai, Qin, & Chen, 2020)
6	Polygalae Radix	Tenuifolin	−7.2–35.9	0.3–41.9	10.1–18.7	6.8–22.1	(Chen, 2017)
7	Angelicae Dahuricae Radix	Imperatorin	−12.1–72.0	1.63–73.2	21.0–39.0	15.5–46.5	(Chen, 2018)
8	Angelicae Sinensis Radix	Ferulic acid	42.5–115	30.4–99.5	55.0–102	49.4–98.5	(Tong, 2017)
9	Angelicae Pubescentis Radix	Cnidii Fructus	−1.06–13.7	0.914–15.5	4.44–9.24	3.03–10.2	(Chen, 2018)
		Columbianadin	−3.36–19.5	0.71–3.80	5.63–10.5	3.83–12.8
10	Saposhnikoviae Radix	Prim-O-glucosylcimifugin	44.9–114	35.9–99.9	55.6–103	49.9–98.7	(Cao et al., 2019)
		4′-O-β-glucosyl-5-O-methylvismmiside	52.5–114	40.6–99.1	58.4–108	53.9–99.8
11	Saposhnikoviae Radix	Prim-O-glucosylcimifugin + 4′-O-β-glucosyl-5-O-methylvismmiside	33.7–106	26.8–98.7	48.8–90.6	41.5–92.8	(Chen, 2017)
12	Saposhnikoviae Radix	β-D-glucopyranosiduronicacid	22.5–119	18.2–100	49.5–91.9	42.6–93.9	(Hao, et al., 2018)
		Wogonin	5.11–116	9.46–99.2	42.3–79.5	34.5–84.5
13	Scrophulariae Radix	Harpagide + Harpagoside	69.6–97.1	68.5–94.3	58.3–108	52.2–99.5	(Chen, 2017)
14	Scrophulariae Radix	Harpagide	32.5–112	30–99.0	50.6–93.9	43.3–94.5	(Xu et al., 2019)
15	Platycodonis Radix	Platycodin D	−6.07–54.7	2.21–58.2	17.1–31.7	37.7–12.1	(Deng, Ming, & Tan, 2018)
16	Asparagi Radix	Protodioscin + Protoneodioscin	58.5–112	47.0–99.6	59.0–73.0	55.1–100	(Jin et al., 2020)
17	Rehmanniae Radix	Catalpol	−0.136–25.9	2.30–29.9	9.01–16.7	6.39–20.9	(Chen, 2018)
18	Rehmanniae Radix	Verbascoside	−3.42–99.1	5.18–93.7	33.5–62.2	65.5–71.3	(Chen, 2018)
19	Glycyrrhizae Radix et Rhizoma	Liquiritin	52.6–101	55.2–94.5	53.7–99.6	47.5–97.5	(Lin et al., 2017)
20	Ginseng Radixet Rhizoma	Ginsenoside ginseng root Rg1 + ginsenoside ginseng root Re	48.5–104	45.5–96.8	53.2–98.8	46.0–96.6	(Zhang et al., 2017)
21	Alismatis Rhizoma	Alisol B 23-acetate	−9.66–31.5	0.00404–36.7	7.64–14.2	5.01–16.6	(Liu et al., 2019)
22	Ephedrae Herba	Ephedrine + Pseudoephedrine	−12.5–82.2	1.39–82.6	24.4–45.3	18.2–53.3	(Tong, 2017)
23	Lonicerae Japonicae Caulis	Loganin	49.3–100	45.0–95.9	52.4–97.2	45.1–95.9	(Chen, 2018)
24	Cinnamomi Ramulus	Dihydrophaseicacid	41.5–115	34.4–100	54.6–102	48.5–98.0	(Liu et al., 2017)
25	Nelumbinis Folium	Quercetin-3-O-glucuronide	14.9–127	13.0–99.0	49.5–92.0	42.9–94.2	(Wang et al., 2020)
		Nuciferine	−6.6–25.7	0.1–30.3	6.7–12.4	4.4–14.7
26	Menthae Haplocalycis Herba	Rosmarinic acid	26.8–108	25.0–97.8	47.3–87.8	39.6–90.9	(Wu, Xia, Li, Li, & Tong, 2019)
27	Lysimachiae Herba	Quercetin dihydrate, kaempferol	10.7–113	12.0–99.1	43.3–80.4	35.7–86.1	(Chen, 2018)
28	Scutellariae Barbatae Herba	Scutellarein	–23.5–88.5	0.000146–86.6	22.8–42.3	16.5–49.2	(Tian et al., 2019)
29	Plantaginis Herba	Plantamajoside	−1.9–38.8	2.9–42.0	12.9–24.0	9.1–29.1	(Chen, 2018)
