Risk assessment of supply chain for pharmaceutical excipients with AHP-fuzzy comprehensive evaluation.

Abstract As the essential components in formulations, pharmaceutical excipients directly affect the safety, efficacy, and stability of drugs. Recently, safety incidents of pharmaceutical excipients posing seriously threats to the patients highlight the necessity of controlling the potential risks. Hence, it is indispensable for the industry to establish an effective risk assessment system of supply chain. In this study, an AHP-fuzzy comprehensive evaluation model was developed based on the analytic hierarchy process and fuzzy mathematical theory, which quantitatively assessed the risks of supply chain. Taking polysorbate 80 as the example for model analysis, it was concluded that polysorbate 80 for injection use is a high-risk ingredient in the supply chain compared to that for oral use to achieve safety application in clinic, thus measures should be taken to control and minimize those risks.


Introduction
Excipients are any component other than active substances intentionally added to the formulation of a dosage form. Excipients, as inert agents, initially are diluents, filler, and solvents, so as to give the dose of the active principle suitable weight, consistency, and volume, and make it more convenient to administer [1][2][3] . Other than the traditional functions of support and vehicle, excipients are developed to improve drug stability 4,5 and other specific functions 6 . Furthermore, the introduction of delivery systems for therapeutic and imaging agents and the advance in biopharmaceutics have raised a new interest in the role and functionality of excipients [7][8][9][10][11][12] . Antimicrobial preservatives, suspending agents, and flavoring agents are widely used in pediatric formulations. The selected excipients in pediatric formulations should be safe and stable 13 . Excipients are an integral part of a completed pharmaceutical product; therefore, the safety and the quality of medicines depend not only on the active principles and production processes but also the safety and performance of excipients. This is contrary to what was believed in the past, excipients are in fact fundamental to guarantee the safety and the efficacy of the final pharmaceutical product. The supply chain of pharmaceutical excipients is the most complex part in the ingredient system. Beginning with the raw materials to ending as a part of the finished drug products, the supply chain includes not only the excipients and pharmaceutical manufacturers but also the distributors and traders. Supply chain risk in pharmaceutical excipients has always been the most prominent problem to threaten the safety of excipients 14 , thereby bringing great difficulties and challenges to the regulation of excipients. As a result, industrial organizations are subject to the vulnerabilities of their supply chain.
Risk can be defined as the combination of the probability of the occurrence of harm and the severity of that harm 15 . Regarding pharmaceutical excipients, although there are a variety of stakeholders, including patients, manufacturers, guilds, as well as the government, the protection of patients should be considered of prime importance. Therefore, the risk study of supply chain in the pharmaceutical excipients starts with a clear problem: the potential harms that excipients may bring to the patient. Risk identification can be performed by examining the entire process of supply chain activities including the source of raw materials, excipient manufacture, distribution, and utilizing the finished products. The definition of risks requires a quantitative risk analysis and risk assessment. The authors insist that the establishment of a quantitative risk assessment framework is the first step to guarantee the safety and quality of excipients.

