Background
Literature review
Methods
Materials and methods
Sample and data sources
Variables construction
Indicators | Min. | Max. | Mean | Std. Dev. |
---|---|---|---|---|
Input | ||||
Physical area of the hospital | 806 | 136,000 | 21,088.68 | 23,472.26 |
Actual number of open beds | 15 | 1470 | 342.66 | 307.36 |
Total fixed assets | 1264 | 635,559 | 56,597.5 | 84,562.53 |
Number of healthcare technicians | 18 | 1403 | 343.18 | 295.22 |
Output | ||||
Total income | 2490 | 942,523 | 139,816.37 | 144,548.81 |
Number of hospital bed rotations | 16.43 | 137.41 | 50.82 | 19.9 |
Number of outpatient and emergency visits | 9372 | 847,318 | 212,314.14 | 172,899.31 |
Number of discharged patients | 93 | 66,737 | 13,425.69 | 12,824.62 |
Variable code | Variable name | Description and measure of the variable |
---|---|---|
y | Efficiency | Hospital technical efficiency score |
Level-1 | Intra-hospital changes | |
t | Time | Years 2012–2016 expressed as 0–4, respectively |
FP | Government financial assistance | Annual financial input (unit: 10000 yuan) |
A2 | Physical area of the hospital | Physical area of the hospital (unit: square meter) |
A3 | Actual number of open beds | Actual number of open beds per year (unit: bed) |
A6 | Number of healthcare technicians | Annual number of hospital healthcare technical personnel (unit: person) |
A11 | Total fixed assets | Total annual fixed assets (unit: 10000 yuan) |
V1 | Daily charge per bed (Cost of every bed-day in hospital: yuan/ bed-day) | Hospitalization income (including medical and pharmaceutical) / actual occupancy bed-days |
V7 | Medical costs per 100-yuan medical income | (Medical business cost + management cost) / (medical income * 100) |
V8 | Total assets turnover | (Medical income + other income) / total assets |
V9 | Ratio of revenue and expenditure | Balance of revenue and expenditure / (medical income + [basic income, financial assistance, and other income]) * 100% |
V10 | Asset-liability ratio | Total liabilities / total assets * 100% |
Level-2 | Inter-hospital differences | |
GHP | Hospital grade | Numbers 0–4 represent unrated, middle second-class, upper second-class, middle first-class, and upper first-class hospitals, respectively |
THP | Hospital category | Taking general hospitals as the reference category, the two virtual variables are transformed into maternal and child healthcare hospitals (FY) and traditional Chinese medicine hospitals (ZY) |
Level-3 | Inter-county differences | |
GDP | Per capita gross domestic product (GDP) | GDP / county population; measures a region’s economic development and standard of living |
D1 | Number of healthcare technicians per 1000 people (person) | Total healthcare technician population / (county population * 1000); measures the level of human resource investment and equity of the distribution of medical and health services |
DP | Population density | Total population / county area; used to measure county health service needs |
HP | Density of medical institutions | Total number of medical institutions in the area / county area; measures county medical institutions’ competition |
CZ | Urbanization rate | Urban population / permanent population; used to measure social and cultural development of a county |
Model development
Results