30	Taraxaci Herba	Caffeic acid	−10.5–31.8	0.03–34.1	7.45–13.8	4.96–16.4	(Bo Sun et al., 2020)
31	Moutan Cortex	Paeoniflorin	79.3–94.2	78.4–93.4	60.7–113	55.4–100	(Jiang et al., 2018)
32	Eucommiae Cortex	Pinoresinoldiglucoside	−3.8–89.0	5.0–86.0	29.8–55.3	22.6–63.2	(Chen, 2018)
33	Albiziae Cortex	(-)-Syringaresnol-4-O-β-D-apiofuranosyl-(1 → 2)-β-D-glucopyranoside	13.9–112	15.7–98.1	43.9–81.6	36.1–86.6	(Chen, 2018)
34	Amomi Fructus	Bornyl acetate	48.2–105	42.5–98.3	53.6–99.5	46.7–97.0	(Chen, 2018)
35	Vinegar Processed Schisandra Chinensis	Schisandrin	−4.9–18.6	0.1–21.1	4.8–8.9	3.2–10.7	(Chen, 2017)
36	Crataegi Fructus	Citric acid monohydrate	−1.49–9.47	0.3–11.1	2.79–5.19	1.9–6.4	(Chen, 2017)
37	Crataegi Fructus	Organic acid	57.7–96.9	55.5–93.6	54.1–101	46.9–97.2	(Chen, 2018)
38	Aurantii Fructus Immaturus	Synephrine	23.3–105	20.9–97.1	44.8–83.2	37.2–88.0	(Shi et al., 2019)
39	Aurantii Fructus Immaturus	Synephrine	22.0–103	19.3–96.8	43.9–81.5	36.2–86.7	(Chen, 2018)
40	Fructus Corni Pulp	Loganin	79.0–97.7	77.9–96.0	61.8–115	57.2–100	(Guo et al., 2019)
41	Forsythiae Fructus	Forsythin	51.6–116	41.2–99.2	58.6–109	54.0–99.9	(Cao et al., 2018)
42	Forsythiae Fructus	Forsythin	6.6–103	8.9–96.1	38.2–70.9	30.6–78.5	(Xu et al., 2018)
43	Ligustri Lucidi Fructus	Nuezhenide	−0.4–118	6.19–99.7	41.1–76.4	33.5–83.0	(Yao et al., 2019)
44	Ligustri Lucidi Fructus	Nuezhenide	−31.6–92.8	1.5–91.4	21.4–39.8	15.4–46.3	(Chen, 2017)
45	Gardeniae Fructus	Geniposide	42.0–113	33.9–100	54.4–101	48.2–97.9	(Xu et al., 2017)
46	Semen Armeniacae Amarum	Amygdalin	64.7–100	62.3–96.4	57.8–107	51.6–99.3	(Zhang et al., 2018)
47	Magnoliae Flos	Magnolin	−11.0–44.8	0.318–48.3	14.0–19.7	8.12–26.1	(Liao, Wang, Hao, Liu, & Zhao, 2020)
48	Lonicerae Japonicae Flos	Chlorogenic acid	53–104	49.6–97.5	55–102	48.3–97.9	(Dai et al., 2017)
49	Chrysanthemi Flos	Cynaroside	41.2–87.0	21.8–98.4	22.7–111	39.1–90.3	(Chen, 2017)
50	Asini Corii Colla	L-hydroxyproline	96.4–99.0	96.2–98.8	68.4–127	70.2–92.7	(Chen, 2018)
		Glycine	96.4–98.7	96.3–98.6	68.3–127	69.9–93.0
		D-alanine	95.8–99.4	95.5–99.1	68.3–127	70.0–92.8
		L-Proline	96.1–99.4	95.8–99.1	68.4–127	70.3–92.6
51	Testudinis Carapaciset Plastri Colla	L-Hydroxyproline	95.1–100	94.5–99.5	68.3–127	70.1–92.8	(Chen, 2018)
		Glycine	95.5–100	95.0–99.4	68.4–127	70.3–92.5
		D-alanine	94.7–100	93.2–99.8	68.2–127	70.0–92.9
		L-proline	96.3–99.1	96.1–99.0	68.4–127	70.2–92.7
52	Cervi Cornus Colla	L-hydroxyproline	96.0–99.5	95.8–99.2	68.4–127	70.4–92.5	(Chen, 2018)
		Glycine	95.7–99.6	95.3–99.3	68.4–127	70.2–92.6
		D-alanine	95.1–99.7	94.6–99.3	68.2–127	69.6–93.3
		L-proline	95.2–99.8	94.6–99.4	68.3–127	70.0–92.9

