Hierarchical diagnosis and treatment optimization method and system based on queuing game model

Abstract

The invention provides a hierarchical diagnosis and treatment optimization method and system based on a queuing game model, and relates to the technical field of game models. According to the optimization method, an optimal coordination policy matched with the market environment is formulated by analyzing the patient scale, the assistance efficiency of the first-class hospital and the influence of the degree of concern of the first-class hospital to the public benefit target on the balance result, and the overall benefit and social welfare of the medical system can be effectively optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of game models, and in particular to a hierarchical diagnosis and treatment optimization method and system based on a queuing game model. Background Art

[0002] With the continuous improvement of living standards, the demand for medical and health services has shown a rapid growth trend. However, the problem of insufficient total quality medical resources and uneven regional distribution has become increasingly prominent. This situation has led to a large number of patients flocking to large comprehensive hospitals with high-quality resources. At the same time, community hospitals and other grassroots medical institutions are facing the dilemma of scarce patients and idle medical resources, and the supply and demand configuration is seriously unbalanced.

[0003] In-depth analysis of the reasons for this situation shows that the weak capacity of primary medical services and lack of trust are the primary factors. In addition, while meeting the needs of patients, large hospitals are also expanding their scale, further absorbing more social resources, and exacerbating the trend of centralization of medical resources. Furthermore, the poor communication channels between large hospitals and grassroots hospitals and the superficial cooperation mechanism have also seriously affected the rational allocation and efficient use of medical resources.

[0004] In order to effectively alleviate the above problems, guide the reasonable diversion of patient needs, and promote the sinking of medical resources to the grassroots level, it is particularly important to study the optimization methods and systems of hierarchical diagnosis and treatment in this context. By deeply exploring the medical selection behavior of patients in the medical system and the decision-making equilibrium state of each game participant, more scientific and reasonable coordination strategy suggestions can be provided for the regulators of the medical system.

[0005] In recent years, domestic and foreign scholars have conducted extensive research on the issue of patient referrals between medical institutions at different levels in the hierarchical diagnosis and treatment system. For example, Li Zhongping et al. studied a medical system consisting of tertiary hospitals and community hospitals, and analyzed the impact of different interest-sharing mechanisms on the operation of the referral system. Specifically, the study explored the following aspects: First, as a system regulator, the government selects appropriate mechanisms to encourage tertiary hospitals to improve their medical capabilities and sink them to grassroots medical institutions in order to improve the service quality of community hospitals in order to improve the overall social welfare. Under the framework of each incentive mechanism, community hospitals achieve their revenue goals by setting up revenue-sharing contracts; tertiary hospitals determine the proportion of their capabilities to sink based on the rewards they receive, guided by the goal of pursuing profit maximization. Ultimately, patients in the system make hospital selection decisions by evaluating their own utility.

[0006] However, the existing hierarchical diagnosis and treatment model does not consider the factors that affect optimization accurately and comprehensively, resulting in poor optimization results, which are specifically manifested in:

[0007] The model fails to accurately describe the specific impact of the transfer of tertiary hospitals' capabilities to community hospitals on the improvement of medical service quality. The model only considers the improvement of community hospital service rate, but in reality, community hospitals usually have idle resources. The main challenge is to improve the quality of medical services to provide higher quality and comprehensive services, so simply optimizing the service rate does not hit the point.

[0008] The model does not fully consider the situation where patients need to be referred after receiving incomplete treatment in community hospitals. Due to the capacity limitations of community hospitals, there may be cases where treatment fails or cannot be completed. The transfer of capacity from tertiary hospitals to community hospitals can improve the cure rate of community hospitals and effectively reduce the need for referrals, but this effect is not reflected in the model.

[0009] The tertiary hospitals in the model only take the maximization of economic benefits as the decision-making goal, ignoring the requirements for the public welfare assessment of tertiary hospitals in recent medical reform policies and related documents. In this context, the return to public welfare may have an important impact on hospital decision-making and government coordination strategies, which is also an aspect that needs further research and in-depth discussion. Summary of the invention

[0010] In view of the shortcomings of the prior art, the present invention provides a hierarchical diagnosis and treatment optimization method and system based on a queuing game model, which solves the problem that the optimization factors of the hierarchical diagnosis and treatment model are not accurately and comprehensively considered and the effect is poor.

