Apply Games Theory to new hospital entry in to Taiwan ’s hospital market

1. Healthcare Economics 2016July 25-26, 2016 Berlin, Germany Apply Games Theory to new hospital entry into Taiwan’s hospital market Tian-Shyug Lee Chung-Yeh Deng Shu-Fang Tseng (Reporter)

2. Outline • Foreword • Materials and data • Methods • Results • Conclusion

3. Foreword1/2 • Taiwan’s health care industry is facing a period of competition between healthcare institutions, shortages in specialized labor, and increasing prevalence of cosmetic medicine. • Based on diagnosis-related groups (DRGs) and the global budget policy of Taiwan’s healthcare system, hospital coopetition is facing the prisoner’s dilemma. • In this study, we empirically analyzed the perspectives of industrial and medical economics and explored how new hospital should optimally respond to games in the medical center market to achieve a new equilibrium.

4. Foreword2/2 • Regarding the ownership of Taiwan’s hospital market in 2009, the number of private hospitals accounted for 84.07%; the number of beds in these hospitals accounted for only 65.87% of the total number of beds. There were fewer public medical college affiliated hospitals (1.21%) than private medical college-affiliated hospitals (2.82%); however, public medical college-affiliated hospitals had more beds (12.87% vs. 6.08%). • Ownership structure can be used to distinguish between vertical and horizontal integration in healthcare systems. • The annual budget for Taiwan’s National Health Insurance (NHI) was determined by using healthcare service costs and the growth rate of service volume divided by actual service volume; in other words, the change in total healthcare service volume influenced payment amount and floating point values. The equation is as follows: E=Σ[(S) ×(UP)] ×[FPV], where E denotes expenditure, S denotes service volume, UP denotes unit price, and FPV denotes floating point value.

5. Materials and data • Statistics from the Taiwan Ministry of Health and Welfare were used to determine the statuses of medical institutions and hospital medical services for 2007–2011. The extracted medical resource are listed as follows: inputs (hospital beds, doctors, nurses, and medical personnel); hospital output (outpatients, emergency patients, and patients discharged from hospital); medical device usage (e.g., X-ray computed tomography (CT), magnetic resonance imaging (MRI), left atrial enlargement (LAE), positron emission tomography (PET), and extracorporeal shock wave lithotripsy (ESWL)); and medical prescriptions. • We examined the time cost for the distance between a medical center and consumers’ residences by using surrogate variables data that were retrieved from the websites of the Taiwan Ministry of the Interior (distribution of population age, and education level of people older than 15 years), the Directorate-General of Budget, Accounting, and Statistics (population, land, and income as well as population density), and National Statistics (household income and expenditure).

6. Methods • We conducted descriptive statistical analysis, performed a cluster analysis, constructed a negative binomial regression model, determined the CR4 market share in Taiwan’s medical center market, investigated sequential games and Hotelling model regarding the hospital market and the “tragedy of the commons.”

7. Results • From 2007 to 2011, 60% of 19 medical centers, 7 public (36.8%) and 12 private (63.2%), were operating in the northern metropolitan area in Taiwan. These possessed substantial resources (80% of all hospital beds, extensive CT, MRI, LAE, PET, and ESWL services; a high number of medical prescriptions; and a substantial labor input) and registered high output; however, the market share of individual medical centers was low (10%–20%). • Hospitals affiliated with private medical colleges had a low market share but high number of beds. Private medical centers were more competitive than public. Outpatient visits to medical centers were consistently high, but the distribution of emergency patient visits was disproportionate among all medical centers (e.g., 0.99% of MC01 emergency patients in 2009). In both public and private medical centers, LAE, PET, and ESWL equipment was used for a high number of patients, and a single type of equipment was used for 40%. Regarding the CR4 measure, the medical centers with the highest total output were MC12, MC04, MC01, and MC15. In 2000 and 2009, 40% of the total budget for healthcare insurance was allotted to 3.00%–4.73% of medical centers. According to CR4 of medical centers in Taiwan’s market were highly competitive and low concentration.

8. Descriptive statistics1/2

9. Descriptive statistics 2/2

10. Clusters of medical center in Taiwan 2007-2011(Input Variables)

11. Clusters of medical center in Taiwan 2007-2011 (Output Variables)

12. Clusters of medical centerin Taiwan 2007-2011 (expensive medical equipment )

13. Negative binomial regression • The 19 medical centers in the hospital market were categorized into various independent groups, and p number of λ-linear regression and exponential functions were generated. The binomial regression models is as follows: log(ni)= log(Li)+β0+β1xi1+β2xi2+…..+βpxip+εi. Eight generalized linear negative binomial regression models (Models 1-1 to 1-4 and Models 2-1 to 2-4) were established using the following variables (based on data for the 2011 fiscal year): number of doctors; number of beds; number of hospitalizations; number of outpatient services; number of emergency room visits; number of physical examinations; number of patients who underwent CT, MRI, LAE, PET, or ESWL examinations; and Li (frequency/year). • Considering Model 1-2 (χ2=10.113, Sig=.006,based on data for the 2008 fiscal year): number of doctors, <500; number of patients discharged from hospital, <30,000; number of clinic visits, 1,000,001 to 1,500,000; number of emergency room visits, <50,000 (MD (mean difference) = 386.00/ -69.00, p = .000). The interaction effect of quasilikelihood under independence model criterion (QICC) with the MD was significant. This model was used to analyze the games.

