Public and private healthcare coordination: An analysis of contract mechanisms based on subsidy payments

Highlights

• A novel model considering hospital preferences of patients based on their utility.

• Social utility is defined as a multi-objective function.

• Different contract mechanisms are compared based on social utility.

• Contract mechanisms are seen to be able to improve the healthcare system.

• Differentiated pricing mechanism improves the social utility significantly.

Abstract

Many healthcare systems are composed of public and private hospitals with different features. In public hospitals, patients generally obtain service at very low prices but there exist high waiting times and lower quality service. Whereas in private ones, although the prices are much higher, the waiting times are low and the level of quality perceived by the patients is high. It is observed that most of the patients prefer to go to the public hospital, mainly because of high prices in private hospitals. This causes overcrowding in public hospitals, while private hospitals are seen to be under-utilized and have excess capacity. The aim of this study is to suggest new contract mechanisms based on pricing and subsidy policies, that can be offered by the government to private hospitals in order to design a more balanced and efficient healthcare system for society. We develop a novel analytical model for patients’ preference between public and private hospitals and present different contract mechanisms based on this model. We determine the optimal parameters of the contracts and compare the results based on their effects on the healthcare system. Numerical results demonstrate that the proposed contract mechanisms can increase the total social utility significantly. In particular, when a contract mechanism based on differentiated subsidy payments is utilized, the expected waiting times in the system can be decreased and higher quality service can be obtained by the society in general without a significant increase in government expenditures.

Introduction

In various countries of the world, health services are handled by both public and private institutions. However, these institutions generally have different features in terms of the quality level of the services as well as the patients’ payments. Public hospitals generally give service at low prices, but there are often long waiting queues because of the large number of patients going to these hospitals. Due to the imbalance between demand and capacity, the quality and patient satisfaction levels at the public hospitals are seen to be low in general. On the other hand, private hospitals charge much higher prices but the service quality is high and waiting times are generally much smaller. In many countries, it is observed that most of the patients are dissatisfied with the healthcare services, especially in public hospitals, due to the long waiting times and low quality of service. Also, the doctors and the nurses in the public hospitals are seen to be overwhelmed with the very high number of patients. On the other hand, private hospitals are seen to have excess capacity due to a much lower demand because of their higher prices.

This study is motivated by the current state of many healthcare systems in different countries, where previously mentioned features about the quality, average waiting times, satisfaction and payment in the public and private hospitals are valid (Mou, 2012, Radman and Eshghi, 2018, Zhang et al., 2012, Zhou et al., 2017). For example, in Turkey, public hospitals are mostly very crowded and have very high waiting times. In addition the service quality at these hospitals are not perceived as very high. On the other hand, private hospitals are seen to offer much higher quality in service and have much lower waiting times. However, mainly due to high prices of private hospitals, most of the patients do not prefer them which leads to an imbalance in the system with overcrowding at public hospitals and excess capacity at private ones. We aim to provide a basis to design more balanced healthcare systems by applying new or modified public policies. Governments or social planners generally have the power to affect the healthcare system in various ways. Pricing policies, investment amounts, and service quality are some of the decisions that can be made to influence the system. Gupta and Mehrotra (2015) analyze the effects of the “bundled payments for care improvement” (BPCI) initiative introduced by The Centers for Medicare and Medicaid Services (CMS). They aim to determine how agencies like CMS can improve healthcare services through contracts. Mehta, Ni, Srinivasan, and Sun (2017) examine the characteristics of insurance plans and analyze how different cost-sharing structures can reduce the inefficiencies in healthcare systems. As a real life example, Turkish Social Security Agency (SGK) proposes a contract to the private hospitals that regulates their prices in return for a subsidy payment per patient. Each private hospital is free to reject this contract and they can set their prices freely, but they can not obtain any subsidy in that case. However, if they accept the contract, their prices will be regulated as defined in the contract and they obtain an additional subsidy payment from SGK for every operation they apply. This contract mechanism aims to direct more patients to private hospitals instead of public ones to decrease the imbalances in the system.