[0011] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0012] A hierarchical diagnosis and treatment optimization method based on a queuing game model, the optimization method comprising the following steps:

[0013] S1. Patients gain benefits when receiving treatment in tertiary hospitals:

[0014] U 1 =Rp 1 -xW 1 ;

[0015] Among them, U 1 represents the utility of M-type patients who go to tertiary hospitals;

[0016] R represents the benefit obtained by the patient’s recovery;

[0017] p 1 It represents the medical expenses of patients in tertiary hospitals;

[0018] x represents the patient’s sensitivity to time delay;

[0019] W 1 It means that the expectation of the tertiary hospitals is to wait for a certain period of time;

[0020] Benefits of receiving treatment in a community hospital:

[0021] U 2 =(1-K)(Rp 2 )-xW 2 +K(Rp 1 -xW 1 -F);

[0022] Among them, U 2 represents the utility of M-type patients who go to community hospitals;

[0023] p 2 It represents the medical expenses of patients in community hospitals;

[0024] K represents the treatment failure rate in community hospitals;

[0025] W 2 Indicates community hospital expectations of waiting time;

[0026] F represents the loss to the patient caused by referral;

[0027] Based on the principle of maximizing the expected utility of each patient, if U 1 >U 2 , the patient goes to a tertiary hospital for treatment; if U 1 2 , the patient goes to the community hospital for treatment; if U 1 =U 2 , patients will randomly select a hospital to visit;

[0028] Thus, we get the indifference point x of the patient's medical decision * , that is, the patient's sensitivity to delay x = x * When x <x * , the patient will go to a tertiary hospital for treatment; x>x * , patients will go to community hospitals for treatment;

[0029] S2. When the patient's choice of medical treatment is predicted, the tertiary hospitals should H Maximize the decision-making assistance effort level v, that is, Solve for the optimal level of assistance effort v * ;

[0030] S3. In the case of predicting patients' medical choices and the support strategies of tertiary hospitals, the regulator decides the transfer payment level T based on the maximization of social welfare S, that is, Solve for the optimal transfer payment level T * ;

[0031] S4, T obtained in S3​* Substitute into S2 to get v * , v * and T * Substitute the obtained θ into S1 * That is the proportion of patients going to tertiary hospitals when the system is in equilibrium.

[0032] Preferably, the expected waiting time of the tertiary hospital is W 1 satisfy:

[0033]

[0034] where λ 1 represents the number of patients who went to tertiary hospitals;

[0035] λ 2 =Λ-λ 1 Represents the number of patients who visited community hospitals.

[0036] Preferably, the treatment failure rate of the community hospital satisfies:

[0037] K(v)=ke -βv ;

[0038] Among them, k represents the treatment failure rate of community hospitals when they are not assisted;

[0039] β represents the assistance efficiency of tertiary hospitals;

[0040] v represents the level of support efforts of tertiary hospitals.

[0041] Preferably, the proportion of patients going to tertiary hospitals is * satisfy:

[0042]

[0043] Where, Δ=K(v)F-(1-K(v))(p 1 -p 2 ), which can reflect the expected loss of each patient choosing a community hospital in the non-time dimension;

[0044] The indifference point x of the patient's medical decision * =θ * When x * <θ * , patients can get higher utility by going to a tertiary hospital; if x * >θ * , patients can get higher utility by going to community hospitals; the number of patients going to tertiary hospitals Number of visits to community hospitals

[0045] Preferably, the proportion of patients going to tertiary hospitals is θ * Closely related to the total number of patients Λ; when the patient scale is small, all patients entering the system will go to tertiary hospitals; when the total number of patients exceeds the threshold When θ , patients began to be diverted, and the proportion of patients going to tertiary hospitals was θ * As the level of support efforts v of the tertiary hospitals increases, it decreases; when the patient scale reaches When the number of patients arriving at tertiary hospitals exceeds the carrying capacity of tertiary hospitals.

