Multilevel Zero-One Inflated Beta Regression Model for the Analysis of the Relationship between Exogenous Health Variables and Technical Efficiency in the Spanish National Health System Hospitals
Abstract
:1. Introduction
2. Materials and Methods
2.1. Decision Making Units (DMUs)
2.2. Variables
2.3. Sources of Information
2.4. Data Analysis
2.4.1. Data Envelopment Analysis
2.4.2. Second-Stage Analysis
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
References
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Mean | Standard Deviation | Maximum | Minimum | |
---|---|---|---|---|
Inputs | ||||
Installed beds a | 484.03 | 331.22 | 1408.00 | 63.00 |
Healthcare personnel b | 2146.58 | 1669.66 | 7947.00 | 169.50 |
Non-healthcare personnel b | 517.68 | 456.44 | 2417.50 | 20.00 |
Adjusted purchases and external services c | 156,561.26 | 53,247.90 | 327,822.98 | 40,261.73 |
Outputs | ||||
Total discharges adjusted case by case d | 18,833.02 | 13,578.33 | 59,811.27 | 1503.74 |
Outpatient activity e | 31,892.54 | 20,207.32 | 108,572.25 | 5720.43 |
Quantitative Variables | Original Variable | Standardized Variable 1 | ||||||
---|---|---|---|---|---|---|---|---|
Minimum | Maximum | Mean | Standard Deviation | Minimum | Maximum | Mean | Standard Deviation | |
Hospital variables | ||||||||
Resident physicians per 100 faculty members | 0.00 | 60.78 | 23.75 | 16.08 | −1.48 | 2.30 | 0.00 | 1.00 |
Emergency physicians per 100 faculty members a | 4.56 | 30.58 | 13.32 | 4.97 | −1.76 | 3.48 | 0.00 | 1.00 |
% Beds in operation in Intensive Care Units b | 0.84 | 9.36 | 4.30 | 1.62 | −2.15 | 3.13 | 0.00 | 1.00 |
% Occupation in Intensive Care Units c | 7.12 | 97.06 | 56.32 | 22.27 | −2.21 | 1.83 | 0.00 | 1.00 |
Regional variables | ||||||||
Public healthcare spending per inhabitant d | 1153.43 | 1710.08 | 1374.11 | 145.35 | −1.52 | 2.31 | 0.00 | 1.00 |
Average annual income per household (Thousands of €) e | 24,375.00 | 39,578.00 | 31,705.28 | 4170.42 | −1.76 | 1.89 | 0.00 | 1.00 |
Installed private beds per 1000 inhabitants f | 0.11 | 1.06 | 0.58 | 0.29 | −1.63 | 1.69 | 0.00 | 1.00 |
Installed public beds per 1000 inhabitants f | 2.14 | 3.77 | 2.83 | 0.55 | −1.25 | 1.73 | 0.00 | 1.00 |
Public beds in operation in Intensive Care Units per 1000 inhabitants | 0.07 | 0.09 | 0.08 | 0.01 | −1.09 | 1.74 | 0.00 | 1.00 |
Emergency physicians per 1000 inhabitants a | 0.16 | 0.30 | 0.20 | 0.03 | −1.56 | 3.89 | 0.00 | 1.00 |
External emergency centers per 1000 inhabitants g | 0.01 | 0.12 | 0.04 | 0.03 | −1.21 | 2.73 | 0.00 | 1.00 |
Primary care doctors and nurses per 1000 people allocated h | 1.12 | 2.01 | 1.44 | 0.21 | −1.52 | 2.77 | 0.00 | 1.00 |
External emergency personnel per 1000 inhabitants i | 0.16 | 1.07 | 0.41 | 0.17 | −1.42 | 3.80 | 0.00 | 1.00 |
Qualitative variables | Number | Percentage | ||||||
Exogenous hospital variables | ||||||||
Hospital type | ||||||||
Public | 147 | 84.97% | ||||||