Limitation of square-root arcsine transformation method

The square-root arcsine transformation can only be used to treat data between 0 and 1. However, it should be noted that it is sometimes reasonable for the transfer rate to exceed 100%.For example, 7-β-O-methylmorroniside in Corni Fructus generates morroniside during a hot-water extraction process, which can result in the transfer rate of morroniside reaching 105.5%−145.8% (Guo et al., 2019) these cases, the distribution of the. In these cases, the distribution of the transfer rate data is still unknown, and the square-root arcsine transformation method is not applicable. The authors analyzed 201 sets of research data for standard decoctions that have been reported in the literature, among which 14 sets of transfer rate data exceeded 100% because of the degradation and transformation of other components. For these data sets, which accounted for 6.97% of the total, the square-root arcsine transformation was not applicable.

Phenomenon of a nonuniform standard range and a potential solution method

Phenomenon of a nonuniform standard range

There are two research papers on setting standards for many prepared slices, including Achyranthis Bidentatae Radix, Saposhnikoviae Radix, Saposhnikoviae Radix, Scrophulariae Radix, Codonopsis Radix, Platycodonis Radix, Rehmanniae Radix, Rehmanniae Radix, Polygoni Multiflori Caulis, Ramulus Perillae Caulis, Menthae Haplocalycis Herba, Moutan Cortex, Dictamni Cortex, Cinnamomi Cortex, Ginger Juice Processed Magnoliae Officinalis Cortex, Citri Sarcodactylis Fructus, Fructus Aurantii sauteed with bran, Aurantii Fructus Immaturus, Ligustri Lucidi Fructus, Prunellae Spica, Xanthii Fructus, Lonicerae Japonicae Flos, Chrysanthemi Flos, Glycyrrhizae Radix et Rhizoma, Ephedrae Herba, Gardeniae Fructus, and Puerariae Lobatae Radix.

Research data on standard decoctions of Paeoniae Radix Alba, Coptidis Rhizoma, Phellodendri Chinensis Cortex, Corni Fructus, Forsythiae Fructus, and Psoraleae Fructus are presented in three different literature reports. Research data on standard decoctions of Chuanxiong Rhizoma are presented in four different literature reports. Table 3 lists the standard ranges obtained by different researchers. For the same prepared slices, the ranges are different to varying degrees. One of the reasons is that the indices used by the researchers were different. For example, in studies on quality standards of Saposhnikoviae Radix, some researchers used cohosh and 5-O-methylvisaminoside as two index components, while others used the sum of cohosh and 5-O-methylvisaminoside. Even if the same index component is used to establish the standard, the standard range is not the same, as in the cases of Platycodonis Radix, Fructus Aurantii sauteed with Bran and other prepared slices of Chinese medicines.

Table 3

Quality standards obtained by different researchers.