[0046] Preferably, the tertiary hospitals maximize the expected utility Π H Under the goal, determine the effort level v of providing assistance, where the expected utility includes:

[0047] The total revenue obtained from providing treatment services to patients arriving at tertiary hospitals 1 p 1 +Kλ 2 p 1 ;

[0048] Cost of efforts to support community hospitals cv 2 , where c is the assistance cost coefficient;

[0049] Transfer payment income from the government Tv;

[0050] Total utility of patients in the system

[0051] That is, the optimization goal of the tertiary hospitals is:

[0052]

[0053] Among them, η∈(0,1) represents the proportion of public welfare goals in the operational goals of tertiary hospitals;

[0054] 1-η represents the proportion of profit target.

[0055] Preferably, when the public interest level η exceeds the threshold η 1 When , the tertiary hospitals will spontaneously help community hospitals, and the optimal level of support effort v * as follows:

[0056] When η<η 1 , that is, when the tertiary hospitals have lower public welfare concerns:

[0057]

[0058] otherwise:

[0059]

[0060] Among them, η 1 Satisfy implicit function T 0 Satisfy implicit function Indicates the minimum transfer payment requirements that tertiary hospitals are willing to provide under lower public welfare concerns;

[0061] T 1 Satisfy implicit function It indicates the share of unit transfer payments that can achieve the goal of all patients going to community hospitals;

[0062] T 2 Satisfy implicit function It means that when patients are successfully diverted, it can motivate tertiary hospitals to further increase their support efforts to improve the minimum transfer payment requirements for community hospitals’ cure rates.

[0063] If the public welfare level of tertiary hospitals is low, η<η 1 It is defined as an economy-oriented hospital, otherwise it is defined as a public welfare-oriented hospital.

[0064] Preferably, the social welfare S includes:

[0065] Community hospital operating income 2 p 2 ;

[0066] Total utility of patients entering the system:

[0067]

[0068] The transfer payment Tv provided by the regulator to motivate the tertiary hospitals. That is, the optimization problem of the regulator is:

[0069]

[0070] According to the regulator's objective function, the optimal coordination condition can be obtained:

[0071] The proportion of patients going to tertiary hospitals θ * and the optimal support effort level of tertiary hospitals v * , when η<η 1 , Λ 1 <Λ<Λ 2 When T * >0, and there is When η>η 1 , Λ 1 <Λ<Λ 3 When T * >0, and there is Otherwise, T *= 0. That is, the optimal unit subsidy cost T * Satisfy the following:

[0072] When η<η 1 , that is, when the tertiary hospitals have lower public welfare concerns:

[0073]

[0074] otherwise:

[0075]

[0076] Among them, Λ 3 <Λ 2 And satisfy the implicit function

[0077] A hierarchical diagnosis and treatment optimization system based on a queuing game model, the optimization system comprising: a selection module, a support strategy formulation module, a coordination strategy formulation module and a game equilibrium module;

[0078] The selection module is used to determine the medical treatment selection according to the patient's expected utility;

[0079] The assistance strategy formulation module is used to solve the optimal assistance effort level according to the utility of the tertiary hospitals themselves;

[0080] The coordination strategy formulation module is used to solve the optimal transfer payment level based on social welfare maximization;

[0081] The game equilibrium module is used to obtain the proportion of patients arriving at tertiary hospitals under the system equilibrium state according to the transfer payment decision equilibrium and the assistance decision equilibrium.

[0082] The present invention provides a hierarchical diagnosis and treatment optimization method and system based on a queuing game model. Compared with the prior art, it has the following beneficial effects:

[0083] In the present invention, the optimization method analyzes the impact of patient scale, the support efficiency of tertiary hospitals and the degree of concern of tertiary hospitals for public welfare goals on the equilibrium results, so as to formulate the optimal coordination policy matching the market environment, which can effectively optimize the overall benefits and social welfare of the medical system. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0085] Figure 1 is a flow chart of an optimization method in an embodiment of the present invention;

[0086] Figure 2 It is a curve diagram showing the influence of the public welfare level η, the patient scale Λ and the assistance efficiency β on the unit transfer payment cost T in the embodiment of the present invention;

[0087] Figure 3 It is a curve diagram showing the influence of the public welfare level η, the patient scale Λ and the support efficiency β on the support level v of the tertiary hospitals in the embodiment of the present invention;

[0088] Figure 4 This is a curve chart showing the impact of the public welfare level η, patient scale Λ and support efficiency β on patients' medical treatment choices in an embodiment of the present invention. DETAILED DESCRIPTION

[0089] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] The embodiments of the present application provide a method and system for optimizing hierarchical diagnosis and treatment based on a queuing game model, thereby solving the problem that optimization factors of the hierarchical diagnosis and treatment model are not accurately and fully considered and the effect is poor.