Descriptive results
Variable name | Years | Min. | Max. | Mean | Std. Dev. |
---|---|---|---|---|---|
Efficiency score | 2012–2016 | 0.42 | 1.00 | 0.83 | 0.16 |
2012 | 0.50 | 1.00 | 0.79 | 0.18 | |
2013 | 0.47 | 1.00 | 0.83 | 0.16 | |
2014 | 0.51 | 1.00 | 0.81 | 0.16 | |
2015 | 0.55 | 1.00 | 0.86 | 0.13 | |
2016 | 0.42 | 1.00 | 0.85 | 0.15 | |
Government financial assistance | 2012–2016 | 0.00 | 0.82 | 0.19 | 0.17 |
Physical area of the hospital | 806.00 | 136,000.00 | 21,088.68 | 23,472.26 | |
Actual number of open beds | 15.00 | 1470.00 | 342.66 | 307.36 | |
Number of healthcare technicians | 18.00 | 1403.00 | 343.18 | 295.22 | |
Total fixed assets | 1264.00 | 635,559.00 | 56,597.50 | 84,562.53 | |
Daily charge per bed (Cost of every bed-day in hospital: yuan/bed-day) | 0.30 | 2.89 | 0.83 | 0.28 | |
Medical costs per 100-yuan medical income | 0.0009 | 0.0247 | 0.0106 | 0.0022 | |
Total assets turnover | 0.09 | 6.06 | 1.20 | 0.70 | |
Ratio of revenue and expenditure | −3.686 | 98.018 | 22.45 | 16.37 | |
Asset-liability ratio | 0.00 | 102.03 | 44.95 | 25.21 | |
Per capita gross domestic product (GDP) | 12,969.47 | 91,552.13 | 37,720.33 | 19,792.18 | |
Number of healthcare technicians per 1000 people (person) | 1.70 | 17.70 | 4.42 | 2.73 | |
Population density | 0.01 | 0.40 | 0.07 | 0.10 | |
Density of medical institutions | 0.06 | 1.92 | 0.35 | 0.41 | |
Urbanization rate | 27.120 | 95.70 | 49.27 | 20.35 |
GHP | THP | ||||
---|---|---|---|---|---|
Groups | N | Percentage (%) | Groups | N | Percentage (%) |
Upper first-class hospital | 30 | 8.3 | General hospitals | 120 | 33.3 |
Upper second-class hospital | 230 | 63.9 | Traditional Chinese medicine hospitals | 120 | 33.3 |
Middle second-class hospital | 65 | 18.1 | Maternal and child healthcare hospitals | 120 | 33.3 |
No grade | 35 | 9.7 | |||
Total | 360 | 100.0 | 360 | 100.0 |
Analytic results
Level | Parameters and Variables | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | Model 7 |
---|---|---|---|---|---|---|---|---|
Fixed Effect | ||||||||
Level 1 | Initial efficiency (π0ij) | |||||||
Intercept (γ000) | 0.829*** (0.017) | 0.798*** (0.021) | 0.792*** (0.022) | 0.798*** (0.019) | 0.843*** (0.068) | 0.695*** (0.092) | 0.823*** (0.061) | |
Linear growth rate (T, π1ij) | ||||||||
Intercept (β100) | 0.016** (0.005) | 0.028* (0.011) | ||||||
Nonlinear growth rate (T2, π2ij) | −0.003 (0.003) | |||||||
Intercept (β200) | ||||||||
FP (π2ij) | 0.337** (0.103) | 0.324** (0.099) | ||||||
A2 (π3ij) | 0.000*** (0.000) | 0.000 (0.000) | ||||||
A3 (π4ij) | 0.000 (0.001) | 0.000 (0.001) | ||||||
A6 (π5ij) | −0.001 (0.003) | −0.006* (0.002) | ||||||
A11 (π6ij) | 0.000 (0.000) | 0.000 (0.000) | ||||||
V1 (π7ij) | 0.119** (0.044) | 0.114** (0.042) | ||||||
V7 (π8ij) | −12.491** (4.575) | −10.366* (4.555) | ||||||
V8 (π9ij) | 0.038** (0.014) | 0.041** (0.013) | ||||||
V9 (π10ij) | −0.001 (0.001) | −0.001 (0.001) | ||||||
V10 (π11ij) | 0.000 (0.001) | 0.000 (0.001) | ||||||
T × A2 (π12ij) | 0.000 (0.000) | |||||||
T × A3 (π13ij) | 0.000 (0.001) | |||||||
T × A6 (π14ij) | 0.003** (0.001) | |||||||
T × A11 (π15ij) | 0.000 (0.000) | |||||||
Level 2 | GHP (β01j) | −0.025 (0.024) | 0.027 (0.025) | −0.042 (0.024) | ||||
IHP (β02j) | 0.019 (0.049) | 0.037 (0.048) | 0.043 (0.046) | |||||
