Inpatient admission assessment in West China Hospital based on hesitant fuzzy linguistic VIKOR method

1 Introduction

Chinese medical institutions are divided into three tiers, which are aiming at the common and frequently occurring diseases, the more complex diseases, the difficult miscellaneous diseases, respectively. The actual situation, however, is different from the ideal situation. As a developing country, China is experiencing a long period of transformation, and the citizens’ livelihood related domains, such as healthcare, have been paid more and more attentions. In a short time, the contradiction between supply and demand on medical resources could not be eased. According to the statistic of National Health and Family Planning Commission of China (NHFPC) shown in Table 1, the overall utilization rate of beds in China’s hospital has been contained and the utilization rate of beds in high level medical institution is already beyond 100 percent. This situation makes the contradiction between supply and demand constantly acute. In this case, the higher level hospitals will be blocked by patients with low intensity, and thus could not launch medical research on urgent diseases. Besides, the low utilization rate of hospital beds in lower level medical institutions shows that the lower medical institutions have the capacity to admit inpatients with common, frequently occurring disease or even complex disease. This phenomenon occurs due to the increasing investment in medical resources and the inclination of patients to cure their disease, even if common cough, in high level medical institutions. This trend makes the medical resources in lower level medical institutions comparatively idle while in higher level medical institutions overusing. Therefore, the policy of classified diagnose and treatment (CDT) has been proposed to alleviate this plight.

Generally speaking, the aim of CDT is to select the most appropriate medicare facilities to implement diagnose and treatment according to the patients’ condition and status. The common principles to implement CDT can be summarized as follows:

distributing more medical resources to the lower level hospitals;

The advantage of principle 1 is that it balances the contradiction between demand and supply on medical resources, while the disadvantage is that it is time consuming. Principle 2 reduces the demand on high level medical service efficiently, but this measure only restrains the citizens in middle and low income classes and thus is essentially unfair. Assessing every patient from a comprehensive view such as necessity and then assigning priority to the one of high degree of inpatient admission, could efficiently and fairly distribute medical resources in overcrowd high level hospitals. In this way, the citizens with low fitness degree of CDT principle will spend more time in waiting, and thus have to tend to lower level hospitals spontaneously, whilst the patients with serious disease could obtain the medical resources quickly and easily. Therefore, the inpatient admission assessment becomes an essential way to implement CDT.

Up to now, a wide range of techniques have been employed to inpatient admission assessment, such as the Coxian phase type model [9], the Markov chain based model [7, 8], the particle swarm optimization based model [10], the semi-closed migration network based model [15], the simulation based model [6, 30] and the queuing model [3, 29]. Generally, all of these models can be viewed as objective programming models with distinct objective functions and various constraints such as the earliest and latest hospitalization period, the sex, the length of stay, the pathology, the contagiousness, the single and double rooms, the incompatibility between pathologies and the contagious patients [27]. However, these principles have obvious drawbacks for Chinese healthcare management: their indicators do not meet the national conditions of China. In many countries, the inpatient admission only focuses on the economic benefit and operational efficiency. In China, however, hospitals should also follow the policy from government, which considers the comprehensive utility of the whole nation. As an important implementation approach of CDT, the inpatient admission process should consider the fitness degree of patients for CDT principle. To achieve this goal, we propose a new index of CDT (ICDT) to measure the closeness degree between these patients and CDT principle. The emergency degree (ED), the necessity to hospitalize (NH) and the value of pathology (VP) are considered as constraints or objectives of inpatient admission model for CDT. Due to the transformation from vague and imprecise information to precise numeric data, the CDT index can be taken as a useful criterion to instruct the inpatient admission problem, which is an innovation for solving inpatient admissionproblem.

Besides, the inpatient admission assessment for CDT problem consists of many vague and imprecise information, in which natural language is the best way to describe the status of each alternative patient. However, the natural language is limited to qualitative analysis. How to transform qualitative information to precise and quantitative data has been a big problem for many years. The hesitant fuzzy linguistic term set (HFLTS) [19, 26] offers a robust way to convert qualitative information to precise and quantitative data and empirical research conforms that its transformation is valid.