Literature review
Risk assessment can be defined as a systematic process of organizing information to support a risk decision to be made during the management process 5 . It consists of the identification of hazards and the analysis and evaluation of risks associated with exposure to those hazards 16 (Figure 1).
As the beginning part of risk assessment, risk identification is a systematic use of information to identify and record hazards referring to the risk question or problem description 17 . Risk identification includes identifying the underlying risk, including scope of influence, the whole incident, the cause, and the potential consequence. Commonly used approaches include evidence-based methods, systematic team approaches, and inductive reasoning techniques.
Risk analysis is the estimation of the risk associated with the identified hazards. It is the qualitative or quantitative process of linking the likelihood of an occurrence and the severity of the resultant harm 18 . Risk analysis provides an excellent approach to deepen our understanding of risk 19 . In addition, it successfully creates an input process to determine whether the risk needs to be cleared and find out the most appropriate strategies and methods to deal with the risk. Risk evaluation compares the identified and analyzed risk against given risk criteria. Risk evaluations consider the strength of evidence for all three of the fundamental questions. The result of risk evaluation should meet the requirements of risk control; otherwise, further analysis is suggested.
The excipient supply chain begins at the raw materials and ends at the administration of drug products. During the whole process, excipient manufacturers, suppliers, and distributors are also included. Wilhelm Gierling 20 believed that the vulnerability of the supply chain was the main cause of hazard from pharmaceutical excipients, as excipients have many diverse uses, functions, manufacturing processes, and origins; therefore, the risks posed to the patient are variable. Hence, a one size fits all definition of GMP is not enough. He suggested classifying excipients with different GMP grades based on the patient's hazard assessment (route of administration, sources of raw materials, production processes, etc.). The classification would define the required extent of GMP. Class (1) should comply with the joint International Pharmaceutical Excipient Council and the Pharmaceutical Quality Group (IPEC-PQG) Good Manufacturing Practices Guide for Pharmaceutical Excipients 21 , and Class (3) should not exceed the European union's Good Manufacturing Practice Medicinal Products for Human and Veterinary Use Part II: Basic Requirements for Active Substances used as Starting Materials/ICH Q7's Good Manufacturing Practice Guidelines for Active Pharmaceutical Ingredients, while the intermediated Class (2) is between the above two classes. Brian A Carlin 22 applied The ''Black Swan'' theory to supply chain risk management activities when he argued excipient unknowns were likely to cause product failure. The proposed pharmaceutical excipient unknown events included pharmaceutical excipient ingredients, functionality, variability, and so on. Excipient unknowns fell into several categories and could be further categorized as being unknown to the user, unknown to the supplier and perhaps even unknown to both. Although many interests were aroused on supply chain risk in pharmaceutical excipients, there was a deficiency of a mathematical modeling to describe the impact of excipient supply chain on drug safety and quality. The author believes that the construction of an effective quantitative risk assessment model is critical to ensure the safety of pharmaceutical excipients.
The Analytic Hierarchy Process (AHP) is a general theory of measurement. It is used to derive ratio scales from both discrete and continuous paired comparisons. These comparisons may be taken from actual measurements or from a fundamental scale which reflects the relative strength of preferences and feelings 23 . In 197123 . In -1975, Saaty developed the AHP as a multiple criteria decision-making tool that has been used in almost all the applications related with decision-making, especially as a potential method for use in social sciences, such as project management 24 , military applications 25 , and many others. The AHP approach was used to carry out an analysis of strategic supplier selection and evaluation in a generic pharmaceutical firm supply chain 26 . The researchers developed a model to evaluate and select the important criteria and the best supplier for a pharmaceutical manufacturing firm. The selected criteria for the evaluation were Supervision and Inspection regulatory compliance, quality, cost, service, supplier profile, and risk. The researchers recommended that the supplier selection process and evaluation represent one of the key activities that organizations must integrate into their core strategic decisions. Based on their research findings, the regulatory compliance selection criterion was most favored, followed by quality, risk, cost, supplier profile, and service. This model also enables researchers to select the best supplier for the case company.
Fuzzy comprehensive evaluation is the comprehensive decision-making methodology for a multivariable problem that deals with complex decision problems 27 . Fuzzy comprehensive evaluation based on fuzzy set theory is proposed as a new decisionmaking method that is particularly useful in multivariable circumstances [28][29][30] . Fuzzy Set Theory was first integrated by Jean Lemaire 31 . Fuzzy set theory can better deal with imprecise information, and yields more informative outcomes. Assume that the objective being evaluated contains n factors, i.e. the index set is The appraisal of the single factor is ð Þ , which can be considered as a fuzzy subset of V, where r im is the fuzzy membership degree of appraisal of factor i to grade m 32 Then experts are invited to evaluate entire project programs based on each factor and calculate the fuzzy appraisal matrix. After the comprehensive evaluation of every program, the appraisal result is obtained.
The AHP-fuzzy comprehensive evaluation method, which is also known as fuzzy hierarchy comprehensive evaluation method, combines the AHP and fuzzy comprehensive evaluation methods 19 by using AHP to determine the weight of each index evaluation system and the fuzzy comprehensive evaluation method assessing index. Aysegul Tas 33 developed a model to aid them in the evaluation and selection of important criteria and hence the best supplier for a pharmaceutical manufacturing firm. The selected criteria for the evaluation were cost, quality, service, and technology. Li-na Zhang 34 utilized AHP-fuzzy comprehensive evaluation method for eco-industrial parks. She took Dalian Economic and Technological Development Zone as an example, 20 criteria were identified which were generally considered when assessing an Economic and Technological Development Zone. Chun-xiu Wang 35 described a fuzzy AHP comprehensive evaluation model and its mathematical principles, and he also powerfully demonstrated fuzzy AHP-fuzzy comprehensive evaluation in the application of job evaluation and Performance Appraisal.

