# Estimation of Association between Healthcare System Efficiency and Policy Factors for Public Health
## 2 Materials and Methods
### Input/Output Selection  
The selection of input and output variables is important when applying the DEA method and should not include factors indiscriminately [20]. In addition, non-discretionary inputs can make the DEA model poorer [22]. It is also critical to identify the output variables that best describe the performance of the healthcare system and the input variables that can have a direct impact on these output variables. In previous studies, [PERSON] et al. [14], who measured the efficiency of healthcare systems in OECD countries, chose infant mortality and life expectancy as the output variables. A relatively recent study, [PERSON] et al. [17] selected the physician density, inpatient bed density, health expenditure _per capita_, gross domestic product (GDP) _per capita_, and the consumption of fruit and vegetables _per capita_ as input variables, and life expectancy at birth and infant survival rate were selected as output variables. Similarly, [PERSON] et al. [23] set the number of doctors, number of hospital beds, and public health expenditures as input variables, and life expectancy at birth, health adjusted life expectancy, and infant mortality rate as output variables. In this study, we chose expenditure on health _per capita_, practicing physicians _per capita_, and the number of beds _per capita_ as input variables, and infant survival rate and life expectancy as output variables. There are several more factors related to the performance of the healthcare system such as cost sensitivity (e.g., cost sensitivity of healthcare consumers for general health care [24]), but those were not taken into account due to the availability of data on a global scale.  
The expenditure on health _per capita_ has been considered as a major factor that is highly associated with health outcomes such as infant mortality and life expectancy [25; 26]. On the other hand, the number of practicing physicians and beds _per capita_ is one of the representative indicators that show the level of public health infrastructure of the country. In particular, the shortage of inpatient hospital beds can lead to emergency department overcrowding that may be a threat to public health [27]. The number of practicing physicians and beds _per capita_ has also been widely used in studies with DEA models [17; 23].  
Since subjective health outcomes such as healthcare satisfaction are not easy to quantify, the objective health outcomes such as life expectancy and infant mortality rate have been widely used in healthcare system efficiency studies [14; 17; 23]. Due to the assumption of DEA that more output is better, the infant mortality rate (IMR) of the OECD is not suitable as an output variable. Therefore, referring to the study of [PERSON] and [PERSON] [28] and [PERSON] et al. [17], IMR was transformed to the infant survival rate (ISR = (1000 \(-\) IMR)/IMR). This can be interpreted as the proportion of surviving infants compared to the number of children that died in the first year of life, a high level of which means better healthcare status.