14. Games • Participants: According to ownership structure, scale, and ranking, the participants who ranked between 10th and 19th (most ranked 13th and 14th); those located in near new hospitals or in an area where there was only one medical center; and 19 medical centers (y，y = y1, y2,…, y19) in the market. The participant (xi，i=1,2,…,19) set was H, in which , and H = (1, 2, …, 19). • Information: The information included the number of patients discharged from hospital, number of clinic visits, number of emergency visits, service volume of expensive medical equipment usage, number of doctors, number of beds, and number of medical personnel for the 2007–2011 period. In addition, information on highly competitive contestants (as determined through a cluster analysis on capacity [number of beds], medical personnel [physician] allocation) as well as on low output participants featuring high competitiveness were included. • Common knowledge: Within the geographical location of the healthcare demand market (New Taipei City), and the gross income and disposable income 45–54-year-olds with a bachelor’s degree was higher for men (NT$568,264; 1 US dollar = 31.890 TWD in July 15, 2016) than for women (NT$423,559; 57.07:42.93) in the new hospitals. The number of men younger than 30 years whose education level was below elementary school differed significantly from the number of women. Considering the rival participants, expenditure on medical insurance (NT$110,241) was higher than disposable incomes (Levels I to V) in new hospitals (NT$1,790,474 > NT$1,748,857); the wealth gap between rich and poor people was large (5.34 > 4.80). The incomes of medical consumers in new hospitals were low (NT$899,146 < NT$995,507); however, their medical expenditures were high (NT$110,241 > NT$ 87,354). The common knowledge thus comprised indicators related to the medical requirements of consumers.

15. Sequential Game • Leaders and followers: the CR4 medical centers were considered leaders Ai(i=1,2,3,4) and the other Bi(i=1,2,…,15) medical centers were considered followers. Hospital capacity and service volume that the hospitals were capable of responding to (x1 and x2) were calculated on the basis of the number of patients discharged (qa= qa1,qa2,qa3,qa4 and qb= qb1,qb2,…,qb15) from Hospital j. Fj(p) represents a cumulative density function (CDF). The results showed that the leaders earned double the payoff of the followers (726.5 > 350.25); in addition, almost twice as many patients were discharged from leader hospitals than from follower hospitals (26 > 17.5). The CDF of leaders are: and followers are , . • Cooperation or noncooperation strategies: to determine the strategy and substrategy regarding the increase–nonincrease of hospitalization volumes (1467.05 persons) of two medical centers and four game strategies were increase–increase, increase–nonincrease, nonincrease–increase, and nonincrease–nonincrease. A total of eight CDFs (F2(P)n1=0.00, F2(P)n2=0.00, F2(P)n3=0.00, F2(P)n4=0.00, and F1(P)o1=0.00, F1(P)o2=0.00, F1(P)o3=0.00, F2(P)o4=0.00) were obtained.. Both new hospitals and rivals adopted volume increase strategies and increased the number of patient discharges to maximize their payoff; they also reduced their intake of inpatients to avoid payment reduction. These strategies negatively influenced the original market equilibrium and caused a prisoner’s dilemma.

16. Hotelling model • Hospitals in Taiwan provide similar products, and share similar characteristics; the NHI participation is nearly 100%; patients were required to pay for only 4.8% of all medical services. Regarding total payments, individual hospitals were often concerned about a fall in point values; accordingly, hospitals often competed for patients and time costs became a crucial factor in how consumers selected which hospital to visit. A competition (Hotelling) model that included a rival (x1) and a new hospital (x2) was constructed. Regarding the medical needs of consumers and hospital profits, the results showed that x1 > x2. This means that the hospitals were not substitutable. Patients were concerned about medical services and time costs and reduced their requirements for x1 (D1 = x1 = -10.61). • The demand function are and profit function are , where two hospital are p1 and p2, t denotes time cost, c denotes unit of product cost.

17. Tragedy of the Commons • The tragedy of the commons means that the total Nash equilibrium service volume of production games (G*) was greater than the total optimal societal service volume (G**). In other words, the optimal marginal costs of hospitals were less than societal marginal costs. For 2011, the results for 20,001–30,000 patients receiving a CT examination and 5,001–10,000 patients receiving an MRI examination in Model 2-4 were consistent (B=.123, SE= 0.0397,χ2=9.630, p=0.002), and the means, and differences (1288.33/(-447.83) were significant (p= .05). The optimal hospital service volume (GCT* = 0.708 and GMRI* = 0.71) was greater than the optimal societal service volume (GCT** = 0.592 and GCT** = 0.593). Therefore, the tragedy of the commons was identified based on the excessive number of patients who underwent CT and MRI examinations. • where G denotes product, π are strategy of profit. • and are volume of production (G*) and societal service volume (G**).

18. Conclusion • According to the results of the leader–follower game, the payoff of the leader hospital and number of patients discharged from the leader hospital were double those of the follower hospital. According to the competition model, the two hospitals were not substitutable; patients were concerned about medical services and time costs and reduced their requirements for x1. • If the NHI Administration maintained the minimum payment point value for the basic quality of medical care provided by hospitals, the following two scenarios may occur: a region with a new hospital but without a major hospital, in which the wealth gap between rich and poor people is large, and reduced incidence of the cost and supplier-induced demand. Accordingly, medical demand and excessive hospital service volumes might increase. This leads to the tragedy of the commons, and the point values of hospitals would decline. • In summary, new hospitals negatively influenced the equilibrium of the medical center market and the payoff equilibrium solution of cooperation or noncooperation strategies. Accordingly, excessive or little use of resources would influence the point values of services, and a prisoner’s dilemma would occur.

19. Thanks for pay attention