Methodology
This study was conducted based on AHP-fuzzy comprehensive evaluation model Two primary principles of AHP-fuzzy comprehensive evaluation are 36 (1) the evaluation of the quality risk should be based on scientific knowledge and ultimately link to the protection of the patient; (2) the level of effort, formality, and documentation of the quality risk management (ICH Q9) process should be commensurate with the level of risk.

Supply chain risk identification
In this paper, brainstorming was utilized as the risk identification tool, starting with hazards induced by excipients to identify risk factor. Excipients have the potential to harm patients in two ways 37 : Introduction of a hazard (i.e. common to many uses) Microbiological (pathogen) Chemical (toxicity, physiological effect) Physical (choking, irritation) Adversely affecting drug product availability or performance (unique to excipients) Finished drug product manufacturing failure (e.g. friability of tablets, dissolution, blending) Stability of finished drug product Dosage of API (e.g. bioavailability, potency, changes in modified release) The authors mainly focus on the risk created by excipients in pharmaceutical applications, and the model has classified the supply chain into four parts: sources of raw materials, manufacturing process, use process, and the administration route. Sources of raw materials can be divided into raw materials derived from a Transmissible Spongiform Encephalopathy (TSE)/ Bovine Spongiform Encephalopathy (BSE) -relevant animal species, complex components containing toxic or allergy ingredients, easily adulterated raw materials, and finally plant sources or biological fermentation materials; manufacturing process includes the introduction of genotoxic impurities, microbiallimited or pyrogen-free ingredients, easily degradable materials or the introduction of harmful substances economically motivated adulteration of excipients. Other specific quantitative risk assessment of supply chain is shown in Table 1. According to the fuzzy set theory, multiple related factors must be considered comprehensively in order to give an appropriate, non-contradicting and logically consistent judgment.
Index set U contains the recognized risk elements, and the appraisal set V provides the basis of assessment for experts. High risk can be replaced with 9; medium high risk with 7; medium risk with 5; low risk with 3.
(2) Determination of weight by AHP Construct a set of pair-wise comparison matrices for each of the lower levels. The pair-wise comparison is made such that the attribute in row i (i ¼ 1,2,3,4,. . .,n) is ranked relative to each of the attribute represented by n columns. The pair-wise comparisons are done in terms of which element dominates another (i.e. based on relative importance of elements). These judgments are then expressed as integer values 1-9 shown in Tables 2 and 3.
If a ij ¼ B i /B j , a ij 40, and a ij ¼ 1/a ji , matrix A is a positive reciprocal matrix, and if in matrix Aa ij *a jk ¼ a ik , i, j, k ¼ 1,2,. . .,n, then matrix A is a completely consistent matrix. For the completely consistent matrix A, there is a unique non-zero eigen-value and the corresponding eigen-vector is used to work out the weight vector W. Finally, in order to avoid artificial errors and the contradiction of different factors, a consistence test is conducted until a satisfactory condition is met.
Saaty recommended using a consistency index (CI) and consistency ration (CR) to check for the consistency associated with the comparison matrix CI CI ¼ l À n n À 1 If CI ¼ 0, matrix A has complete consistence. If CI 6 ¼ 0, but CI is close to 0, matrix A has satisfactory consistence. To effectively measure CI, Saaty introduced RI for calculation (Table 4). He randomly constructed 500 comparison matrixes A 1 , A 2 ,. . ., A 500 and obtained the results CI 1 , CI 2 ,. . .,CI 500 Finally we arrive at the equation: CR ¼ CI RI , when CR50.1, the degree of inconsistency is accepted. In other words, as the consistence test is passed, the normalized eigen-vector can be regarded as the weight vector. (4) Determination of gray level and subjection function Grey theory, which was proposed by Deng in 1982, is one of the new mathematical theories born out of the concept of the grey set 24 .The grey number can be defined as a number with uncertain information. For example, the ratings of attributes are described by the linguistic variables; there will be a numerical interval expressing it. This numerical interval will contain uncertain information.
Generally, the grey number is written as ''ÈG''. Quantization of membership is mainly determined by a membership function: according to the appraisal set established above, four different kinds of Grey whiteness functions are proposed ( Figure 2): Class One ''(risk) high level'', assuming ÈG 2 ½x À 2, x, þ1 Class Two ''(risk) medium high'', assuming ÈG 2 ½y À 2, y, y þ 1 Class Three ''(risk) medium'', assuming ÈG 2 ½z À 2, z, z þ 1 Factor i is equally important to factor j 3 Factor i is slightly more important than factor j 5 Factor i is clearly more important than factor j 7 Factor i is strongly more important than factor j 9 Factor i is extremely more important than factor j 2, 4, 6, 8 Intermediate values Reciprocal a i : factor i compared with factor j, a ji : factor j compared with factor I a ji ¼ 1/a ij Class Four ''(risk) low'', assuming ÈG 2 ½m À 2, m, m þ 1

