考虑复诊患者异质性的线上线下综合医疗定价与报销比例优化

doi:10.16381/j.cnki.issn1003-207x.2024.0595

Abstract

Abstract:

As a novel medical service， telemedicine contributes to alleviating the difficulty of seeing a doctor for the patients and the unbalanced distribution of medical resources in the traditional offline medical system in China. For a medical service system composed of the government， a hospital， and patients， the geographically heterogeneous patients are considered that face to visit the clinic periodically with chronic disease. A three-stage sequential game model is constructed and the equilibrium solution of the government’s medical reimbursement ratio and hospital’s medical service price for the mixed online and offline medical service is deduced. Benchmarking the traditional single offline medical service， through theoretical analysis and numerical experiments， the impact of clinical feasibility， fixed online setting fees， etc.， on patients’ choice of medical treatment， hospital profits， social welfare， etc.， after the adoption of telemedicine is compared and analyzed. It shows that the government’s medical reimbursement ratio is positively correlated with the hospital’s medical service price， and the adoption of telemedicine does not change the relationship between offline medical price and reimbursement ratio. The mixed online and offline medical service is a potential and efficient approach to improve social welfare and realize that all patients visit the clinic. Improving the method and technology of telemedicine by artificial intelligence， reducing the membership fee of telemedicine， decreasing the setting fees of patients’ hardware and software equipment， and developing the traffic system to control the traffic cost are all conducive to the implementation of telemedicine.

Key words: telemedicine service, heterogeneous patients, medical service pricing, reimbursement policy, social welfare

CLC Number:

F294

Xiaoyan Zhu,Jing Cui,Ting Zhang, et al. Optimum of Pricing and Reimbursement Policy for Mixed Online and Offline Medical Service Considering Heterogeneous Patients[J]. Chinese Journal of Management Science, 2026, 34(6): 239-249.

Figures/Tables 8

符号	含义
模型参数
$α$	单位距离的交通成本
$ρ$	远程医疗初始设置成本
$θ$	线上诊疗的比例，即远程医疗适用性因子
$β 1$	线下医疗成本
$β 2$	线上医疗成本
决策变量
$p 1$	线下医疗价格， $p 1 > β 1$
$p 2$	线上医疗价格， $p 2 > β 2$
$r 1$	线下医疗报销比例
$r 2$	线上医疗报销比例
其他
$x$	患者与医院之间的距离
$f (x)$	患者到医院距离的概率密度函数
$n 0, n 1, n 2$	未就诊、线下就诊、线上就诊患者人数比例
$U, U 1 x, U 2 x$	患者总效用函数、全程线下就诊患者效用函数、混合线上就诊患者效用函数
$R$	医院利润函数
$W$	社会福利函数

参数	线上线下综合医疗模式	单一线下医疗模式
情形	图2（a）： $0 ≤ x 0 < x 1 < x 2 ≤ 1$	图2（b）： $0 ≤ x 1 ≤ 1$
条件	$y 2 < 1 - ρ θ$ ， $y 1 - y 2 ≤ ρ θ$ ， $(1 - θ) y 1 + θ y 2 ≥ 1 - ρ - (1 - θ) α 2$	$y 1 ≥ 1 - α$ ， $y 1 ≤ 1$
$n 1$	$ρ α θ - y 1 α + y 2 α$	$1 - y 1 α$
$n 2$	$θ - ρ α θ (1 - θ) - y 2 α (1 - θ)$	$0$
$n 0$	$1 - 1 - ρ α (1 - θ) + y 1 α + θ y 2 α (1 - θ)$	$1 - 1 - y 1 α$
$U$	$(1 - y 1) 2 2 α + (θ - ρ - θ y 2) 2 2 α θ (1 - θ)$	$(1 - y 1) 2 . 2 α$