[0091] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0092] Example:

[0093] like Figure 1 to Figure 4 As shown, the present invention provides a hierarchical diagnosis and treatment optimization method based on a queuing game model, and the optimization method comprises the following steps:

[0094] S1. Patients’ medical treatment choices

[0095] When patients need medical treatment, they will choose to go to a tertiary hospital or a community hospital. When they receive treatment in a tertiary hospital, they can obtain the following benefits:

[0096] U 1 =Rp 1 -xW 1 ;

[0097] Among them, U 1 represents the utility of M-type patients who go to tertiary hospitals;

[0098] R represents the benefit obtained by the patient’s recovery;

[0099] p 1 It represents the medical expenses of patients in tertiary hospitals;

[0100] x represents the patient's sensitivity to delay, which follows a uniform distribution U[0,1]. The larger the x, the more disgusted the patient is with waiting.

[0101] W 1 It means that the expectation of the tertiary hospitals is to wait for a certain period of time;

[0102] Benefits of receiving treatment in a community hospital:

[0103] U 2 =(1-K)(Rp 2 )-xW 2 +K(Rp 1 -xW 1 -F);

[0104] Among them, U 2 represents the utility of M-type patients who go to community hospitals;

[0105] p 2 It represents the medical expenses of patients in community hospitals;

[0106] K represents the treatment failure rate in community hospitals;

[0107] W 2 Indicates community hospital expectations of waiting time;

[0108] F represents the loss caused to the patient by referral, including the expenses of the community hospital during the treatment phase and the loss caused by the worsening of the disease.

[0109] Based on each patient's expected utility maximization behavior, if U 1 >U 2 , the patient will go to a tertiary hospital for treatment; if U 1 2 , patients will choose community hospitals; if U 1 =U 2 , patients will randomly select a hospital to visit;

[0110] From this, we can get the indifference point x of the patient's medical decision * , that is, the patient's sensitivity to delay x = x * When x <x * , the patient will go to a tertiary hospital; x>x * , patients will choose community hospitals for medical treatment.

[0111] S2. Support strategies of tertiary hospitals ​

[0112] When the patient's medical choice is predicted, the tertiary hospitals will use their own utility function Π H Maximize the decision-making assistance effort level v, that is, So as to solve the optimal assistance effort level v * .

[0113] S3. Coordination strategies of regulators

[0114] In the case of predicting patients' medical choices and the support strategies of tertiary hospitals, the regulator decides the transfer payment level T based on the maximization of social welfare S, that is, Thus, the optimal transfer payment level T is solved * .

[0115] S4. Game equilibrium of hierarchical diagnosis and treatment model

[0116] T obtained in S3 * That is, the regulator's transfer payment decision equilibrium, T * Substitute the v obtained in S2 into * That is, the support decision balance of the tertiary hospitals, v * and T * Substitute the obtained θ into S1 one by one * That is the proportion of patients arriving at tertiary hospitals under system equilibrium conditions.

[0117] Assume that the potential patient flow entering the system for diagnosis and treatment obeys a Poisson distribution with parameter Λ. Tertiary hospitals and community hospitals provide services to patients based on the first-come, first-served rule. Tertiary hospitals can provide comprehensive services to both types of patients, and patients can receive complete treatment here; community hospitals are constrained by their capabilities and resources and can only provide limited services to patients, that is, there is a certain failure rate K in treatment, and patients who fail treatment will be transferred to tertiary hospitals for further treatment; patients are considered rational and can independently choose tertiary hospitals or community hospitals based on utility. If treatment fails in community hospitals, they will be transferred to tertiary hospitals.