As in many service systems (e.g. Adida et al., 2016, Afèche, 2013, Zhan & Ward (2019)), the scheme of payments and subsidies affect the choices of patients, as well as performance and quality of healthcare systems (Dai and Tayur, 2019, Savva et al., 2019). In many healthcare systems, governments can make contracts with the private institutions that will regulate the benefit of all sides. Even though contract mechanisms are widely studied in supply chain management literature (e.g. Cai et al., 2019, Hu et al., 2019, Li et al., 2018, Taleizadeh et al., 2018, Wang et al., 2017, Zhou et al., 2018), they are not analyzed as extensively in health policy studies. Some studies for healthcare management have suggested models for public and private partnership in order to develop, finance and provide health infrastructure and services (Roehrich et al., 2014, Torchia et al., 2015, Wright et al., 2019). Barlow, Roehrich, and Wright (2013) propose new models for partnering European governments with the private sector to underwrite the costs of constructing and operating public hospitals and other healthcare facilities. The prices charged by the private hospitals can also be negotiated in these contracts and also the government can provide certain subsidies to the private institutions. In that case, more patients will prefer the private hospitals instead of the public ones and more patients can achieve better service from the private hospitals. In addition, the waiting times in the public ones will decrease and a more balanced system can be obtained. On account of this, we propose new contract mechanisms based on pricing and subsidy payments to induce public-private partnerships. The governments can propose these contracts to the private hospitals in order to obtain a more balanced healthcare system. These contract mechanisms are intended to increase the total social utility in the system, composed of both the total individual utilities of the patients and expenditures of the governments for healthcare operations.

In a healthcare system including both public and private hospitals, the patients make their choice among these hospitals based on their own utilities and this choice affects the system (Kumar & Bardhan, 2019). There are several studies in the literature of service systems that analyze the behavior of such strategic customers based on various queuing models (Afeche and Pavlin, 2016, Burnetas et al., 2017, Dimitrakopoulos and Burnetas, 2016, Guo and Hassin, 2011, Manou et al., 2017, Shone et al., 2013). In a similar way, we assume that the individuals are strategic patients and they make a choice between the public and private institutions based on their perceived quality level, expected waiting times and the payment amounts. Some of the patients in the population select the private hospital if the quality of service is more important for them than the payment and others choose the public ones if they do not want to pay the high fees, and do not care much about the lower quality service and higher waiting times. Radman and Eshghi (2018) and Zhang et al. (2012) investigate the choices of patients in a system consisting of health service providers with different characteristics. Hoel and Sæther (2003) design a model, where most of the healthcare services are publicly provided and there are long waiting times for several types of treatments, while in private healthcare the waiting times are small. They state that waiting time induces patients with high waiting costs to choose private treatment and thus reduces the cost of public health care that everyone pays for. They also show that even zero waiting time can be achieved at no cost at public healthcare services, the self-selection induced redistribution may imply that it is socially optimal to provide healthcare publicly with longer waiting times. Zhou et al. (2017) analyze the effects of government subsidy policies in a system with two different hospital quality levels. They propose models to solve problems that the governments face to provide affordable and equitable basic health care for people.

The influences of subsidy payments on patient choices and performances of healthcare systems are investigated only in a few studies in the literature. Qian, Guo, and Lindsey (2017) analyze the impacts of subsidy schemes on waiting times in public healthcare organizations. Qian and Zhuang (2017) state that with an appropriate amount of subsidies, it is possible to direct patients with high sensitivity to delay to private health service providers. These studies all assume a fixed subsidy payment that is applicable to all patients, however, as stated by Hoel and Sæther (2003), patients have different preferences and valuations for quality and waiting times. Price differentiation strategy is a proper strategy that can increase the profit when consumers have different tastes and valuations, which is implemented by airlines (Raza, 2015), hotels (Xu, Zhao, & Xu, 2014), insurance companies, etc. (Borsenberger et al., 2016, Gao et al., 2015, Wolk and Ebling, 2010). Detailed information about differentiated pricing exists in the literature of management science (Phillips, 2005, Talluri and Van Ryzin, 2006). Despite its positive impacts, there are not many studies in the healthcare management literature considering differentiated subsidizing and pricing policies. One of the aims of this study is to contribute to the healthcare management literature on this approach. We propose contract mechanisms considering differentiated subsidy payments in addition to fixed subsidy mechanisms and analyze the effects of such policies on the system results.

Different from the literature, we develop a novel model that defines patient preferences based on their own utility functions. We define the social utility as an objective function consisting of patients’ payments, expected waiting times, total service quality obtained by the society and the public expenses for healthcare operations. We first investigate a model in which there is no contract between the government and the private hospital. Then, we propose new contract mechanisms which include fixed and differentiated subsidy payments or financial incentives, and aim to increase patients’ satisfaction levels and decrease public expenses. We determine the optimal parameters of the contracts and analyze the effects of these contracts on the system results. In the next sections, we first describe the system and the developed models. Then, we explain the proposed mechanisms. In the numerical results section, based on a case study from Turkey we compare the models with each other and analyze the effects of the parameters on the system results. Finally, we present our conclusion and future work in the last section.