情形

参数条件

r 1 *, r 2 *

p 1 *, p 2 *

n 1 *, n 2 *, n 0 *

$12 < β 1 < 1$ ，

$m a x (1 - α - β 1 θ + α + β 1 - β 2$ , $β 1 - β 2$ ,

$1 - 2 β 2) < ρ θ < 1 - β 2$

$r 1 * = 1 β 1 - 1$ ，

$r 2 * = θ - ρ θ β 2 - 1$

$p 1 * = β 1 2 + 1 2 1 - r 1 *$

$p 2 * = β 2 2 + 1 - ρ / θ 2 (1 - r 2 *)$

$n 1 * = ρ α θ + β 2 - β 1 α$ ，

$n 2 * = 1 - ρ - β 2 α (1 - θ) - ρ α θ$ ，

$n 0 * = 1 - β 2 - β 1 α - 1 - ρ - β 2 α (1 - θ)$

$m a x (1 - α - β 1 θ + α, 1 - 2 β 1 2 θ) + β 1 - β 2 < ρ θ ≤ β 1 - β 2$ ，

$1 + 2 θ β 1 - β 2 - 2 β 1 < 2 θ - 1 ρ θ < 1 + 2 θ β 1 - β 2 - 2 β 1 + β 2$

$r 1 * = 2 θ - 1 + 1 - 2 ρ - 2 θ β 2 β 1$ ,

$r 2 * = 1 - 2 θ + ρ θ β 2 + 1 - 2 ρ - 2 (1 - θ) β 1 β 2$

$n 1 * = 0$ ，

$n 2 * = β 2 - β 1 α + 1 - ρ - β 2 α 1 - θ,$

$n 0 * = 1 - β 2 - β 1 α - 1 - ρ - β 2 α 1 - θ$

m a x (1 - 2 α - β 1 2 θ + α + β 1 - β 2, β 1 - β 2) < ρ θ < m i n (0, 1 - 2 α 2 θ, 1 - α - β 1 θ) + α + β 1 - β 2

，

1 - 2 (1 - θ) (α + β 1 - β 2) - β 2 < (2 θ - 1) ρ θ < 1 - 2 (1 - θ) (α + β 1 - β 2)

$r 1 * = 1 - 2 θ + 2 α 1 - θ + 2 θ β 2 + 2 ρ - 1 β 1,$

$r 2 * = 2 θ - 1 - ρ θ β 2 + 2 α + β 1 1 - θ + 2 ρ - 1 β 2$

$n 1 * = ρ α θ + β 2 - β 1 α,$

$n 2 * = 1 - ρ α θ - β 2 - β 1 α,$

$n 0 * = 0$

1 - β 1 2 < α 1 - θ < 12

1 - 2 α (1 - θ) - β 2 < ρ θ < m i n (β 1 - β 2, 1 - α - β 1 θ + α + β 1 - β 2, 1 - 2 α 1 - θ)

