On the Relationships among Nurse Staffing, Inpatient Care Quality, and Hospital Competition under the Global Budget Payment Scheme of Taiwan’s National Health Insurance System: Mixed Frequency VAR Analyses
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data and Variables
2.2. VAR Models
2.3. Granger Causality Tests
2.4. Impulse-Response and Variance Decomposition
3. Results
3.1. Descriptive Statistics
3.2. Unit Root Tests
3.3. Granger Causality Tests
3.4. Impulse-Response Analyses
3.5. Variance Decomposition
4. Discussion
5. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
1 | Inpatient care expenditure per admission was calculated using total inpatient care expenditure divided by total admissions in a specific type of hospital, and it was measured using the 2016 price level (constant 2016 USD). The patient-to-nurse ratio was defined as the mean of number of patients divided by the nurse staffing number within three shifts per day in a specific type of hospital. The quarterly and monthly sample periods start from 2015: Q1 to 2021: Q4 and 2015: M1 to 2021: M12, resulting in a total of 28 and 84 quarterly and monthly observations, respectively. The IQR and JB statistics represent the interquartile range and Jarque-Bera statistics, respectively. ”**”, ”*” denote 1% and 5% significance levels for the rejection of null hypothesis of the normality of time series, respectively. |
2 | All variables are defined in the same way as for Table 1. The lag length is selected based on Bayesian Information Criterion (BIC) with the maximal lag as eight. ”**” and “*” represent 1% and 5% significance levels, respectively. , k = MC, RH, and DH define cyclic components of aggregate monthly PNR. |
3 | Quarterly data on cyclical components of quality of care indicators (such as the 3-day EDV rate and 14-day readmission rate), inpatient care expenditure per admission, and monthly data on cyclical components of the patient-to-nurse ratio were used to estimate the MF-VAR model. The monthly data on cyclical components of the patient-to-nurse ratio were aggregated into quarterly data (PNRA) when the LF-VAR model was estimated. The lag length is selected based on Newey and West’s automatic lag selection with the maximal lag as 3 [52]. “PNRA EDV”, for example, represents the null hypothesis of non-causality from PNRA to RER. The bold font of PNR denotes the vector of cyclical components of PNR symbolized by [C_lnPNR1, C_lnPNR2, C_lnPNR3]’. “PNR EDV”, for example, represents the null hypothesis of joint non-causality from the vector of cyclical components of PNR to the cyclical component of EDV. The p values were calculated using the heteroscedasticity-robust parametric bootstrap of Gonçalves and Kilian [53] with 10,000 replications. “***”,”**”,”*” represent 1%, 5%, and 10% significance levels, respectively. |