Assessing alternative patients is a multiple criteria decision making (MCDM) problem, and it involves many conflicting criteria. For the fuzzy MCDMproblem with conflict and non commensurable criteria, Opricovic [25] introduced the fuzzy VIKOR method which solves problems in fuzzy circumstances where both criteria and weights could be fuzzy sets. In his model, the triangular fuzzy numbers were employed to represent imprecise numerical quantities. As for the situation where the decision makers’ opinions are represented as trapezoidal fuzzy numbers, Shemshadi et al. [28] proposed the fuzzy VIKOR method which extracted and deployed the objective weights of the criteria based on Shannon entropy concept, and then applied the method into the supplier selection problem. To evaluate the website quality of professional accounting firms, Chow and Cheng [4] developed a hybrid approach which combines the fuzzy analytic network process (FANP) and the fuzzy VIKOR together. Liao and Xu [18] introduced the hesitant fuzzy VIKOR method and used it to evaluate the domestic airlines’ service quality. Zhang and Wei [35] employed the hesitant fuzzy VIKOR method to help the enterprise’s board of directors evaluate the candidate large projects. Based on the Shapley value based L _p  - metric, Zhang and Wei [36] introduced an extended hesitant fuzzy VIKOR method to deal with the correlative MCDM problem under hesitant fuzzy circumstances. Liao et al. [23] proposed the HFL-VIKOR method which is a great innovation of traditional VIKOR for its robustness to handle fuzzy information in MCDM problem.The HFL-VIKOR method is very useful in handling the qualitative MCDM problems especially when the criteria conflict with each other and the evaluation values of the alternatives are represented as linguistic expressions or simple linguistic terms. All the above mentioned extended forms of VIKOR methods are based on different types of quantitative information thus can not be implemented in qualitative situations. As HFLTS is the newest form of linguistic representation model and more flexible in depicting the human cognitions, the HFL-VIKOR, which combines the HFLTS and the VIKOR method together, can describe the real preferences of decision makers and reflect their uncertainty, hesitancy and inconsistency, eliminate the vague and imprecise information from natural language, and assess each alternative patient according to conflicting criteria at the same time [31–33, 37].

Therefore, applying the HFL-VIKOR method in inpatient admission assessment could efficiently solve the inpatient admission assessment problem. West China hospital (WCH) is one of the most influential and powerful hospital in China, and it also suffers the plight of inefficiency. Considering such situation, we applied the HFL-VIKOR method to WCH’s inpatient admission assessment problem, and achieved valid distinction results for each patient. Based on the previous work, further work is to employ the distinction results as constrains or decision objectives in WCH’s inpatient admission problem.

The remainder of this paper is organized as follow: Section 2 describes the theory of HFL-VIKOR method. Section 3 applies the HFL-VIKOR method to WCH’s patient assessment to obtain the rank of patients and ICDT in WCH. In Section 4, we conclude the advantage of this method in patient assessment and discuss the study in future work.

2 Methodology

West China Hospital (WCH), located in Chengdu, is one of the largest single-site hospitals in the world and a leading medical center of West China, treating complicated and severe cases, especially in the fields of living donor liver transplantation, severe acute pancreatitis, and clinical anesthesia. During the past long time, a great number of patients, which beyond the capacity of WCH, are applying for the hospitalization admission. Among them, a small part have the necessity to applying for the admission of WCH due to their high intensity diseases and distinctive value of pathology; besides, the rest of them are the patients suffer low intensity diseases, such as cough and influenza, which could be cured by low level medical institution readily.

In December 2011, WCH established an inpatient admission service center, for the purpose of optimizing the hospitalization admission process. The inpatient admission service center indeed reduces the trifles of patients for hospitalization matters and improves the efficiency of utilizing hospital resources. Acute contradiction, however, still exists due to the extremely finite medical resource and the considerable demand of citizens who irrationally pursuing higher level medical resource. Therefore, an efficient decision support technique should be employed to assess the patients who apply for hospitalization admission after the preliminary diagnose by doctors in ambulant clinic to guarantee that the scarce medical resources are implemented to the most desirable patients.

In this section, the HFL-VIKOR is employed as a key technique to handle the inpatient admission assessment problem. Not all patients have the necessity to hospitalize, for that the patients’ status varying. A feasible way to solve this problem is to assess the fitness degree of each patient and make sure that admission decisions depend on the numeric assessment results. Under the circumstance of CDT, the assessment results is called ICDT, which will influence the priority in admission to a large extent. Due to the transformation from vague and imprecise information to precise numeric data, ICDT could be a useful criteria to instruct the inpatient admission problem, which is an innovation for inpatient admission problem. In this case, ICDT would be a constraint or an objective of inpatient admission programme problem. We define ICDT as the formula given below:

ICDT = 1 - HFLC + 1 I(8)

where I is the amount of patient waiting in the queue. In inpatient admission, HFLGU and HFLIR respectively represent the maximum group utility for the majority and the minimum individual regret for the opponent. Besides, HFLC is the compromise measure of the maximum utility and minimum regret in inpatient admission selection and can be obtained by Formula 4. The smaller the value of the hesitant fuzzy compromise measure HFLC, the fitter the patient for CDT principle.

Huang et al. [14] proposed that the core meaning of the implementation of CDT is to effectively divert patients to the appropriate medical institution to give appropriate treatment, without delay, waste of medical resources and health care funds, and finally construct a ideal environment for both doctors and patients. However, CDT covers many comprehensive domains, and there is no explicit instruction to measure CDT principle. Therefore, based on the research of Li [16] and He et al. [13], and the discipline development prospect of WCH, the criteria of CDT are finally selected as follow:

Emergency degree (ED), describes how emergent the patient need to be hospitalized, is a positive index for CDT. For example, the patient with chronic pharyngitis has a inferior ED compared to the one with acute pendicitis.