$r 1 * = 1 - 1 - 2 α (1 - θ) β 1$ ，

$r 2 * = 1 + ρ θ β 2 - 1 - 2 α 1 - θ β 2$

$n 1 * = 0$ ，

$n 2 * = 1,$

$n 0 * = 0$

$m a x (- 2 α 1 - θ, 1 - θ 1 - 2 α - β 1 θ + 1 - β 2$

$< ρ θ < m i n 0, 1 - θ 1 - 2 α θ, 2 1 - θ 1 - α - β 1 θ$

$+ 1 - β 2$ ， $(2 θ - 1) ρ θ ≤ 1 - 2 (1 - θ) (α + β 1 - β 2) - β 2$

$r 1 * = 1 + 2 α β 1 - 1 - θ β 2 - ρ 1 - θ β 1,$

$r 2 * = 0$

$n 1 * = 1 - 1 - ρ - β 2 2 α 1 - θ + ρ 2 α θ$ ,

$n 2 * = 1 - ρ - β 2 2 α (1 - θ) - ρ 2 α θ$ ，

$n 0 * = 0$

$ρ θ < m i n (- α 1 - θ, 1 - θ 1 - 2 α - β 1 θ)$

$+ 1 - β 2$ ， $α (1 - θ) < 1 - β 1$

$r 1 * = 0,$

$r 2 * = 0$

$p 1 * = 1 - α 1 - θ$ ,

$p 2 * = 1 - α 1 - θ - ρ θ$

$n 1 * = 0,$

$n 2 * = 1,$

$n 0 * = 0$

情形

参数条件

r 1 *

p 1 *

n 1 *, n 0 *

12 < β 1 < 1,1 - β 1 ≤ α ≤ 1

r 1 * = 1 β 1 - 1

p 1 * = β 1 2 + 1 2 (1 - r 1 *)

n 1 * = 1 - β 1 α

，

n 0 * = 1 - 1 - β 1 α

$12 < β 1 < 1$ 且 $1 - β 1 2 < α < 1 - β 1$ ，

或 $β 1 ≤ 12$ 且 $1 - β 1 2 < α < 12$

r 1 * = 1 - 1 β 1 + 2 α β 1

n 1 * = 1, n 0 * = 0

α ≤ 1 - β 1 2

r 1 * = 0

p 1 * = 1 - α

n 1 * = 1, n 0 * = 0

医疗模式	情形	全程线下自付费用	混合线上自付费用
线上线下综合	1（a）	$β 1$	$(1 - θ) β 1 + θ β 2$
	1（b）	$ρ + (1 - θ) β 1 + θ β 2$	$(1 - θ) β 1 + θ β 2$
	1（c）	$1 - ρ - 1 - θ α + θ (β 1 - β 2)$	$1 - ρ - 1 - θ α$
	1（d）	$1 - 1 - θ α$
	1（e）	$2 - θ 1 + β 2 - ρ 2 1 - θ - α$
	1（f）	$1 - 1 - θ α$
单一线下	2（a）	$β 1$	—
单一线下	2（b）, 2（c）	$1 - α$	—