No.	Prepared slices	Batch number	Transfer components	Transfer rate / %	Dry matter yield rate / %	References
1	Achyranthis Bidentatae Radix	16	Ecdysone	40.4–74.9	22.4–41.5	(Shi, Zhu, Cao, Wang, & Meng, 2019)
2	Achyranthis Bidentatae Radix	15	/	/	15.5–28.5	(Chen, 2017)
3	Saposhnikoviae Radix	12	Cimicifugoside + 4-O-β-D-gulcosyl-5-O-methylvisamminol	52.9–96.3	18.0–44.0	(Chen, 2017)
4	Saposhnikoviae Radix	11	Cimicifugoside	66.8–97.0	34.3–46.3	(Cao et al., 2019)
			4-O-β-D-gulcosyl-5-O-methylvisamminol	70.4–98.2
5	Scutellariae Radix	15	Baicalin	57.1–84.0	37.2–44.2	(Hao et al., 2018)
			β-D-glucopyranosiduronic acid	37.7–96.2
			Baicalein	39.0–79.7
			Wogonin	34.8–85.6
6	Scutellariae Radix	39	Baicalin	43.9–78.3	20.5–53.1	(Song, Wang, Wang, Qian, & Yang, 2020)
7	Scrophulariae Radix	14	Harpagide	46.6–88.9	43.1–68.0	(Xu et al., 2019)
			Harpagoside	37.5–62.9
8	Scrophulariae Radix	15	Harpagide + Harpagoside	72.3–88.9	48.0–62.5	(Chen, 2017)
9	Codonopsis Radix	14	/	/	34.0–63.0	(Chen, 2017)
10	Codonopsis Radix	13	Lobetyolin	41.2–85.3	36–63	(Yu et al., 2017)
11	Platycodonis Radix	15	Platycodin D	12.2–42.6	/	(Deng et al., 2018)
12	Platycodonis Radix	15	Platycodin D	16.5–34.3	21.9–34.3	(Wang, 2018)
13	Rehmanniae Radix	15	Catalpol	3.1–22.6	37.5–61.0	(Chen, 2018)
			Verbascoside	16.7–42.1
14	Rehmanniae Radix	15	Verbascoside	25.6–80.0	/	(Chen, 2018)
15	Rehmanniae Radix Praeparata	15	Verbascoside	0.020–0.047	40.2–61.8	(Chen et al., 2018)
16	Rehmanniae Radix Praeparata	10	Verbascoside	54.6–78.9	56.7–67.9	(Li, Chen, & Li, 2020)
17	Polygoni Multiflori Caulis	15	2,3,5,4′-Tetrahydroxy stilbene-2-O-β-D-glucoside	10.4–40.2	5.00–13.5	(Fan et al., 2019)
			Emodin-8-glucoside	8.62–28.8
18	Polygoni Multiflori Caulis	12	2,3,5,4′-Tetrahydroxystilbene-2-O-β-D-glucoside	42.4–72.1	10.0–25.0	(Chen, 2018)
19	Cinnamomi Ramulus	15	trans-Cinnamic acid	56.9–94.1	3.3–9.6	(Chong Liu et al., 2017)
20	Cinnamomi Ramulus	14	trans-Cinnamaldehyde	1.01–1.72	6.06–8.95	(Deng et al., 2017)
21	Menthae Haplocalycis Herba	10	Rosmarinic acid	47.2–85.9	14.2–26.6	(Wu et al., 2019)
22	Menthae Haplocalycis Herba	12	/	/	18.0–33.0	(Chen, 2018)
23	Moutan Cortex	15	Paeoniflorin	83.5–91.0	24.5–29.9	(Jiang et al., 2018)
			Paeonol	15.8–25.6
24	Moutan Cortex	14	Paeonol	43.9–67.3	22.0–38.7	(Jiao et al., 2018)
25	Dictamni Cortex	16	Obacunon	34.3–56.3	34.3–56.3	(Chen, 2017)
			Fraxinellon	35.4–52.0
26	Dictamni Cortex	15	Obacunon	25.1–44.1	20.6–34.4	(Li et al., 2018)
			Fraxinellon	22.6–32.9
27	Cinnamomi Cortex	14	trans-Cinnamaldehyde	29.6–54.5	6.0–9.0	(Chen, 2017)
28	Cinnamomi Cortex	14	trans-Cinnamaldehyde	25.0–68.4	3.7–10.1	(Deng et al., 2018)
29	Magnoliae Officinalis Cortex	16	Honokiol + Magnolol	3.41–7.14	6.5–12.0	(Jing, Deng, Sun, Lan, & Liu, 2019)
30	Magnoliae Officinalis Cortex	12	Honokiol + Magnolol	3.4–7.6	9.5–12.0	(Chen, 2018)
31	CitriSarcodactylis Fructus	15	Naringin	0.0124–0.0315	/	(Sun et al., 2019)
			Hesperidin	0.0161–0.0672
			Naringin + Hesperidin	0.0299–0.0849
32	CitriSarcodactylis Fructus	15	Hesperidin	12.7–32.2	28.5–35.5	(Chen, 2018)
33	Aurantii Fructus	13	Naringin	21.1–37.1	19.1–30.5	(Tan et al., 2019)
			Neohesperidin	25.2–40.9
34	Aurantii Fructus	12	Naringin	30.0–62.1	21.5–27.0	(Chen, 2017)
			Neohesperidin	27.3–61.3
35	Aurantii Fructus Immaturus	16	Synephrine	35.7–92.7	13.8–43.8	(Shi et al., 2019)
36	Aurantii Fructus Immaturus	13	Synephrine	35.0–93.3	14.5–26.0	(Chen, 2018)
37	LigustriLucidi Fructus	11	Nuezhenide	31.6–83.8	/	(Yao et al., 2019)
38	LigustriLucidi Fructus	12	Nuezhenide	10.3–85.7	13.0–22.5	(Chen, 2017)
39	Prunellae Spica	14	Rosmarinic acid	42.6–78.4	10.0–13.5	(Chen, 2017)
40	Prunellae Spica	15	Caffeic acid	152–284	9.1–12.9	(Wang, Wang, Ma, & Niu, 2018)