[0118] The tertiary hospitals and community hospitals provide treatment for patients based on the M / M / 1 queue, and the treatment time of patients is subject to the parameters μ 1 and μ 2 Independent exponential distribution; under the M / M / 1 service rule, according to Little's theorem, the average waiting time for each patient receiving treatment services in a tertiary hospital is:

[0119]

[0120] where λ 1 represents the number of patients who went to tertiary hospitals;

[0121] λ 2=Λ-λ 1 represents the number of patients who visit community hospitals;

[0122] The current situation of community hospitals being deserted reflects the low patient arrival rate and the average waiting time. 2 Small, for the convenience of calculation, its impact on utility will be ignored, that is, assuming that W 2 =0.

[0123] Considering the particularity of medical services, treatment failure will bring great losses to patients. Therefore, compared with waiting time, patients are more concerned about the treatment failure rate of community hospitals. Due to the limitations of medical conditions, community hospitals cannot provide comprehensive medical services, and there is a possibility of treatment failure or inability to treat. This is also an important reason why patients prefer to go to tertiary hospitals even if they face longer waiting times.

[0124] Most existing studies assume that the cure rate of community hospitals is fixed. In fact, when considering the transfer of capacity between superior and subordinate medical institutions in the context of medical alliances, the assistance of superior hospitals can directly optimize the cure rate of subordinate hospitals, but relevant literature rarely studies this relationship. Therefore, the treatment failure rate of community hospitals is studied as an endogenous variable, expressed as:

[0125] K(v)=ke -βv ;

[0126] Among them, k represents the treatment failure rate of community hospitals when they are not assisted;

[0127] β represents the assistance efficiency of tertiary hospitals, that is, the contribution of tertiary hospitals’ assistance to reducing the failure rate, and can also reflect the degree of cooperation between the two levels of hospitals;

[0128] v represents the level of support efforts of tertiary hospitals.

[0129] In view of the above model assumptions, the present invention adopts the reverse induction method, firstly determining the patient's medical choice, then determining the support decision of the tertiary hospitals, and finally determining the coordination strategy of the regulator, so as to obtain the game equilibrium of the hierarchical diagnosis and treatment model.

[0130] The proportion of patients going to tertiary hospitalsθ * satisfy:

[0131]

[0132] Where, Δ=K(v)F-(1-K(v))(p 1 -p 2 ), which can reflect the expected loss of each patient choosing a community hospital in the non-time dimension;

[0133] The indifference point x of the patient's medical decision* =θ * When x * <θ * , patients can get higher utility by going to a tertiary hospital; if x * >θ * , patients can get higher utility by going to community hospitals; the number of patients going to tertiary hospitals Number of visits to community hospitals

[0134] The proportion of patients going to tertiary hospitalsθ * Closely related to the total number of patients Λ; when the patient scale is small, all patients entering the system will go to tertiary hospitals; when the total number of patients exceeds the threshold When θ , patients began to be diverted, and the proportion of patients going to tertiary hospitals was θ * As the level of support efforts v of the tertiary hospitals increases, it decreases; when the patient scale reaches When the number of patients arriving at tertiary hospitals exceeds the carrying capacity of tertiary hospitals.

[0135] As resource-rich hospitals, tertiary hospitals are able to help community hospitals improve their cure rates through expert consultations, physician training, and case database sharing. Public hospitals need to pay more attention to the public welfare of medical services when operating, that is, to increase the total utility of patients entering the medical system. Therefore, in anticipating patients' medical choices, tertiary hospitals maximize expected utility Π H Under the goal, determine the effort level v of providing assistance, where the expected utility includes:

[0136] The total revenue obtained from providing treatment services to patients arriving at tertiary hospitals 1 p 1 +Kλ 2 p 1 ;

[0137] Cost of efforts to support community hospitals cv 2 , where c is the assistance cost coefficient;

[0138] Transfer payment income from the government Tv;

[0139] Total utility of patients in the system

[0140] That is, the optimization goal of the tertiary hospitals is:

[0141]

[0142] Among them, η∈(0,1) represents the proportion of public welfare goals in the operating goals of tertiary hospitals, which can reflect the degree of concern of tertiary hospitals for public welfare services. The corresponding 1-η represents the proportion of profit goals.