4 | Figure 1 plots the impulse response functions (IRFs) for monthly horizons h = 0, 1, 2, …, 12 based on the MF-VAR model of quarterly data on cyclical components of quality of care indicators (such as the 3-day EDV rate and 14-day readmission rate), inpatient care expenditure per admission, and three individual monthly cyclical components of the patient-to-nurse ratio symbolized by C_lnPNR1, C_lnPNR2, and C_lnPNR3 in a quarter timespan. The Cholesky decomposition with order PNR1, PNR2, PNR3, EDV (or RAD), and ICE is selected. The sample period covers 2015:Q1–2021:Q4. The responses of variable Y (say, EDV) to 1σ shock in X (say, PNR1) at monthly horizon h is written as “PNR1=>RER”. MC, RH, and DH represent medical centers, regional hospitals, and district hospitals, respectively. Blue shaded areas denote 90% confidence intervals of IRFs based on the Monte Carlo simulation method with 10,000 replications. |
5 | Figure 2 plots the impulse response functions (IRFs) for monthly horizons h = 0, 1, 2, …, 12 based on the MF-VAR model of quarterly data on cyclical components of quality of care indicators (such as the 3-day EDV rate and 14-day readmission rate), inpatient care expenditure per admission, and three individual monthly cyclical components of the patient-to-nurse ratio symbolized by C_lnPNR1, C_lnPNR2, and C_lnPNR3 in a quarter timespan. The Cholesky decomposition with order PNR1, PNR2, PNR3, EDV (or RAD), and ICE is selected. The sample period covers 2015:Q1~2021:Q4. The responses of variable Y (say, EDV) to 1σ shock in X (say, ICE) at monthly horizon h is written as “ICE =>EDV”. Blue shaded areas denote 90% confidence intervals of IRFs based on the Monte Carlo simulation method with 10,000 replications. MC, RH, and DH denote medical centers, regional hospitals, and district hospitals, respectively. |
6 | Notations presented in this table are the same as those used in Table 3. The sum of variance decomposition may not equal 100 due to rounding. |
7 | The directions of arrows were drawn based on the Granger causality tests. The arrows with bold (dot) lines represent significant (insignificant) paths connecting two target variables based on 90% confidence intervals of the impulse-response effects accumulated across a 3-month cycle of a quarter timespan over a 12-month period. MC, RH, and DH denote medical centers, regional hospitals, and district hospitals, respectively. |
8 | EDV and RAD represent the 3-day EDV rate and 14-day readmission rate, respectively. ICE is real inpatient care expenditure per admission at the 2016 price level (USD). PNR symbolizes the patient-to-nurse ratio. MC, RH, and DH represent medical centers, regional hospitals, and district hospitals, respectively. Light blue and grey shaded areas show the post-acute care intervention period and COVID-19 strike waves, respectively. |
9 | All notations used in this figure are the same as for Figure 1. represents the natural logarithm transformation. |