			Rosmarinic acid	28.3–58.1
41	Xanthii Fructus	15	Ferulic acid	21.7–56.2	3.88–5.09	(Geng et al., 2019)
42	Xanthii Fructus	13	Chlorogenic acid	8.0–16.1	20.5–25.5	(Chen, 2018)
43	Lonicerae Japonicae Flos	12	Chlorogenic acid	68.0–90.0	30–39	(Dai et al., 2017)
44	Lonicerae Japonicae Flos	15	Chlorogenic acid	45.3–64.0	/	(Zhu et al., 2019)
			Cynaroside	16.2–24.6
45	Chrysanthemi Indici Flos	15	Linarin	22.0–66.2	24.7–32.5	(Guo et al., 2019)
46	Chrysanthemi Indici Flos	15	Linarin	29.6–38.2	23.1–31.4	(Tian et al., 2018)
47	Glycyrrhizae Radix et Rhizoma	15	Liquiritin	56.2–78.8	20.5–32.5	(Chen, 2017)
			Glycyrrhizic acid	39.3–77.2
48	Glycyrrhizae Radix et Rhizoma	15	Liquiritin	59.4–87.4	29.9–38.9	(Lin et al., 2017)
			Glycyrrhizic acid	49.8–78.9
49	Ephedrae Herba	13	Ephedrine + Pseudoephedrine	20.3–51.8	7.2–26.6	(Tong et al., 2017)
50	Ephedrae Herba	15	Ephedrine + Pseudoephedrine	18.7–83.5	12–22	(Tong, 2017)
51	Gardeniae Fructus	15	Geniposide	95.0–114	25.2–29.6	(Hu et al., 2019)
52	Gardeniae Fructus	15	Geniposide	60.3–97.1	24.4–34.7	(Xu et al., 2017)
53	Puerariae Lobatae Radix	10	Puerarin	54.3–79.1	19.0–38.5	(Sun, Guo, Li, Chen, & Sun, 2016)
54	Puerariae Lobatae Radix	15	Puerarin	41.7–57.3	15.7–24.4	(Ji, 2018)
55	Paeoniae Radix Alba	15	Paeoniflorin	61.6–98.9	19.0–34.5	(Chen, 2017)
56	Paeoniae Radix Alba	15	Paeoniflorin	75.0–91.3	20.3–25.2	(Ge, 2018)
57	Paeoniae Radix Alba	10	Paeoniflorin	61.5–85.2	19.0–26.5	(Zhu, Li, & Chen, 2016)
58	Coptidis Rhizoma	15	Berberine	26.6–47.6	8.3–23.9	(Guo et al., 2019)
			Coptisine	26.5–52.2
			Palmatine	40.1–71.6
59	Coptidis Rhizoma	15	Epiberberine	55.6–70.7	17.5–26.8	(Mao et al., 2018)
			Coptisine	52.5–64.9
			Palmatine	56.4–67.9
			Berberine	53.3–66.0
60	Coptidis Rhizoma	14	Epiberberine	79.3–112	17.1–22.3	(Cui et al., 2017)
			Coptisine hydrochloride	54.6–76.2
			Palmatine chloride	45.7–70.7
			Berberine hydrochloride	43.5–64.4
61	Phellodendri Chinensis Cortex	15	Phellodendrine chloride	46.3–83.3	12.8–19.4	(Wang et al., 2018)
			Berberine hydrochloride	36.4–56.6
62	Phellodendri Chinensis Cortex	15	Berberine hydrochloride	31.4–49.3	13.0–19.5	(Chen, 2017)
			Phellodendrine chloride	46.1–84.4
63	Phellodendri Chinensis Cortex	10	Palmatine chloride + Berberine hydrochloride	51.3–65.9	11.2–28.1	(Li, Qiu, Shi, Li, & Xu, 2019)
64	Corni Fructus	15	Morroniside	55.8–90.8	43.9–48.2	(Wang et al., 2019)
			Loganin	52.8–68.3
			Cornuside	47.2–62.6
65	Corni Fructus	12	Loganin + Morroniside	7.7–15.3	47.5–62.0	(Chen, 2017)
66	Corni Fructus	15	Morroniside	117–138	49.9–57.3	(Guo et al., 2019)
			Loganin	81.7–93.8
67	Forsythiae Fructus	15	Forsythin	49.8–78.7	12.3–26.1	(Xian & Bei, 2018)
68	Forsythiae Fructus	16	Forsythin	62.8–98.0	12.5–26.1	(Cao et al., 2018)
			Forsythoside A	22.8–55.6
69	Forsythiae Fructus	12	Forsythin	31.2–92.0	3.9–22.5	(Xu et al., 2018)
			Forsythoside A	25.2–50.1
70	salt-processed Psoraleae Fructus	15	Psoralen + angelicin	13.6–23.6	16.3–20.6	(Shen, Liu, Bi, Xu, & Luan, 2018)
71	salt-processed Psoraleae Fructus	16	Psoralenoside + isopsoralenoside + psoralen + Angelicin	46.4–78.0	16.3–20.6	(Shen, 2019)
72	salt-processed Psoraleae Fructus	12	Psoralen	9.4–26.4	14–27	(Chen, 2018)
			Angelicin	7.7–22.7
73	Chuanxiong Rhizoma	15	Ferulic acid	40.8–65.2	20.0–41.5	(Chen, 2018)
74	Chuanxiong Rhizoma	15	Ferulic acid	9.52–17.0	6.20–10.7	(Feng et al., 2019)
75	Chuanxiong Rhizoma	15	Ferulic acid	16.4–33.1	12.7–19.8	(Cheng et al., 2019)
			Senkyunolide I	33.3–56.0
			Senkyunolide 3-N-butyl-4,5-dihydrophthalide	6.63–11.8
			Ligustilide	1.26–3.73
76	Chuanxiong Rhizoma	15	Ferulic acid	31.3–53.8	18.8–25.1	(Zhou et al., 2018)
			Chlorogenic acid	0.327–0.566
			Caffeic acid	0.0177–0.0504