(6) Results
The result of AHP-fuzzy comprehension evaluation is calculated using the following equation: where W is the weight matrix corresponding to the risk elements (Class 1); C is the evaluated scores corresponding to the risk elements (Class 1). C is represented by the following equation: where V is hundred-mark transforming matrix; ; B is the acquired score matrix corresponding to each risk element (Class 2). B is represented by the following equation: where A is the weight matrix corresponding to risk elements; R is the grey decision matrix. After a series of calculations, we get the result of an AHPfuzzy comprehension evaluation, then transform the result in a hundred-mark manner corresponding to the rank the order of risk level and ensure the risk level of excipients (Table 5).

Case studies
In this section, two types of polysorbate 80, both for injection and for oral use, were used as an example to illustrate the application of the AHP-fuzzy comprehensive evaluation model. Polysorbate 80, commercially also known as Tween Õ 80 is a mixture of polyoxyethylene ethers and partial oleic acid esters of sorbitol anhydrides and related compounds. As a nonionic surfactant, Polysorbate80 is widely used in pharmaceutical products for solubilizing, emulsifying or stabilizing the active ingredients 38,39 .
Polysorbate 80 in injection induces one of the main adverse clinical reactions. Therefore, a successful supply chain risk assessment is imperative.
(1) Definition of index set and appraisal set As mentioned above, we started with the definition of index set and appraisal set so as to identify the risk elements and gave the basis of assessment for experts.
appraisal set V ¼ ð9, 7, 5, 3Þ (2) Determination of weight vector A According to the method presented in section Methodology, the weight vector A is determined and a consistence test is carried   Consistence test: According to the scores given by 10 experts (Table 6), the fuzzy evaluation matrix D ¼ (d ij ) m Â n , m ¼ 10, n ¼ 16 is constructed (4) Determination of gray level, the subjection function, and construction of grey decision matrix and the results after a series of calculation According to the method presented in section Methodology, scores are given by 10 experts in dimensionless treatment, then results are worked out as follows: P 11 ¼ 7:4444, P 12 ¼ 9:2857, P 13 ¼ 0:0000, P 14 ¼ 0:0000, Risk assessment of supply chain 681   On account of different routes in administration, the risk of microbial limit of polysorbate 80 for oral use is much lower compared to polysorbate 80 for injection use (Tables 6 and 7). Therefore, after processing, the polysorbate 80 for oral use got a score of 72.3625, reflecting it is an excipient with moderate risk in supply chain.