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Panel A: Quarterly Data Description | Mean | Standard Deviation | Median | IQR | Max | Min | JB Stat |
2.489 | 0.139 | 2.483 | 0.149 | 2.807 | 2.208 | 0.077 | |
2.814 | 0.170 | 2.832 | 0.202 | 3.199 | 2.504 | 0.396 | |
2.559 | 0.175 | 2.539 | 0.246 | 2.918 | 2.241 | 0.723 | |
6.428 | 0.241 | 6.467 | 0.411 | 6.871 | 6.103 | 1.860 | |
7.259 | 0.228 | 7.239 | 0.413 | 7.675 | 6.947 | 2.198 | |
7.460 | 0.256 | 7.473 | 0.303 | 7.983 | 6.772 | 0.705 | |
:USD, Constant at 2016 price level, USD 1 = TWD 30 | 2629.971 | 179.855 | 2589.845 | 200.537 | 3078.093 | 2401.06 | 6.270 * |
:USD, Constant at 2016 price level, USD 1 = TWD 30 | 1826.339 | 139.494 | 1795.955 | 182.638 | 2146.892 | 1649.037 | 4.762 |
:USD, Constant at 2016 price level, USD 1 = NTD 30 | 1679.079 | 97.236 | 1645.423 | 99.390 | 1943.214 | 1587.140 | 13.179 ** |
Panel B: Monthly Data Description | Mean | Standard Deviation | Median | IQR | Max | Min | JB Stat |
7.436 | 0.256 | 7.434 | 0.388 | 7.880 | 6.706 | 0.809 | |
7.474 | 0.251 | 7.478 | 0.347 | 7.866 | 7.018 | 1.309 | |
7.394 | 0.242 | 7.375 | 0.329 | 7.798 | 6.788 | 0.245 | |
7.439 | 0.275 | 7.466 | 0.386 | 7.880 | 6.706 | 0.930 | |
9.261 | 0.365 | 9.365 | 0.393 | 10.007 | 7.649 | 75.585 ** | |
9.292 | 0.349 | 9.420 | 0.387 | 9.906 | 8.201 | 10.223 ** | |
9.205 | 0.325 | 9.202 | 0.507 | 9.928 | 8.568 | 0.288 | |
9.286 | 0.421 | 9.372 | 0.315 | 10.007 | 7.649 | 68.002 ** | |
7.573 | 0.399 | 7.602 | 0.314 | 8.314 | 5.943 | 51.089 ** | |
7.605 | 0.392 | 7.614 | 0.337 | 8.314 | 6.333 | 13.500 ** | |
7.524 | 0.356 | 7.541 | 0.410 | 8.309 | 6.733 | 0.259 | |
7.589 | 0.453 | 7.669 | 0.314 | 8.295 | 5.943 | 38.238 ** |
Panel A: Quarterly Data | |||||||
Levels | Cyclical Components | ||||||
Mean | Standard Deviation | Constant (C) | Constant+ Trend (T) | Mean | Standard Deviation | Without C+T | |
0.911 | 0.056 | −3.473 * | −3.405 | 0.000 | 0.052 | −3.952 ** | |
1.033 | 0.060 | −2.329 | −3.330 | 0.000 | 0.050 | −3.874 ** | |
0.937 | 0.068 | −3.247 * | −3.341 | 0.000 | 0.060 | −3.917 ** | |
1.860 | 0.038 | −2.518 | −2.455 | 0.000 | 0.033 | −2.904 ** | |
1.982 | 0.031 | −2.698 | −3.462 | 0.000 | 0.025 | −3.719 ** | |
2.009 | 0.035 | −3.370 * | −4.306 * | 0.000 | 0.031 | −4.250 ** | |
7.873 | 0.066 | 0.036 | −2.412 | 0.000 | 0.025 | −4.347 ** | |
7.507 | 0.074 | 1.087 | −1.824 | 0.000 | 0.025 | −3.164 ** | |
7.424 | 0.056 | 0.676 | −1.303 | 0.000 | 0.024 | −2.221 * | |
Panel B: Monthly Data | |||||||
Levels | Cyclical Components | ||||||
Mean | Standard Deviation | Constant (C) | Constant+ Trend (T) | Mean | Standard Deviation | Without C+T | |
2.006 | 0.035 | −4.253 ** | −4.611 ** | 0.000 | 0.027 | −5.740 ** | |
2.225 | 0.041 | −4.434 ** | −4.596 ** | 0.000 | 0.035 | −5.397 ** | |
2.023 | 0.055 | −3.434 * | −5.079 ** | 0.000 | 0.037 | −5.515 ** | |
Panel C: Aggregate Monthly Data | |||||||