Private | 12 | 6.94% | ||||||
Public-Private Partnership | 14 | 8.09% |
Variable a | Coefficient | Standard Error | Credibility Interval b | PCP c | NCP c | Bulk-ESS | Tail-ESS | RMAI d | ||
---|---|---|---|---|---|---|---|---|---|---|
Average Efficiency Index Model | ||||||||||
Intercept | 1.00 | 0.21 | 0.58 | 1.40 | 1.00 | 0.00 | 1.00 | 10,710 | 8026 | |
Hospital type | ||||||||||
Public | Reference | Reference | Reference | Reference | Reference | Reference | Reference | |||
Public-Private Partnership | 1.45 | 0.41 | 0.69 | 2.32 | 1.00 | 0.00 | 1.00 | 22,111 | 13,024 | 4.27 |
Private | 0.64 | 0.39 | −0.08 | 1.48 | 0.96 | 0.04 | 1.00 | 25,642 | 10,668 | 1.90 |
Resident physicians per 100 faculty members | 0.22 | 0.08 | 0.06 | 0.38 | 1.00 | 0.00 | 1.00 | 16,751 | 12,123 | 1.25 |
Emergency physicians per 100 faculty members | 0.03 | 0.08 | −0.12 | 0.18 | 0.64 | 0.36 | 1.00 | 19,586 | 12,303 | 1.03 |
Occupation in Intensive Care Units (%) | 0.00 | 0.07 | −0.14 | 0.14 | 0.52 | 0.48 | 1.00 | 20,699 | 11,979 | 1.00 |
Beds in operation in Intensive Care Units (%) | −0.01 | 0.06 | −0.12 | 0.11 | 0.45 | 0.55 | 1.00 | 26,946 | 13,022 | 0.99 |
Public healthcare spending per inhabitant | 0.29 | 0.46 | −0.59 | 1.23 | 0.77 | 0.23 | 1.00 | 6240 | 5652 | 1.33 |
Average annual income per household (thousand €) | 0.10 | 0.48 | −0.87 | 1.09 | 0.59 | 0.41 | 1.00 | 5279 | 5106 | 1.11 |
Primary care doctors and nurses per 1000 people allocated | 0.09 | 0.50 | −0.92 | 1.10 | 0.58 | 0.42 | 1.00 | 5313 | 4869 | 1.09 |
Installed private beds per 1000 inhabitants | 0.00 | 0.22 | −0.45 | 0.41 | 0.51 | 0.49 | 1.00 | 11,941 | 8845 | 1.00 |
External emergency centres per 1000 inhabitants | −0.02 | 0.52 | −1.08 | 1.00 | 0.49 | 0.51 | 1.00 | 5423 | 5204 | 0.98 |
External emergency personnel per 1000 inhabitants | −0.10 | 0.40 | −0.91 | 0.71 | 0.37 | 0.63 | 1.00 | 5471 | 5073 | 0.90 |
Installed public beds per 1000 inhabitants | −0.11 | 0.40 | −0.91 | 0.66 | 0.37 | 0.63 | 1.00 | 7459 | 6470 | 0.90 |
Emergency physicians per 1000 inhabitants | −0.18 | 0.42 | −1.04 | 0.67 | 0.30 | 0.70 | 1.00 | 5015 | 4809 | 0.83 |
Public beds in operation in Intensive Care Units per 1000 inhabitants | −0.23 | 0.42 | −1.09 | 0.63 | 0.26 | 0.74 | 1.00 | 5455 | 5540 | 0.80 |
Probability of Being Situated on the Efficiency Frontier Model | ||||||||||
Intercept | −3.00 | 0.44 | −3.94 | −2.21 | 0.00 | 1.00 | 1.00 | 12,108 | 10,551 | |
Hospital type | ||||||||||
Public | Reference | Reference | Reference | Reference | Reference | Reference | Reference | |||
Public-Private Partnership | 3.74 | 1.22 | 1.57 | 6.37 | 1.00 | 0.00 | 1.00 | 17,875 | 11,484 | 42.06 |
Private | 2.10 | 1.14 | −0.07 | 4.40 | 0.97 | 0.03 | 1.00 | 20,600 | 11,977 | 8.17 |
Beds in operation in Intensive Care Units (%) | 0.41 | 0.26 | −0.09 | 0.93 | 0.95 | 0.05 | 1.00 | 25,157 | 11,536 | 1.50 |
Occupation in Intensive Care Units (%) | −0.08 | 0.35 | −0.76 | 0.61 | 0.42 | 0.58 | 1.00 | 22,315 | 12,218 | 0.93 |