[0143] According to the objective function of the tertiary hospitals, the conditions for supporting the hospitals can be obtained, which are as follows:

[0144] The proportion of patients going to tertiary hospitals θ * , if and only if the public interest concern level η exceeds the threshold η 1 When , the tertiary hospitals will spontaneously help community hospitals, and the optimal level of support effort v * as follows:

[0145] When η<η 1 , that is, when the tertiary hospitals have lower public welfare concerns:

[0146]

[0147] otherwise:

[0148]

[0149] Among them, η 1 Satisfy implicit function T 0 Satisfy implicit function Indicates the minimum transfer payment requirements that tertiary hospitals are willing to provide under lower public welfare concerns;

[0150] T 1 Satisfy implicit function It indicates the share of unit transfer payments that can achieve the goal of all patients going to community hospitals;

[0151] T 2 Satisfy implicit function It means that when patients are successfully diverted, it can motivate tertiary hospitals to further increase their support efforts to improve the minimum transfer payment requirements for community hospitals’ cure rates.

[0152] If the public welfare level of tertiary hospitals is low, η<η 1 It is defined as an economy-oriented hospital, otherwise it is defined as a public welfare-oriented hospital.

[0153] If the regulator does not promise to provide transfer payments, then after weighing the economic losses and public welfare improvements caused by the assistance, economically oriented hospitals will not provide any assistance, while public welfare oriented hospitals will still choose to support community hospitals.

[0154] As transfer payments increase, both types of tertiary hospitals will gradually increase their support efforts until all patients go to community hospitals. At this point, the willingness of tertiary hospitals to provide support is further reduced, and further increase in transfer payments is unlikely to have an incentive effect. Only when transfer payments are above a certain level will tertiary hospitals continue to strengthen their support. At this time, support will not improve the diversion of patients, but will optimize the cure rate of community hospitals. It is worth noting that the threshold η here is 1 It is closely related to factors such as patient scale, assistance efficiency, service efficiency, and service price. The classification of tertiary hospitals is different for different medical market environments. In addition, regulators can guide tertiary hospitals to transform between economic orientation and public welfare orientation through assessment and supervision.

[0155] Medical system regulators need to improve the efficiency of the system by formulating relevant policies to guide patient diversion and motivate hospitals to help. As a non-profit organization, community hospitals will invest most of their income in the construction of the medical system, including improving medical infrastructure and providing profit sharing. With the predicted equilibrium arrival rate of patients and the level of assistance efforts of tertiary hospitals, we now explore the optimal transfer payment decision T of regulators with the goal of maximizing social welfare S.

[0156] Social welfare S includes:

[0157] Community hospital operating income 2 p 2 ;

[0158] Total utility of patients entering the system:

[0159]

[0160] The transfer payment Tv provided by the regulator to motivate the tertiary hospitals. That is, the optimization problem of the regulator is:

[0161]

[0162] According to the regulator's objective function, the optimal coordination condition can be obtained:

[0163] The proportion of patients going to tertiary hospitals θ * and the optimal support effort level of tertiary hospitals v * , when η<η 1 , Λ 1 <Λ<Λ 2 When T * >0, and there is When η>η 1 , Λ 1 <Λ<Λ 3 When T * >0, and there is Otherwise, T * = 0. That is, the optimal unit subsidy cost T * Satisfy the following:

[0164] When η<η 1 , that is, when the tertiary hospitals have lower public welfare concerns:

[0165]

[0166] otherwise:

[0167]

[0168] Among them, Λ 3 <Λ 2 And satisfy the implicit function

[0169] The transfer payment strategy of the regulator to coordinate the reasonable allocation of resources of the two-level medical system under different market environments, the type of tertiary hospitals and the scale of patients jointly determine whether the regulator should adopt the transfer payment policy. In the face of economic-oriented hospitals, if the number of patients reaches a certain scale, then the transfer payment incentive of the regulator is necessary, and the larger the patient scale, the higher the incentive demand. If the number of patients is small, all patients will go to tertiary hospitals, and no one will care about community hospitals. At this time, the assistance behavior and coordination policy will lose their meaning. For public welfare-oriented hospitals, since the improvement of patient utility brought by their assistance can make up for the economic losses of the hospital, the initiative of assistance is strong, and the transfer payment required by the government is greatly reduced. When the patient scale is large, the system congestion makes the patient utility more threatened, and the motivation of tertiary hospitals to provide assistance will be further strengthened. Therefore, as the patient scale expands, the importance of transfer payments will gradually decrease.