Discussions
Quantitative risk assessment of excipient risks in the supply chain is a challenging task. This is principally due to the following three reasons: (1) the quantitative nature; (2) the complexities of excipient supply chain; and (3) the uncertainties involved in the decision-making process. Most of the existing methods of supply chain risk assessment are limited for these reasons. Analytic hierarchy process can handle both qualitative and quantitative variables and tackle the first challenge. However, this approach is not optimal for addressing the uncertainties in real-life applications of the complex supply chain process and many uncertain variables associated with the whole supply chain. As a result, we introduce fuzzy logic into our model, which is a widely used method of incorporating uncertain elements into the decisionmaking process. The AHP-fuzzy comprehensive evaluation is constructed with analytic hierarchy determining the weight of each index evaluation system, and with fuzzy comprehensive evaluation to form a selection (decision-making) model. Compared with other fuzzy AHP models, AHP-fuzzy comprehensive evaluation is simple with respect to the computational power, as most numerical calculations were computed using MATLAB 7.0 (MathWorks, Natick, MA). The new model is tractable enough to tackle the vagueness of the uncertainties and complexities of excipients in the supply chain. In addition to the mentioned polysorbate 80 for parenteral and oral use, some widely used excipients (e.g., poloxamer 188, phosphatidylcholine, chitosan, pullulan, talc, sodium alginate, lactose, sodium hyaluronate, polyvinylpyrrolidone K30, hydroxypropyl methylcellulose) in formulations are also assessed by our model to constitute a safety database of pharmaceutical excipients for potential risks management (Supplementary Materials Tables S1-15). Unfortunately, there are some limitations and weaknesses of this AHP-fuzzy comprehensive evaluation. Risks can be identified by several methods, including brain-storming, Delphi technique, and interviews 40 . Here we used brain storming as risk identification technique in which ideas came from different expert groups. Finally, 16 sub-criteria were mentioned as risk elements as a result of risk identification. Users have to make subjective decisions during the period of risk identification. Thus, it is inevitable that the risk factors of this model are affected by the knowledge and expertise of the assessors, which may result in minor deviances. Furthermore, the success of the application of pair-wise comparison matrices and grey decision matrices are also dependent on the data given by experts.
Another limitation is that the proposed model regarding the route of administration is a risk factor of risk assessment, even though administration route is not an integrated part of supply chain. It seems inappropriate but the route of administration is indeed closely associated with safety of all excipients. It is obvious that different routes of application represent distinct exposure levels to the human body and the greater level of exposure, the higher purity standard needed for excipients. For instance, the intravenous route requires pyrogen-free materials. The same kind of excipient may have various different administration routes and this should not be ignored when we conduct the risk assessment of excipients in the supply chain. For most of the excipients on the market, the result of the application of this new model reasonably conformed to the existing safety situation of excipients.

Conclusion
The security of pharmaceutical excipients in the supply chain has been a focal point in many countries. This paper adopted the AHP-fuzzy comprehensive evaluation model to quantitatively assess supply chain risks. The evaluation system could be used to guide the supply chain management in many countries, and provide useful information regarding the regulation of pharmaceutical excipients.