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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (12): 2445-2456    DOI: 10.3785/j.issn.1008-973X.2020.12.020
    
Referral coordination mechanism of gatekeeper healthcare system
Yue ZHANG(),Zhao GAO,Na LI*()
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
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Abstract  

A referral model with general hospitals (GH) and community health centers (CHC) was established to analyze the coordination problem of the gatekeeper healthcare system. The non-competitive and competitive models respectively studied the optimal referral strategies and the optimal contract forms from centralized decision-making and service payment contract cooperation, and provided the conditions for system coordination. Results show that reducing the unit service costs in the system can effectively improve the system, and competition can increase the referral threshold to promote community first diagnosis. The non-competitive and competitive systems for service payment contract coordination at different scales are feasible. The coordination efficiency of small-scale is better than that of large-scale in competitive system, then designing multiple small competitive hospitals can bring higher social efficiency.

Key words： gatekeeper system      healthcare system      referral decisions      coordination mechanism      competition     
Received: 09 December 2019      Published: 31 December 2020
CLC:  F 202  
Corresponding Authors: Na LI     E-mail: zy_0036@sjtu.edu.cn;nali-03@sjtu.edu.cn
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Yue ZHANG
Zhao GAO
Na LI
Cite this article:

Yue ZHANG,Zhao GAO,Na LI. Referral coordination mechanism of gatekeeper healthcare system. Journal of ZheJiang University (Engineering Science), 2020, 54(12): 2445-2456.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.12.020     OR     http://www.zjujournals.com/eng/Y2020/V54/I12/2445


“守门人”医疗系统中的转诊协调机制

为了探究“守门人”医疗系统的协调问题，建立系统内综合医院与社区医院间的转诊博弈模型，分别对非竞争型和竞争型的2种系统建模. 模型分别研究系统集中决策下的最优转诊阈值策略以及服务支付契约合作模式下的最优契约形式. 结论表明，降低系统内单位人员服务成本能够有效提升系统效用，引入竞争可以降低转诊率、促进社区医院首诊；非竞争与竞争型系统在不同规模下的服务支付契约对于实现系统协调均具有可行性，竞争系统下小规模设置的协调效率高于大规模设置的. 在医疗系统设计中若无法避免竞争的存在，设置多个小型竞争医院能带来更高的社会效率.


