In 1995, Taiwan launched National Health Insurance (NHI) that covers 99% of Taiwan's 23 million people with a single-payer universal healthcare scheme that ensures that every resident has access to quality, affordable medical care. The comprehensive coverage includes inpatient, outpatient, dental, and home nursing care, prescription drugs, and traditional Chinese medicine. In addition, 92% of clinics and hospitals are contracted to NHI, and patients have a free choice of doctors or hospitals. Hence, patients can go directly to a medical center with a very low extra copayment [1]. Initially, the Bureau of National Health Insurance (BNHI) reimbursed healthcare providers on a fee-for-service basis and then implemented a global budget system gradually to each of the major healthcare sectors covered. In addition, the Diagnosis-Related Group payments system in Taiwan (Tw-DRG) was introduced in 2009 to control costs and enhance medical efficiency under the universal coverage, single-payment insurance system: National Health Insurance (NHI).
According to the Taiwan Statistics of Medical Care Institution's Status & Hospital Utilization 2018, the number of beds medical centers owned accounts for 24% of the total number of beds, 44% of doctors, and 34% of non-physician medical staff. These resources are used to cover 27% of the entire hospitalization days in Taiwan (https://www.mohw.gov.tw/lp-4932-2.html). However, different medical centers were established and developed from diverse backgrounds, and include public, private, and foundation hospitals. For example, among the foundation hospitals, the business philosophies differ because of the ownership background, and all may affect the hospitals' performance.
Increasing demands for greater accountability require managers to give more attention to hospital performance. Charnes and Banker proposed Data Envelopment Analysis (DEA) initially and this model is referred to commonly as a CCR model [2, 3]. It is a linear programming approach to measure and evaluate the relative efficiency of similar decision-making units (DMUs). DEA can manage multiple inputs and outputs simultaneously without any assumptions about the data distribution. The DMUs on the DEA frontier are those with maximum output levels for given input levels or minimum input levels for given output levels. DEA provides efficiency scores for individual units as their technical efficiency measure, with a score of one assigned to the frontier (efficient) units.
DEA has been a method suggested to evaluate the efficiency of decision-making units (DMUs) in different sectors, including the health sector [4, 5]. The classical DEA models—CCR and BCC—are the most popular models used to assess the efficiency of hospitals, other healthcare facilities, and healthcare systems worldwide. Based upon these models, hospital performance has been used popularly to compare an estimated efficient frontier comprising the best-performing hospitals [6, 7]. Leleu et al. adopted the DEA approach to investigate the efficiency of private hospitals in the United States and the factors that affect it and found that hospitals located in more competitive markets were more efficient than those located in less competitive markets [8]. Some European researchers have performed DEA to measure the efficiency of public healthcare systems and the healthcare industry in general [9, 10]. Jiang et al. employed the DEA model to evaluate hospitals' efficiency and effectiveness before and after healthcare reforms were implemented in China, and found that reform did not improve the efficiency of hospital operations in Chia to any great extent [11]. Nakata et al. adopted the standard DEA to calculate each surgeon's technical efficiency in Japan and then demonstrated the effect of surgeons' revenue as a proxy variable in technical efficiency results [12].
However, classical DEA models, which are referred to as static models, ignore time effects and the inefficiencies of an organization's internal processes [13]. Even when time has been considered, DEA models were used to evaluate the efficiency of each time period separately or each DMU was treated at a different time period as a separate unit [14, 15]. Thus, the traditional models ignore changes in efficiency over time and carry-over effects, and the connecting activities between terms are not accounted for explicitly [16]. Hence, performance analyses that address dynamic changes in efficiency over time are demanded in many applications. Färe et al. developed the DEA-based Malmquist productivity index with the CCR model [17, 18]. The DEA-based Malmquist productivity is a combined index that decomposes the productivity change in DMUs over time into catch-up and innovation (frontier-shift) effects. These models have inputs and outputs for each term, but they do not account explicitly for the effect of carry-over activities between two consecutive terms.
The Malmquist index is the most popular method to measure efficiency changes over time; however, this approach neglects carry-over activities between two consecutive terms, and focuses only on the local optimization in each period, even if these models can take into account the time change effect. In the real world, long-term planning and investment are always a subject of great concern to businesses; hence, a single-period optimization model cannot evaluate performance perfectly. To cope with the long-term issue, the dynamic DEA model incorporates carry-over activities into the model and allows us to measure period-specific efficiency based upon the long-term optimization during the entire period.
The theoretical concept of dynamic DEA, DDEA were introduced by Tone and Tsutsui [14, 19]. Compared to the classical DEA model, this model allows the transition elements between subsequent observations of activities and establishes the interdependence between periods. Thus, the DDEA model can quantify the dependence between periods attributable to dynamic factors using specific elements that include information, characteristics of organizational systems, their physical structure, etc. [20]. The advantage of DDEA is that it can use carry-over activities as constraints between periods in efficiency evaluation, which play a significant role in measuring efficiency during consecutive periods. Importantly, in this model, an output from one period is treated as an input for the following period.
Hung et al. employed the DDEA model to evaluate the performance of Taiwanese business groups [21]. Kawaguchi et al. estimated the dynamic changes in efficiency based upon current reforms’ policy effects in Japan's municipal hospitals [22]. Mariz et al. provided a detailed overview of DDEA models that included the characteristics of the DMUs, the analysis period, and input, output, and intermediate elements [15]. This overview explained the flexibility of DDEA applications in various sectors, such as industry, service companies (banks, hotels, hospitals, employment agencies), transport infrastructure (railways and harbors), etc. Thus, it is noticed that the numbers of DMUs and elements (inputs, outputs and intermediates) can vary according to studies. The above studies provided evidences that the DDEA analyses were appropriate for dynamic efficiency between periods.
The selection of inputs and outputs is crucial for efficiency estimation. In general, inputs should incorporate all necessary resources, and outputs need to describe the managerial objectives of the DMU. O'Neill et al. (2008) and Ozcan (2014) proposed similar guidelines to choose the inputs and outputs for the DEA analysis [23, 24]. They identified three major input categories as capital investment, labor, and other operating costs. On the output side, they introduced case-mix adjusted outpatient visits, admissions or discharges, and teaching for those hospitals engaged in medical education. Kohl (2019) reviewed 262 papers of DEA applications in healthcare that specifically focused on hospitals and found that the principal inputs are the number of beds, medical staff, and nurses while the principal outputs are outpatients, other/total cases, and inpatients [25]. Besides that, supplies have seen the highest growth in input category usage, including medical supply expenses, Pharmaceutical costs, and other operational expenses.
The National Health Insurance has implemented measures to reduce hospital outpatient visits in medical centers since 2018. The decreasing rate has been set by 2% each year until it reaches 10% in 5 years. Under Taiwan's single-payer, global budget health insurance system, hospitals encounter constraint finance in providing quality patient care. Accordingly, hospitals, particularly medical centers, must seek more efficient management actively. Although the DDEA model has theoretical advantages, few studies have applied it to measure healthcare institutions' performance. To improve the weakness of static analysis in previous studies, we adopted the DDEA method to evaluate all medical centers (DMUs) in Taiwan during 2015–2018. In this study, we also incorporated a general industry EBITDA measure (Earnings before Interest, Taxes, Depreciation and Amortization, EBITDA), which no previous research has used in analysis. The results will help hospital managers scrutinize their operation efficiency compared to their peers.