Levels | Cyclical Components | ||||||
Mean | Standard Deviation | Constant (C) | Constant+ Trend (T) | Mean | Standard Deviation | Without C+T | |
-------- | -------- | -------- | -------- | 0.000 | 0.057 | −5.383 ** | |
-------- | -------- | -------- | -------- | 0.000 | 0.071 | −6.482 ** | |
-------- | -------- | -------- | -------- | 0.000 | 0.073 | −2.231 * |
Panel A: | Re-Emergency-Department-Visit Rate in the Same Hospital within 3 Days after Discharge as the Quality of Care Indicator | |||||||||
Types of | MF-VAR Model | LF-VAR Model | ||||||||
Hospitals | Null Hypothesis | χ2 | p Value | Null Hypothesis | χ2 | p Value | ||||
EDV | PNR | 10.935 | 0.090 * | EDV | PNRA | 1.977 | 0.372 | |||
ICE | PNR | 3.213 | 0.782 | ICE | PNRA | 2.346 | 0.309 | |||
Medical | PNR | EDV | 16.029 | 0.014 ** | PNRA | EDV | 3.075 | 0.215 | ||
Centers | ICE | EDV | 3.254 | 0.776 | ICE | EDV | 2.841 | 0.242 | ||
PNR | ICE | 14.095 | 0.029 ** | PNRA | ICE | 1.291 | 0.524 | |||
EDV | ICE | 14.635 | 0.023 ** | EDV | ICE | 7.013 | 0.030 ** | |||
EDV | PNR | 12.035 | 0.061 * | EDV | PNRA | 0.520 | 0.771 | |||
ICE | PNR | 4.706 | 0.582 | ICE | PNRA | 5.716 | 0.057 * | |||
Regional | PNR | EDV | 13.365 | 0.038 ** | PNRA | EDV | 3.121 | 0.210 | ||
Hospitals | ICE | EDV | 6.021 | 0.421 | ICE | EDV | 3.564 | 0.168 | ||
PNR | ICE | 18.311 | 0.005 *** | PNRA | ICE | 1.871 | 0.392 | |||
EDV | ICE | 4.700 | 0.583 | EDV | ICE | 0.366 | 0.833 | |||
RER | PNR | 8.592 | 0.198 | EDV | PNRA | 0.557 | 0.757 | |||
ICE | PNR | 4.797 | 0.570 | ICE | PNRA | 4.162 | 0.125 | |||
District | PNR | EDV | 12.614 | 0.049 ** | PNRA | EDV | 5.049 | 0.080 * | ||
Hospitals | ICE | EDV | 2.749 | 0.840 | ICE | EDV | 0.540 | 0.763 | ||
PNR | ICE | 13.519 | 0.035 ** | PNRA | ICE | 1.438 | 0.487 | |||
RER | ICE | 7.127 | 0.309 | EDV | ICE | 5.761 | 0.056 * | |||
Panel B: | Unplanned Re-Admission Rate within 14 Days after Discharge as the Quality of Care Indicator | |||||||||
Types of | MF-VAR Model | LF-VAR Model | ||||||||
Hospitals | Null Hypothesis | χ2 | p Value | Null Hypothesis | χ2 | p Value | ||||
RAD | PNR | 8.933 | 0.177 | RAD | PNRA | 5.054 | 0.080 * | |||
ICE | PNR | 6.004 | 0.423 | ICE | PNRA | 4.763 | 0.092 * | |||
Medical | PNR | RAD | 7.822 | 0.251 | PNRA | RAD | 6.941 | 0.031 ** | ||
Centers | ICE | RAD | 8.972 | 0.175 | ICE | RAD | 7.418 | 0.024 ** | ||
PNR | ICE | 13.079 | 0.042 ** | PNRA | ICE | 2.848 | 0.241 | |||
RAD | ICE | 4.386 | 0.625 | RAD | ICE | 1.159 | 0.560 | |||
RAD | PNR | 9.952 | 0.127 | RER | PNRA | 0.281 | 0.869 | |||
ICE | PNR | 5.990 | 0.424 | ICE | PNRA | 3.839 | 0.147 | |||
Regional | PNR | RAD | 8.200 | 0.224 | PNRA | RAD | 6.799 | 0.033 ** | ||
Hospitals | ICE | RAD | 8.635 | 0.195 | ICE | RAD | 4.140 | 0.126 | ||
PNR | ICE | 13.674 | 0.033 ** | PNRA | ICE | 3.684 | 0.158 | |||
RAD | ICE | 3.943 | 0.684 | RER | ICE | 2.161 | 0.339 | |||