ZY (β03j) | −0.079* (0.038) | − 0.078* (0.037) | − 0.063 (0.035) | |||||
FY (β04j) | 0.073 (0.056) | 0.097 (0.055) | 0.117* (0.052) | |||||
Level 3 | GDP (γ001) | 0.000 (0.000) | 0.000 (0.000) | 0.003 (0.003) | 0.003 (0.003) | |||
D1 (γ002) | 0.003 (0.021) | 0.006 (0.024) | 0.001 (0.025) | 0.002 (0.026) | ||||
DP (γ003) | 1.105 (0.699) | 0.753 (0.842) | 1.216 (0.782) | 1.224 (0.779) | ||||
HP (γ004) | −0.103 (0.141) | −0.050 (0.149) | −0.092 (0.129) | − 0.105 (0.133) | ||||
CZ (γ005) | −0.005 (0.003) | −0.004 (0.003) | − 0.005 (0.003) | −0.005 (0.003) | ||||
Growth rate (T, π0ij) | ||||||||
Intercept (γ100) | 0.016** (0.005) | 0.028* (0.011) | 0.016** (0.005) | 0.020 (0.190) | 0.023 (0.026) | 0.025* (0.013) | ||
Level 2 | GHP (β11j) | −0.001 (0.005) | 0.001 (0.004) | 0.004 (0.004) | ||||
IHP (β11j) | 0.003 (0.014) | −0.006 (0.013) | −0.009 (0.013) | |||||
ZY (β11j) | 0.013 (0.011) | 0.011 (0.011) | 0.008 (0.008) | |||||
FY (β11j) | −0.019 (0.015) | −0.032 (0.018) | − 0.036** (0.014) | |||||
Level 3 | GDP (γ101) | 0.000 (0.000) | 0.000 (0.000) | −0.001 (0.001) | −0.001 (0.001) | |||
D1 (γ102) | 0.007* (0.003) | 0.007* (0.003) | 0.009* (0.004) | 0.009* (0.004) | ||||
DP (γ103) | −0.075 (0.157) | − 0.095 (0.187) | −0.332* (0.169) | − 0.310 (0.175) | ||||
HP (γ104) | −0.016 (0.031) | −0.013 (0.034) | 0.009 (0.029) | 0.007 (0.029) | ||||
CZ (γ105) | 0.000 (0.001) | 0.000 (0.001) | 0.001 (0.001) | 0.001 (0.001) | ||||
Variance Components | ||||||||
σ2 | Initial efficiency | 0.011*** (0.001) | 0.008*** (0.001) | 0.007*** (0.000) | 0.008*** (0.001) | 0.008*** (0.001) | 0.007*** (0.001) | 0.006*** (0.001) |
σ2r0 | Initial efficiency | 0.012*** (0.002) | 0.021*** (0.004) | 0.020*** (0.000) | 0.021*** (0.004) | 0.014*** (0.003) | 0.013*** (0.003) | 0.012*** (0.003) |
Growth rate | 0.001** (0.000) | 0.004 (0.000) | 0.001** (0.000) | 0.001 (0.000) | 0.001* (0.000) | 0.000* (0.000) | ||
σ2u0 | Initial efficiency | 0.002 (0.002) | 0.002 (0.003) | 0.003 (0.003) | 0.001 (0.004) | 0.002 (0.003) | 0.002 (0.002) | 0.003 (0.003) |
Growth rate | 0.000** (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | 0.000 (0.000) | ||
Covariance | ||||||||
Level 2 | Initial efficiency and growth rate | −0.003** (0.001) | −0.002 (0.002) | −0.003** (0.001) | −0.002 (0.001) | −0.001 (0.001) | −0.001 (0.001) | |
Level 3 | 0.000 (0.000) | −0.001 (0.001) | 0.000 (0.001) | 0.000 (0.001) | 0.000 (0.000) | 0.000 (0.001) | ||
Model fit | Np | 4 | 9 | 16 | 19 | 27 | 37 | 41 |
LL | 228.239 | 247.529 | 250.324 | 251.646 | 260.718 | 292.292 | 302.857 | |
AIC | − 448.490 | − 477.059 | − 468.649 | −465.291 | −467.436 | − 510.584 | −523.713 | |
BIC | − 432.946 | − 442.084 | − 406.471 | − 392.455 | − 362.511 | −366.798 | − 364.383 | |
ICC | Level 2 | 0.482 | ||||||
Level 3 | 0.081 |
Group | Simple slope equation | Significance of slope (p) |
---|---|---|
low D1—GHS—low A6 | y = −0.014 T + 0.823 | 0.482 |
high D1—GHS—low A6 | y = 0.030 T + 0.823 | 0.091 |
low D1—GHS—high A6 | y = 0.021 T + 0.823 | 0.184 |
high D1—GHS—high A6 | y = 0.064 T + 0.823 | 0.000*** |
high D1—MCHHS—low A6 | y = − 0.049 T + 0.823 | 0.002** |
low D1—MCHHS—low A6 | y = − 0.006 T + 0.823 | 0.694 |
high D1—MCHHS—high A6 | y = − 0.015 T + 0.823 | 0.294 |
low D1—MCHHS—high A6 | y = 0.029 T + 0.823 | 0.097 |