Cause of phenomenon of a nonuniform standard range

The same kind of prepared slices can differ depending on the origin, growth environment, processing methods and storage conditions. Using only 15 batches of prepared slices of Chinese crude drugs may not represent the average quality of a given variety. Researchers may also have certain differences in the conditions used to prepare standard decoctions. Therefore, using the data obtained to establish quality standards for standard decoctions may produce very different results.

Solution to this problem

It is generally believed that the more data are collected from different batches of prepared slices, the stronger the representativeness is and the more reliable the established standard ranges obtained are. This paper proposes merging the data of multiple research groups to establish a unified quality standard that is more representative of the average quality of prepared slices than the data of one research group. However, it should be noted that not all data are suitable for merging.

If the data obtained by different researchers have a similar central tendency and a similar dispersion tendency, then multiple sets of data can be merged into one. Otherwise, the data cannot be merged. The reasons may include systemic deviation, human operation error and insufficient sample representativeness in the preparation process.

Regarding the central tendency of the data, if multiple sets of data can be merged, the locations of the data obtained by different researchers should be consistent. Because the transfer rate and dry matter yield rate data do not strictly follow a normal distribution, using the median to represent the data distribution position is suggested. In practice, the Kruskal-Wallis test (nonparametric test of multiple independent samples) or Mann-Whitney test (nonparametric test of two independent samples) can be used. For the published dry matter yield rate or transfer rate data for the same prepared slice in different papers, it is necessary to determine whether there is a significant difference in the median. In this paper, the significance level of nonparametric tests was 0.05. If P > 0.05, it is considered that the difference is not large and the central tendency of the data is similar.

In terms of data dispersion, if multiple sets of data can be merged, the dispersion of each group of data should be close. There are many indicators of data dispersion, such as the range, interquartile range (IQR), and standard deviation. However, the standard deviation is not suitable for describing the dispersion of highly nonnormal data, and the range will be affected by individual extreme values. This article proposes the concept of the IQR, which can be used for nonnormal data and is not affected by data extremes.

This article proposes a method to determine whether datasets have similar data dispersion; their IQRs can be arranged from the largest to the smallest one as , where n is the number of data sets from different sources that are considered to be merged. First, the difference between the largest IQR and the second largest IQR is considered. The formula is . When the is less than or equal to the threshold T, the different data sets are considered to have similar data dispersions and can be merged. When the is greater than the threshold T, the different sets of data have very different dispersions and cannot be directly merged. In this case, the data set with the largest IQR is considered to be unsuitable for merging with the other data. Subsequently, the second largest IQR is compared with the third largest IQR by calculating . If the is less than the threshold T, the remaining data can be merged. If the is still greater than the threshold T, the data set with the second IQR is also considered to be unsuitable for merging with the other data, and so on. The following sections use T = 5% as the data merging standard. After data merging, the authors believe that the representativeness of data will be better after most occasions.