[0170] The present invention provides a hierarchical diagnosis and treatment optimization system based on a queuing game model, the optimization system comprising: a selection module, a support strategy formulation module, a coordination strategy formulation module and a game equilibrium module;

[0171] The selection module is used to determine the medical treatment selection according to the patient's expected utility;

[0172] The assistance strategy formulation module is used to solve the optimal assistance effort level according to the utility of the tertiary hospitals themselves;

[0173] The coordination strategy formulation module is used to solve the optimal transfer payment level based on social welfare maximization;

[0174] The game equilibrium module is used to obtain the proportion of patients arriving at tertiary hospitals under the system equilibrium state according to the transfer payment decision equilibrium and the assistance decision equilibrium.

[0175] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0176] In the embodiment of the present invention, the optimization method analyzes the impact of patient scale, the support efficiency of tertiary hospitals and the degree of concern of tertiary hospitals for public welfare goals on the equilibrium results, so as to formulate the optimal coordination policy matching the market environment, which can effectively optimize the overall benefits and social welfare of the medical system.

[0177] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0178] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A hierarchical diagnosis and treatment optimization method based on a queuing game model, characterized in that: The optimization method includes the following steps: S1. When a patient receives treatment in a tertiary hospital, the utility obtained is: U1 = R - p1 - xW1; where U1 represents the utility of type-M patients going to a tertiary hospital; R represents the benefit obtained by the patient's recovery; p1 represents the medical expenses of the patient in the tertiary hospital; x represents the patient's sensitivity to time delay; W1 represents the expected waiting time in the tertiary hospital; When receiving treatment in a community hospital, the utility that can be obtained is: U2 = (1 - K)(R - p2) - xW2 + K(R - p1 - xW1 - F); where U2 represents the utility of type-M patients going to a community hospital; p2 represents the medical expenses of the patient in the community hospital; K represents the treatment failure rate of the community hospital; W2 represents the expected waiting time in the community hospital; F represents the loss brought to the patient by referral; Based on the principle of maximizing the expected utility of each patient, if U1 > U2, the patient goes to the tertiary hospital for treatment; if U1 < U2, the patient goes to the community hospital for treatment; if U1 = U2, the patient will randomly choose a hospital for treatment; Thus, we get the indifference point x of the patient's medical decision * , that is, the patient's sensitivity to delay x = x * When x <x * , the patient will go to a tertiary hospital for treatment; x>x * , patients will go to community hospitals for treatment; S2. When the patient's choice of medical treatment is predicted, the tertiary hospitals should H Maximize the decision-making assistance effort level v, that is, Solve for the optimal level of assistance effort v * ; S3. In the case of predicting patients' medical choices and the support strategies of tertiary hospitals, the regulator decides the transfer payment level T based on the maximization of social welfare S, that is, Solve for the optimal transfer payment level T * ; S4, T obtained in S3 * Substitute into S2 to get v * , v * and T * Substitute the obtained θ into S1 * That is the proportion of patients going to tertiary hospitals when the system is in equilibrium.

2. The hierarchical diagnosis and treatment optimization method based on the queuing game model according to claim 1 is characterized in that: The expected waiting time W1 of the tertiary hospital satisfies: where λ1 represents the number of patients going to the tertiary hospital; λ2 = Λ - λ1 represents the number of patients going to the community hospital.

3. The hierarchical diagnosis and treatment optimization method based on the queuing game model according to claim 1, characterized in that: The treatment failure rate of the community hospital satisfies: K(v)=ke -βv , where k represents the treatment failure rate of the community hospital without assistance; β represents the assistance efficiency of the tertiary hospital; v represents the assistance effort level of the tertiary hospital.