关键词： “守门人”系统,  医疗系统,  转诊博弈,  协调机制,  竞争 
Fig.1 Model 1：non-competitive referral coordination model
Fig.2 Model 2：competitive referral coordination model
医疗服务机构 SDF
情形1 情形2 情形3 情形4
CHC $\dfrac{1}{3}x + 1$ $3{x^2} + 1$ $3{e^x} - 2$ $3{e^x} - 2$
GH $\dfrac{1}{2}x + \dfrac{3}{2}$ $\dfrac{1}{2}x + \dfrac{3}{2}$ $\dfrac{1}{2}x + \dfrac{3}{2}$ $4{e^x} - \dfrac{5}{2}$
Tab.1 SDF settings for medical service institutions in different medical environment
方案 ${c_{\rm{w}}}$ ${c_{\rm{m}}}$ $c_{\rm{s}}^{{\rm{chc}}}$ $c_{\rm{s}}^{{\rm{gh}}}$
A 0.3 0.5 1/3 2/3
B 0.3 0.5 1/6 2/3
C 0.3 0.1 1/3 2/3
D 0.1 0.1 1/3 2/3
E 0.3 0.5 1/3 3/5
Tab.2 Parameters design for experiments′ scenes min
Fig.3 Total utility function in different scenes for small scale non-competitive model
Fig.4 Total utility function in different scenes for large scale non-competitive model
Fig.5 Perfect coordination solutions in different scenes for non-competitive model
就医环境情形 规模 $r_0^{ {\rm{NC*} } }$ ${\varPi ^{ {\rm{NC} } } }$ ${\omega _{\rm{p}}}^*$ $r_{{\rm{np}}}^{ {\rm{NC*} } }$ $\omega _{{\rm{np}}}^{ {\rm{NC*} } }$ ${\pi ^{{\rm{gh}}}}{\rm{ + }}{\pi ^{{\rm{chc}}}}$ ${\pi ^{{\rm{chc}}}}$ ${\pi ^{{\rm{gh}}}}$ $e$/%
1 S 0.459 27.515 2.886 0.627 2.795 27.345 11.690 15.655 99.38
L 0.469 295.538 2.949 0.644 2.846 293.723 125.748 167.975 99.39
2 S 0.358 27.353 2.827 0.653 2.370 26.459 9.385 17.074 96.73
L 0.374 293.980 2.898 0.663 2.449 285.528 104.640 180.888 97.12
3 S 0.197 26.905 2.752 0.583 1.998 25.168 6.100 19.068 93.54
L 0.228 289.617 2.835 0.598 2.090 273.302 74.047 199.255 94.37
4 S 0.534 9.213 2.109 0.730 1.631 8.585 4.847 3.738 93.18
L 0.554 125.156 2.191 0.740 1.740 119.406 62.493 56.913 95.41
Tab.3 Coordination analysis table for non-competitive GK model
Fig.6 Total utility function in different scenes for small scale competitive model
Fig.7 Total utility function in different scenes for large scale competitive model
Fig.8 Perfect coordination solutions in different scenes for competitive model
$\gamma $ β $r_0^{\rm{C*}}$ ${\varPi ^{\rm{C}}}$ $\omega _{{\rm{p}},i}^{{C*}}$ $r_{{\rm{np}}}^{\rm{C*}}$ $\omega _{{\rm{np}},i}^{{C*}}$ $2{\pi ^{{\rm{gh}}}}{\rm{ + }}{\pi ^{{\rm{chc}}}}$ $2{\pi ^{{\rm{gh}}}}$ ${\pi ^{{\rm{chc}}}}$ $e$/%
0.2 0.5 0.379 26.440 2.801 0.180 2.989 26.128 6.683 12.762 98.82
0.6 0.379 26.440 2.801 0.182 2.988 26.133 6.689 12.755 98.84
0.7 0.379 26.440 2.801 0.183 2.987 26.135 6.692 12.751 98.85
0.3 0.5 0.379 26.440 2.801 0.173 2.993 26.108 6.657 12.793 98.74
0.6 0.379 26.440 2.801 0.177 2.991 26.120 6.672 12.776 98.79
0.7 0.379 26.440 2.801 0.179 2.989 26.126 6.680 12.766 98.81
0.4 0.5 0.379 26.440 2.801 0.159 2.999 26.064 6.607 12.850 98.58
0.6 0.379 26.440 2.801 0.170 2.994 26.097 6.645 12.808 98.70
0.7 0.379 26.440 2.801 0.175 2.992 26.112 6.662 12.788 98.76
Tab.4 Coordination analysis for small scale compositing GK model
$\gamma $ $\beta $ $r_0^{\rm{C*} }$ ${\varPi ^{\rm{C} } }$ $\omega _{{\rm{p}},i}^{{C*} }$ $r_{{\rm{np}}}^{\rm{C*} }$ $\omega _{{\rm{np}},i}^{{C*} }$ $2{\pi ^{{\rm{gh}}}}{\rm{ + }}{\pi ^{{\rm{chc}}}}$ ${\pi ^{{\rm{chc}}}}$ $2{\pi ^{{\rm{gh}}}}$ $e$/%
0.2 0.5 0.380 291.104 2.890 0.126 3.131 286.244 71.630 142.985 98.33
0.6 0.380 291.104 2.890 0.128 3.130 286.297 71.694 142.909 98.35
0.7 0.380 291.104 2.890 0.129 3.130 286.330 71.735 142.861 98.36
0.3 0.5 0.380 291.104 2.890 0.119 3.135 286.004 71.345 143.314 98.25
0.6 0.380 291.104 2.890 0.123 3.133 286.143 71.508 143.127 98.30
0.7 0.380 291.104 2.890 0.125 3.132 286.217 71.598 143.021 98.32
0.4 0.5 0.380 291.104 2.890 0.105 3.142 285.488 70.774 143.940 98.07
0.6 0.380 291.104 2.890 0.116 3.137 285.879 71.202 143.475 98.21
0.7 0.380 291.104 2.890 0.121 3.134 286.049 71.397 143.254 98.26
Tab.5 Coordination analysis for large scale competitive GK model
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