Establishment of standards after data merging

The method described in Section 4.3 was used to determine whether the reported standard decoction data on the dry matter yield rates of Paeoniae Radix Alba, Scrophulariae Radix, Coptidis Rhizoma, Cinnamomi Cortex, ginger juice processed Magnoliae Officinalis Cortex, Aurantii Fructus sauteed with Bran, Forsythiae Fructus, Prunellae Spica, and Chrysanthemi Floscan could be merged. There were nine data sets to be merged. After data merging, the standards were calculated with the square root arcsine transformation method. The standards calculated with the merged data are shown in Table 4, which shows that in most cases, the ranges of the calculated standards after the data merger lie in the middle of the ranges of calculated standards before the data merger. With a larger data size, the standard developed after data merger should become more reliable.

Table 4

Standards calculated for dry matter yield rates after merging data obtained by different research groups.

No.	Prepared slices	P-value obtained from median nonparametric test	Interquartile range / %	Interquartile range difference / %	X-±3SD		X-±30%X-		References
					After conversion and before merge / %	After the merge and conversion / %	After conversion and before merge / %	After merge and conversion / %
1	Paeoniae Radix Alba	0.134	1.05	4.42	18.1–25.2	12.3–36.9	11.0–34.5	12.0–37.3	(Ge, 2018)
			3.33		14.9–29.7		11.1–34.9		(Zhu, Li, & Chen, 2016)
			7.75		12.1–40.9		12.9–39.7		(Chen, 2017)
2	Scrophulariae Radix	0.205	5.25	0.14	38.7–74.5	40.4–70.7	31.8–80.5	31.0–79.2	(Xu et al., 2019)
			5.39		42.9–66.2		30.2–77.9		(Xu et al., 2019)
3	Coptidis Rhizoma	0.694	2.19	0.69	11.5–30.8	12.9–28.3	10.3–32.6	10.2–32.2	(Mao et al., 2018)(Cui et al., 2017)
			2.88		14.8–25.2		10.0–31.8
4	Cinnamomi Cortex	0.066	1.50	0.11	2.7–15.2	3.4–13.0	3.9–12.9	3.7–12.4	(Deng et al., 2018)(Liu et al., 2017)
			1.39		4.7–10.1		3.6–11.9
5	Magnoliae Officinalis Cortex	0.294	1.55	0.08	5.9–15.4	6.7–14.9	5.1–16.8	5.2–17.2	(Jing et al., 2019)(Chen, 2018)
			1.63		8.3–13.7		5.4–17.9
6	Aurantii Fructus	0.060	1.25	2.65	19.4–29.3	17.3–34.1	12.4–38.4	13.0–39.9	(Chen, 2018)(Tan et al., 2019)
			3.90		16.8–36.9		13.5–41.4
7	Forsythiae Fructus	0.089	5.31	3.66	8.1–35.7	4.6–38.2	10.2–32.3	9.3–29.5	(Xian & Bei, 2018)(Cao et al., 2018)(Xu et al., 2018)
			7.09		7.5–34.8		9.8–31.0
			10.75		1.2–39.8		7.5–24.3
8	Prunellae Spica	0.106	1.75	0.25	7.3–14.8	7.8–15.1	5.4–17.7	5.6–18.4	(Xu et al., 2018)(Chen, 2017)
			1.50		8.6–15.0		5.8–19.0
9	Chrysanthemi Indici Flos	0.271	3.95	0.60	20.9–35.4	20.3–34.9	14.4–43.7	14.1–42.9	(Guo et al., 2019)(Tian et al., 2018)
			3.35		19.8–34.3		13.8–42.2

The index component transfer rate data of baicalin (Saposhnikoviae Radix) and forsythoside A (Forsythiae Fructus) can also be merged. There are two groups of merged data. After processed with square root arcsine transformation method, the merged results are obtained and shown in Table 5.

Table 5

Standards calculated for transfer rates after merging data obtained by different research groups.