4. The hierarchical diagnosis and treatment optimization method based on the queuing game model according to claim 1, characterized in that: The proportion of patients going to tertiary hospitals θ * satisfy: where Δ = K(v)F - (1 - K(v))(p1 - p2), which can reflect the expected loss of each patient choosing a community hospital in the non-time dimension; The indifference point x of the patient's medical decision * =θ * When x * <θ * , patients can get higher utility by going to a tertiary hospital; if x * >θ * , patients can get higher utility by going to community hospitals; the number of patients going to tertiary hospitals Number of visits to community hospitals 5. The hierarchical diagnosis and treatment optimization method based on the queuing game model according to claim 1, characterized in that: The proportion of patients going to tertiary hospitalsθ * Closely related to the total number of patients Λ; when the patient scale is small, all patients entering the system will go to tertiary hospitals; when the total number of patients exceeds the threshold When θ , patients began to be diverted, and the proportion of patients going to tertiary hospitals was θ * As the level of support efforts v of the tertiary hospitals increases, it decreases; when the patient scale reaches When the number of patients arriving at tertiary hospitals exceeds the carrying capacity of tertiary hospitals.

6. The hierarchical diagnosis and treatment optimization method based on the queuing game model according to claim 1, characterized in that: The tertiary hospitals maximize the expected utility Π H Under the goal, determine the effort level v of providing assistance, where the expected utility includes: The total revenue obtained from providing treatment services to patients arriving at the tertiary hospital is λ1p1 + Kλ2p1; Cost of efforts to support community hospitals cv 2 , where c is the assistance cost coefficient; The transfer payment income Tv obtained from the government; Total utility of patients in the system That is, the optimization goal of the tertiary hospital is: where η ∈ (0, 1) represents the proportion of the public welfare goal in the operation goal of the tertiary hospital; 1 - η represents the proportion of the profit goal.

7. The hierarchical diagnosis and treatment optimization method based on the queuing game model according to claim 6, characterized in that: When the public welfare concern level η exceeds the threshold η1, the tertiary hospitals will spontaneously help the community hospitals, and the optimal level of support effort v * as follows: When η < η1, that is, when the tertiary hospital has a low public welfare concern goal: Otherwise: Among them, η1 satisfies the implicit function T0 satisfies the implicit function Indicates the minimum transfer payment requirements that tertiary hospitals are willing to provide under lower public welfare concerns; T1 satisfies the implicit function It indicates the share of unit transfer payments that can achieve the goal of all patients going to community hospitals; T2 satisfies the implicit function It means that when patients are successfully diverted, it can motivate tertiary hospitals to further increase their support efforts to improve the minimum transfer payment requirements for community hospitals’ cure rates. If the public welfare level of the tertiary hospital is low, when η < η1, it is defined as an economy-oriented hospital, otherwise it is a public welfare-oriented hospital.

8. The hierarchical diagnosis and treatment optimization method based on the queuing game model according to claim 1, characterized in that: The social welfare S includes: The operating income of the community hospital λ2p2; The total utility of patients entering the system: The transfer payment Tv provided by the regulator to incentivize the tertiary hospital. That is, the optimization problem of the regulator is: According to the objective function of the regulator, its optimal coordination condition can be obtained: The proportion of patients going to tertiary hospitals θ * and the optimal support effort level of tertiary hospitals v * , when η<η1, Λ1<Λ<Λ2, T * >0, and there is When η>η1, Λ1<Λ<Λ3, T * >0, and there is Otherwise, T * = 0. That is, the optimal unit subsidy cost T * Satisfy the following: When η < η1, that is, when the tertiary hospital has a low public welfare concern goal: Otherwise: Among them, Λ3<Λ2 and satisfies the implicit function 9. A hierarchical diagnosis and treatment optimization system based on a queuing game model, characterized in that: The optimization system includes: a selection module, an assistance strategy formulation module, a coordination strategy formulation module, and a game equilibrium module; The selection module is used to determine the medical treatment choice through the expected utility of the patient; The assistance strategy formulation module is used to solve the optimal assistance effort level according to the utility of the tertiary hospital itself; The coordination strategy formulation module is used to solve the optimal transfer payment level according to the maximization of social welfare; The game equilibrium module is used to obtain the proportion of patients arriving at the tertiary hospital in the system equilibrium state according to the transfer payment decision equilibrium and the assistance decision equilibrium.

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