The terms of the above criteria vary in different contexts, thus it’s necessary to make sure that every linguistic term in this application be out of ambiguity. Through the interview with doctors in WCH, we determine the linguistic term sets for these three criteria:

S _ED = {s_-3 = very non urgent, s_-2 = non urgent, s_-1 = a little non urgent, s₀ = medium, s₁ = a little urgent, s₂ = urgent, s₃ = very urgent}.

With these linguistic term sets and also the context-free grammar shown in Definition 2, officer in the inpatient admission service center in WCH provides descriptions of 50 patients waiting for hospitalisation admission, which are shown in Table 3 (for more details, please refer to Example 1):

The linguistic expressions shown in Table 3 are similar to the human way of thinking and they can reflect the decision makers hesitant cognition intuitively. To assess each patient’s closeness degree to CDT principle, The linguistic expressions must be transformed to the HFLTS judgment matrix, in the form of which the distance between each patient in the aspect of attribute could be calculated. Ignoring the affection of different linguistic term sets on criteria, the transformation function H _{G E} given in Definition 3 is employed to obtain the following HFLTS judgment matrix(for more details, please refer toExample 2):

ℍ = [ { s 2 , s 3 } { s 2 , s 3 } { s - 3 , s - 2 } { s - 2 , s - 1 , s 0 } { s 3 } { s 1 , s 2 } ⋯ ⋯ ⋯ { s - 2 , s - 1 , s 0 } { s 1 , s 2 , s 3 } { s 0 } ](9)

Based on the semantics of different criteria, we can see that all of the three criteria are benefic criteria, i.e., the higher the value, the better the alternative. According to Definition 4 and Definition 5, we can calculate the score function value and variance function value for each HFLTS. Then, we obtain

max(ED) = {s₂, s₃}, min(ED) = {s_-3}

f j + = max i f ij and f j - = min i f ij are the best and worst values of a _i over the benefit-type criterion c _j , respectively. In this case, the positive ideal solution for this HFL-MCDM problem is f⁺ = ({s_-3, s_-2, s_-1} , {s₃} , {s_-2, s_-1, s₀})  ^T , whereas the negative ideal solution is f^- = ({s_-3} , {s₃} , {s_-3, s_-2, s_-1, s₀})  ^T .

The upper bound is defined as a n-tuple of the highest degree in each criterion, and the lower bound is similar. In this case, the upper bound and the lower bound are 3-tuples. Especially, for patient P₁, the upper bound and lower bound are (s₃, s₃, s_-2) and (s₂, s₂, s_-3) respectively. Figure 2 depicts the upper bound and lower bound of each patient, and the raw data of each patient can be found in it.

The weight matrix for ED, NH and VP from the head administrator is [0.1, 0.5, 0.4] ^T . θ refers to the weight of the strategy of the majority of criteria or the maximum overall utility to generate the HFLC. In this case, θ is set to be 0.5 to avoid losing generality. The HFLGUs, HFLIRs and HFLCs are shown in Fig. 3. This figure record every patient in the way of HFLGUs, HFLIRs and HFLCs, which show strong positive correlation. According to the HFLCs, we obtain the priority rank, shown in Table 4, where M₁ refers to HFL-TOPSIS and M₂ refers to HFL-VIKOR. The results show that the top 5 ranks are (P₂₄, P₄₉, P₂₉, P₃₈, P₂₈) and (P₁₄, P₄₆, P₂₅, P₃₃, P₃₁), and it indicates that HFL-VIKOR is more stable, for that it didn’t prefer to extreme value, such as {s_-3} and {s₃} of P₂₈, shown in Table 5. Besides, the top 5 ICDTs are 1.0200, 0.8940, 0.8853, 0.8826 and 0.8127, respectively.

There is a much long period before Chinese medical contradiction between supply and demand be remarkably alleviate. The police of CDT, which values social utility and fairness more, is proposed to ease this contradiction. Among all implement approaches, inpatient admission is the most fair and practical one, therefore need be paid more attention.

In the field of inpatient admission, a feasible way to solve medical resource deficiency is to assess social value according to CDT principle, and the scheduling process should optimize the ICDT or ensure the ICDT attains a certain high level. From the application of HFL-VIKOR in patient assessment in WCH, we can draw a conclusion that, HFL-VIKOR method could efficiently assess the closeness, between the alternative patient and CDT principle, to increase the comprehensive utility of inpatient admission management. This ability mainly lies in the following four advantages of HFL-VIKOR:

Firstly, comparing to the traditional VIKOR method and its extensions, the HFL-VIKOR method is proposed to handle the MCDM problems in which all the evaluation values of each alternative over the criteria are represent as linguistic expressions or simple linguistic terms.

In this paper, ICDT is proposed as measurement for the fitness degree of patients for CDT principle, to assess the priority should be assigned in inpatient admission problem. Different from earlier works, we consider each patient with distinct status, for that different kinds of medical institutions involve different kinds of goals. The proposition of ICDT reveals a new way to solve inpatient admission problem, that is to consider ICDT, which refers to the comprehensive influence, as a important factor when process hospitalization scheduling. Further research will be done by employing ICDT of alternative patients to optimise the inpatient admission process in WCH.