No.	Prepared slices	Transfer compound	P-value obtained from median nonparametric test	Interquartile range / %	Interquartile range difference / %	X-±3SD		X-±30%X-		References
						After conversion and before merge / %	After merge and conversion / %	After conversion and before merge / %	After merge and conversion (%)
1	Scutellariae Radix	Baicalin	0.917	9.92	1.73	43.4–91.1	42.6–91.0	41.0–92.4	40.7–92.1	(Hao et al., 2018)
				11.65		40.9–91.5		40.4–91.8		(Li et al., 2017)
2	Forsythiae Fructus	Forsythoside A	0.871	14.01	4.32	11.5–72.2	11.7–69.8	21.0–59.8	20.4–58.4	(Cao et al., 2018)
				18.33		11.6–67.3		19.6–56.5		(Xu et al., 2018)

Potential problems of present method

In Section 4.3, a method is presented for judging whether data from different publications can be merged. In this work, the significance level of nonparametric tests (Kruskal-Wallis and Mann-Whitney tests) was set at 0.05 to determine whether there was a significant difference in the median comparison. However, the significance level value is subjective. If data sets with larger sample sizes can be collected, the significance level is suggested to be lowered, such as 0.01 or 0.005.

The IQR is used to characterize the difference in data dispersion. A value of T = 5% was used as the threshold to evaluate the difference in data dispersion. However, this value of T is also very subjective. For certain kinds of prepared slices, if the quality variation of different batches collected from genuine or main production areas is relatively large, the threshold value of T should also be larger.

Consideration of number of batches (n) of prepared slices for establishing quality standards

Estimation of number of batches (n) of prepared slices

According to the newly issued “Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules,” no less than 15 batches of representative prepared slices should be used for establishing quality standards. However, the reason for the number of batches of no less than 15 is still unclear. In this paper, the authors tried to estimate an appropriate number of batches.

Irrespective of whether or is used when establishing the standard, the average value is required to be accurate. Thus, we should find a way to reduce the standard error of the estimated average value. Assuming that the dry matter yield rate and transfer rate data both obey a binomial distribution, the standard error (S) of the value of the dry matter yield rate or transfer rate should be obtained by the following formula:

In formula (12), p is the dry matter yield rate or transfer rate, and n is the number of batches of prepared slices. The standard error S is affected by both the number of batches n of the prepared slice and the dry matter yield rate or transfer rate value. Fig. 2 shows the calculated value of the S of the mean as p and n change.

Fig. 2

Influence of number of batches (n) and rate value (p) on standard error of mean.

As shown in Fig. 2, as p approaches 0.5, the standard error gradually increases. As the number of batches n of prepared slices increases, the standard error gradually decreases. At present, at least 15 batches of prepared slices are required. When n = 15, the standard error of the mean is likely to be greater than 10%, especially when the dry matter yield rate or transfer rate is nearly 50%. If the standard error of the mean is to be controlled below 10%, it is necessary to use at least 30 batches of prepared slices. Of course, the larger the number of batches of prepared slices is, the smaller the standard error of the obtained mean but the greater corresponding research workload. The above analysis results also confirm the need to merge the data obtained by different research groups.

Potential problem of estimation

In Section 5.1, the dry matter yield rate or the transfer rate data are assumed to follow a binomial distribution. However, binomial distribution is a discrete distribution, while dry matter yield rate and transfer rate data are continuous variables. Accordingly, the assumption that the data follow binomial distributions is not completely in line with the actual situation. Until now, the data distribution of the dry matter yield rate or transfer rate is still unknown. The authors suggest that pharmaceutical companies collect industrial big data for the dry matter yield rate and transfer rate to determine the data distribution.

Conclusion

Since 2016, much research on standard decoctions has been performed by academia and industry. However, relying on standard decoctions to establish quality standards has presented a number of statistical problems. The purpose of this study was to analyze and discuss these statistical problems.

and are two methods mentioned in the “Technical Requirements for Quality Control and Standard Establishment of Chinese Medicine Formula Granules.” The implicit conditions for their use are given in this article. The method requires that the transfer rate or dry matter yield rate data obey a normal distribution. The derivations of these methods show that the conditions for using to establish the standard are and , while requires .

We recommend using arcsine square root transformation to address the phenomenon of unreasonable standard ranges. To address the inconsistency across standards, we suggest that when the central tendency and the discrete tendency are similar, the data obtained from different research groups should be merged to establish a standard. Finally, we recommend that no less than 30 batches of prepared slices are used in the preparation of standard decoctions for establishing their quality standards.

The pharmaceutical companies may encounter difficulties in data treatment using the methods presented in this work. Therefore, a software for establishing standards needs to be developed in future.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.