Resident physicians per 100 faculty members | −0.38 | 0.43 | −1.23 | 0.48 | 0.19 | 0.81 | 1.00 | 14,282 | 12,800 | 0.68 |
Emergency physicians per 100 faculty members | −0.43 | 0.37 | −1.18 | 0.29 | 0.12 | 0.88 | 1.00 | 20,060 | 12,905 | 0.65 |
Average annual income per household (thousands of €) | 1.86 | 1.38 | −0.90 | 4.62 | 0.91 | 0.09 | 1.00 | 4774 | 6823 | 6.43 |
Primary care doctors and nurses per 1000 people allocated | 1.09 | 1.27 | −1.29 | 3.72 | 0.80 | 0.20 | 1.00 | 5435 | 7190 | 2.97 |
Public beds in operation in Intensive Care Units per 1000 inhabitants | 0.23 | 1.03 | −1.83 | 2.29 | 0.58 | 0.42 | 1.00 | 5450 | 7804 | 1.26 |
Emergency physicians per 1000 inhabitants | 0.12 | 1.12 | −2.23 | 2.29 | 0.54 | 0.46 | 1.00 | 5126 | 7031 | 1.13 |
External emergency personnel per 1000 inhabitants | 0.12 | 1.13 | −2.19 | 2.30 | 0.54 | 0.46 | 1.00 | 5716 | 7733 | 1.12 |
Public healthcare spending per inhabitant | −0.28 | 1.16 | −2.57 | 2.03 | 0.41 | 0.59 | 1.00 | 5110 | 6895 | 0.75 |
External emergency centres per 1000 inhabitants | −0.43 | 1.25 | −2.97 | 1.96 | 0.37 | 0.63 | 1.00 | 5775 | 8174 | 0.65 |
Installed public beds per 1000 inhabitants | −0.84 | 0.91 | −2.63 | 0.98 | 0.18 | 0.82 | 1.00 | 6257 | 8963 | 0.43 |
Installed private beds per 1000 inhabitants | −0.98 | 0.57 | −2.19 | 0.05 | 0.03 | 0.97 | 1.00 | 17,535 | 11,127 | 0.37 |
Accuracy. Conditional Probability of Inflation one and Random Effect | ||||||||||
Precision () | 14.27 | 1.77 | 11.01 | 17.92 | 1.00 | 18,753 | 11,620 | |||
Probability of One-Inflation () | 0.97 | 0.03 | 0.89 | 1.00 | 1.00 | 19,419 | 7510 | |||
Random Effect | 0.57 | 0.31 | 0.17 | 1.34 | 1.00 | 3041 | 4251 |
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Ocaña-Riola, R.; Pérez-Romero, C.; Ortega-Díaz, M.I.; Martín-Martín, J.J. Multilevel Zero-One Inflated Beta Regression Model for the Analysis of the Relationship between Exogenous Health Variables and Technical Efficiency in the Spanish National Health System Hospitals. Int. J. Environ. Res. Public Health 2021, 18, 10166. https://doi.org/10.3390/ijerph181910166
Ocaña-Riola R, Pérez-Romero C, Ortega-Díaz MI, Martín-Martín JJ. Multilevel Zero-One Inflated Beta Regression Model for the Analysis of the Relationship between Exogenous Health Variables and Technical Efficiency in the Spanish National Health System Hospitals. International Journal of Environmental Research and Public Health. 2021; 18(19):10166. https://doi.org/10.3390/ijerph181910166
Chicago/Turabian StyleOcaña-Riola, Ricardo, Carmen Pérez-Romero, Mª Isabel Ortega-Díaz, and José Jesús Martín-Martín. 2021. "Multilevel Zero-One Inflated Beta Regression Model for the Analysis of the Relationship between Exogenous Health Variables and Technical Efficiency in the Spanish National Health System Hospitals" International Journal of Environmental Research and Public Health 18, no. 19: 10166. https://doi.org/10.3390/ijerph181910166