References 20

[1]	张丽莉，胡圆圆，李丽，等.我国互联网医院发展面临的主要问题及对策分析［J］.中国卫生质量管理，2021，28（9）：1-3.
	Zhang L L， Hu Y Y， Li L， et al. Analysis of main problems and countermeasures in the development of internet hospitals in China［J］. Chinese Health Quality Management，2021，28（9）：1-3.
[2]	潘毅，杨郁青，夏云. 上海市三级综合医院试点“互联网+”医疗服务纳入医保支付的效果分析［J］. 现代医院， 2023， 23（1）： 18-20.
	Pan Y， Yang Y Q， Xia Y. An analysis of the effect of “Internet +” medical services incorporated into medical insurance payment in tertiary general hospitals in Shanghai［J］. Modern Hospitals， 2023， 23（1）： 18-20.
[3]	Ma Y， Zhao C， Zhao Y， et al. Telemedicine application in patients with chronic disease： A systematic review and meta-analysis［J］. BMC Medical Informatics and Decision Making， 2022， 22（1）： 105.
[4]	Van Enst W A， Weng Y C， Wanten S A C， et al. Is telemedicine suitable for patients with chronic inflammatory skin conditions？ A systematic review［J］. Acta Dermato-Venereologica， 2024， 104： 23901.
[5]	Song S H， Yuan B B， Zhang L Y， et al. Increased inequalities in health resource and access to health care in rural China［J］. International Journal of Environmental Research and Public Health， 2019， 16（1）： 49.
[6]	Alam M S， Tabassum N J， Tokey A I. Evaluation of accessibility and equity to hospitals by public transport： Evidence from six largest cities of Ohio［J］. BMC Health Services Research， 2023， 23（1）： 598.
[7]	Barbosa W， Zhou K， Waddell E， et al. Improving access to care： Telemedicine across medical domains［J］. Annual Review of Public Health， 2021， 42： 463-481.
[8]	李忠萍，王建军. 分级诊疗体系中优质服务能力再配置决策与利益共享协调机制设计［J］. 中国管理科学， 2023， 31（4）： 205-217.
	Li Z P， Wang J J. High-quality service capacity reallocation decision and profit-sharing coordination scheme design in the hierarchical healthcare systems［J］. Chinese Journal of Management Science， 2023， 31（4）： 205-217.
[9]	Wang J J， Li Z P， Shi J， et al. Hospital referral and capacity strategies in the two-tier healthcare systems［J］. Omega， 2021， 100： 102229.
[10]	Wang X， Zhang Z， Yang L， et al. Price and capacity decisions in a telemedicine service system under government subsidy policy［J］. International Journal of Production Research， 2021， 59（17）： 5130-5143.
[11]	Guo P， Tang C S， Wang Y， et al. The impact of reimbursement policy on social welfare， revisit rate， and waiting time in a public healthcare system： Fee-for-service versus bundled payment［J］. Manufacturing & Service Operations Management，2019，21（1）： 154-170.
[12]	陈妍，周文慧，华中生，等. 面向延时敏感患者的转诊系统定价与能力规划［J］.管理科学学报，2015，18（4）： 73-83.
	Chen Y， Zhou W H， Hua Z S， et al. Pricing and capacity planning of the referral system with delay-sensitive patients［J］. Journal of Management Sciences in China， 2015， 18（4）： 73-83.
[13]	甘筱青，尤铭祥，胡凯. 医保报销比例差距、患者行为选择与医疗费用的关系研究——基于三阶段动态博弈模型的分析［J］. 系统工程理论与实践， 2014， 34（11）： 2974-2983.
	Gan X Q， You M X， Hu K. Reimbursement gap， patient behavior and medical expenses： A three-stage dynamic game analyses［J］. Systems Engineering —Theory & Practice， 2014， 34（11）： 2974-2983.
[14]	蔡雁岭，张孝鹏，石金铭，等. 远程医疗背景下医生和患者行为选择演化分析［J］. 中国医院管理， 2019， 39（9）： 15-19.
	Cai Y L， Zhang X P， Shi J M， et al. Evolution analysis of doctors and patients’ behavior choice under the background of telemedicine［J］. Chinese Hospital Management， 2019， 39（9）： 15-19.
[15]	王文娟，王季冬. 过度医疗与转诊制：一个排队论下的博弈模型［J］.管理科学学报，2019， 22（2）： 63-76.
	Wang W J， Wang J D. Overtreatment and referral systems： A game embedded in a queuing model［J］. Journal of Management Sciences in China， 2019， 22（2）： 63-76.
[16]	Qian Q， Zhuang W. Tax/subsidy and capacity decisions in a two-tier health system with welfare redistributive objective［J］. European Journal of Operational Research， 2017， 260（1）： 140-151.
[17]	孔乐佳，侯玉梅，郑迪文. 基于动态博弈的远程医疗政策与患者社会福利研究［J］. 中国管理科学， 2023， 31（1）： 176-186.
	Kong L J， Hou Y M， Zheng D W. A study of telemedicine policy and patients’social welfare based on dynamic game［J］. Chinese Journal of Management Science， 2023， 31（1）： 176-186.
[18]	Sirintrapun S J， Lopez A M. Telemedicine in cancer care［J］. American Society of Clinical Oncology Educational Book， 2018（38）： 540-545.
[19]	Shores M M， Ryan-Dykes P， Williams R M， et al. Identifying undiagnosed dementia in residential care veterans： Comparing telemedicine to in-person clinical examination［J］. International Journal of Geriatric Psychiatry， 2004， 19（2）： 101-108.
[20]	Rajan B， Tezcan T， Seidmann A. Service systems with heterogeneous customers： Investigating the effect of telemedicine on chronic care［J］. Management Science， 2019， 65（3）： 1236-1267.

Optimum of Pricing and Reimbursement Policy for Mixed Online and Offline Medical Service Considering Heterogeneous Patients

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