RAD | PNR | 13.511 | 0.036 ** | RER | PNRA | 1.753 | 0.416 | |||
ICE | PNR | 8.614 | 0.196 | ICE | PNRA | 4.366 | 0.113 | |||
District | PNR | RAD | 4.441 | 0.617 | PNRA | RAD | 2.971 | 0.226 | ||
Hospitals | ICE | RAD | 5.582 | 0.472 | ICE | RAD | 1.988 | 0.370 | ||
PNR | ICE | 12.169 | 0.058 * | PNRA | ICE | 1.653 | 0.438 | |||
RAD | ICE | 2.303 | 0.890 | RER | ICE | 0.765 | 0.682 |
Quality | Model | Medical Centers (%) | Regional Hospitals (%) | District Hospitals (%) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Variable | Horizon | h = 2 | h = 7 | h = 12 | Variable | Horizon | h = 2 | h = 7 | h = 12 | Variable | Horizon | h = 2 | h = 7 | h = 12 | ||
Panel A: RER as Quality Indicator | EDV | EDV ICE PNRA | 86.320.22 13.46 | 63.67 6.80 29.53 | 61.75 9.52 28.73 | EDV | EDV ICE PNRA | 82.96 7.04 10.0 | 64.87 16.37 18.76 | 58.74 15.33 25.93 | EDV | EDV ICE PNRA | 88.71 1.79 9.49 | 45.95 9.40 44.65 | 33.08 20.12 46.79 | |
LF-VAR | ICE | EDV ICE PNRA | 0.38 45.28 54.34 | 30.38 26.15 43.48 | 30.51 25.37 44.12 | ICE | EDV ICE PNRA | 0.81 57.91 41.28 | 4.79 55.43 39.78 | 7.17 53.07 39.75 | ICE | EDV ICE PNRA | 0.58 53.66 45.76 | 19.57 33.91 46.53 | 19.38 35.37 45.25 | |
PNRA | EDV ICE PNRA | 8.13 0.69 91.19 | 8.87 11.78 79.35 | 10.57 12.15 77.27 | PNRA | EDV ICE PNRA | 0.01 7.32 92.67 | 9.94 27.75 62.32 | 11.55 27.13 61.31 | PNRA | EDV ICE PNRA | 0.06 3.86 96.08 | 1.19 23.89 74.92 | 4.89 25.31 69.80 | ||
EDV | EDV ICE PNR=ΣPNRi | 78.28 0.03 21.70 | 53.24 0.88 45.87 | 51.96 1.59 46.45 | EDV | EDV ICE PNR=ΣPNRi | 91.76 1.80 6.45 | 62.08 4.82 33.11 | 45.48 8.05 46.47 | EDV | EDV ICE PNR=ΣPNRi | 74.44 0.37 25.20 | 42.62 1.18 56.19 | 36.38 2.41 61.21 | ||
ICE | EDV ICE PNR=ΣPNRi | 0.40 25.72 73.87 | 16.42 11.71 71.88 | 15.23 10.05 74.71 | ICE | EDV ICE PNR=ΣPNRi | 2.22 47.92 49.88 | 6.22 40.84 52.94 | 7.69 31.27 61.03 | ICE | EDV ICE PNR=ΣPNRi | 0.60 25.28 74.12 | 6.57 14.65 78.77 | 5.97 13.03 80.99 | ||
MF-VAR | PNR1 | EDV ICE PNR=ΣPNRi | 0.88 0.29 98.84 | 1.44 1.02 97.53 | 2.23 1.39 96.38 | PNR1 | EDV ICE PNR=ΣPNRi | 9.88 3.16 86.97 | 8.52 8.00 83.49 | 15.74 6.56 77.71 | PNR1 | EDV ICE PNR=ΣPNRi | 4.76 0.72 94.52 | 3.91 2.68 93.40 | 3.60 3.64 92.77 | |
PNR2 | EDV ICE PNR=ΣPNRi | 32.33 0.00 67.66 | 27.31 2.83 69.85 | 29.15 2.67 68.18 | PNR2 | EDV ICE PNR=ΣPNRi | 11.67 0.30 88.03 | 11.67 18.31 70.01 | 9.69 14.84 75.47 | PNR2 | EDV ICE PNR=ΣPNRi | 2.62 0.00 97.38 | 3.80 4.32 91.88 | 4.10 4.09 91.80 | ||
PNR3 | EDV ICE PNR=ΣPNRi | 0.13 0.00 99.88 | 2.29 1.29 96.43 | 2.29 1.62 96.09 | PNR3 | EDV ICE PNR=ΣPNRi | 5.23 0.70 94.08 | 13.00 7.94 79.07 | 16.19 4.86 78.95 | PNR3 | EDV ICE PNR=ΣPNRi | 0.67 0.00 99.32 | 3.88 2.96 93.16 | 3.29 3.34 93.36 | ||
Quality | Model | Variable | Horizon | h = 2 | h = 7 | h = 12 | Variable | Horizon | h = 2 | h = 7 | h = 12 | Variable | Horizon | h = 2 | h = 7 | h = 12 |
