# Estimation of Association between Healthcare System Efficiency and Policy Factors for Public Health
## 3 Results  
The efficiency score of 35 countries derived from bootstrapped DEA (Table 2) was 0.7802 on average and the standard deviation was 0.1259. It shows that Luxembourg, Greece, and Israel had the highest healthcare system efficiency and Germany, Austiria, and the Slovak Republic had the lowest efficiency. Luxembourg has a relatively low practicing physicians _per capita_ (2.86, 23 rd), but showed relatively high infant survival rate (356.14, 9 th) and life expectancy (85.2, 6 th). Germany, on the other hand, injected the sixth highest health care expenditure (5200.1) and the third highest number of hospital beds (8.23), but its average life expectancy (83.6) and infant survival rate (311.50) were similar to the average (83.34, 302.21). Mean and standard deviations of efficiency scores were compared to determine if there was a difference in efficiency depending on the type of healthcare system. The results are shown in Table 3. Note that the case of the PHS to which the US belongs and the social-based mixed-type to which Slovenia belongs were excluded because of the lack of samples. Comparing the average value of efficiency by healthcare system shows that the health care efficiency of the Social Health Insurance system was remarkably low. Especially when compared to the National Health Service system, we could see a large difference in the efficiency score of 0.1911. However, it showed no significant difference between the four types of systems (except PHS due to lack of data) as a result of a one-way ANOVA (analysis of variance) test at the 0.05 significant level (\(p=0.1157\)). Regression analysis was conducted to confirm whether the difference in efficiency was caused by the difference in health policy. Among the health policy indicators, [PERSON] et al. [31] presented, ten indicators were selected as potential factors. However, it may distort the causal relationship between variables if many indicators were used as independent variables in the regression analysis [33]. [PERSON] [34] noted that for logistic regression analysis, the number of events per predictive variablesless than 10 could cause major problems regarding the biases. Considering that this restriction can be slightly relaxed in most cases [35], we decided to select up three independent variables. Before the regression analysis, we tried to derive some policy indicators that showed a significant difference in the relatively efficient group and others. To do this, we divided the efficient and inefficient countries based on the median of the efficiency scores and verified whether there was a difference in the score of the policy indicators between the two groups using the Mann-Whitney U test. The results are shown in Table 4. User information (on the quality on prices of various health care services), and decentralization (to sub-national governments) was equal to or less than 0.05 in \(p\) value, which means that the two policy indicators between the two group showed a significant difference. User choice of insurers (for basic insurance coverage) showed a marginal significance (\(p=0.053\)).