Panel B: URR as Quality Indicator | RAD | RAD ICE PNRA | 83.73 8.14 8.13 | 73.30 15.14 11.56 | 71.73 15.87 12.40 | RAD | RAD ICE PNRA | 75.56 12.24 12.20 | 51.37 24.29 24.34 | 46.51 27.97 25.51 | RAD | RAD ICE PNRA | 89.73 9.58 0.69 | 56.37 20.43 23.21 | 43.57 27.87 28.56 | |
LF-VAR | ICE | RAD ICE PNRA | 2.55 37.82 59.63 | 19.93 32.89 47.18 | 19.43 34.41 46.16 | ICE | RAD ICE PNRA | 2.08 66.07 31.84 | 3.13 58.67 38.21 | 3.39 58.37 38.23 | ICE | RAD ICE PNRA | 0.50 59.39 40.10 | 4.00 53.57 42.43 | 4.08 53.93 41.99 | |
PNRA | RAD ICE PNRA | 14.55 0.17 85.28 | 14.89 29.15 55.96 | 14.69 29.28 56.04 | PNRA | RAD ICE PNRA | 1.62 3.33 95.05 | 1.55 28.30 70.15 | 2.18 32.03 65.78 | PNRA | RAD ICE PNRA | 0.21 7.04 92.75 | 2.76 32.36 64.87 | 3.72 35.16 61.12 | ||
RAD | RAD ICE PNR=ΣPNRi | 60.54 2.27 37.20 | 50.90 5.03 44.06 | 47.97 5.24 46.80 | RAD | RAD ICE PNR=ΣPNRi | 73.70 4.72 21.57 | 45.46 8.05 46.49 | 38.00 12.14 49.87 | RAD | RAD ICE PNR=ΣPNRi | 81.99 6.11 11.89 | 56.39 15.33 28.29 | 48.59 20.14 31.27 | ||
ICE | RAD ICE PNR=ΣPNRi | 2.99 22.94 74.07 | 16.21 12.87 70.93 | 14.00 12.08 73.91 | ICE | RAD ICE PNR=ΣPNRi | 7.23 56.11 36.65 | 8.59 35.53 55.87 | 8.50 30.44 61.06 | ICE | RAD ICE PNR=ΣPNRi | 0.67 49.48 49.86 | 7.19 32.90 59.90 | 10.06 30.98 58.95 | ||
MF-VAR | PNR1 | RAD ICE PNR=ΣPNRi | 0.59 0.05 99.37 | 6.37 5.54 88.09 | 6.66 8.03 85.31 | PNR1 | RAD ICE PNR=ΣPNRi | 16.34 1.25 82.42 | 11.66 9.88 78.46 | 9.22 9.43 81.35 | PNR1 | RAD ICE PNR=ΣPNRi | 16.46 2.33 81.21 | 15.23 9.89 74.88 | 13.06 15.41 71.52 | |
PNR2 | RAD ICE PNR=ΣPNRi | 16.47 0.65 82.87 | 15.16 14.33 70.51 | 12.61 9.87 77.53 | PNR2 | RAD ICE PNR=ΣPNRi | 0.02 3.62 96.37 | 12.73 15.16 72.11 | 10.13 13.02 76.85 | PNR2 | RAD ICE PNR=ΣPNRi | 2.50 2.23 95.27 | 22.17 11.29 66.54 | 21.45 10.76 67.79 | ||
PNR3 | RAD ICE PNR=ΣPNRi | 0.17 0.56 99.27 | 6.98 4.28 88.74 | 7.79 4.85 87.35 | PNR3 | RAD ICE PNR=ΣPNRi | 0.91 0.07 99.02 | 8.61 6.45 84.93 | 9.49 5.81 84.70 | PNR3 | RAD ICE PNR=ΣPNRi | 0.48 0.26 99.25 | 16.06 5.07 78.87 | 15.53 7.37 77.09 |
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Chen, W.-Y. On the Relationships among Nurse Staffing, Inpatient Care Quality, and Hospital Competition under the Global Budget Payment Scheme of Taiwan’s National Health Insurance System: Mixed Frequency VAR Analyses. Systems 2022, 10, 187. https://doi.org/10.3390/systems10050187
Chen W-Y. On the Relationships among Nurse Staffing, Inpatient Care Quality, and Hospital Competition under the Global Budget Payment Scheme of Taiwan’s National Health Insurance System: Mixed Frequency VAR Analyses. Systems. 2022; 10(5):187. https://doi.org/10.3390/systems10050187
Chicago/Turabian StyleChen, Wen-Yi. 2022. "On the Relationships among Nurse Staffing, Inpatient Care Quality, and Hospital Competition under the Global Budget Payment Scheme of Taiwan’s National Health Insurance System: Mixed Frequency VAR Analyses" Systems 10, no. 5: 187. https://doi.org/10.3390/systems10050187