Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit
Abstract
:1. Introduction
2. Materials and Methods
2.1. Phase Type Survival Tree (PHTST)
2.2. PHTST Construction
2.3. Extended PHTST
2.4. Modelling Blocking State
2.4.1. Single-Absorbing State
2.4.2. Multi-Absorbing State
3. Results
3.1. The Stroke Unit of the Belfast City Hospital
3.1.1. Discharge Delay Distribution without Clustering Based on Discharge Destinations
3.1.2. Discharge Delay for the Patients Expected to Be Discharged to Private Nursing Homes
3.1.3. Discharge Delay with the Patients Expected to Be Discharged to Other Destinations
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Node | Covariate | Covariate Value | Number of Patients | Mean LOS | Standard Deviation (LOS) | Coefficient of Variation | WIC | Number of Phases | Total WIC | Gain in WIC |
---|---|---|---|---|---|---|---|---|---|---|
All | Complete dataset | Root node | 1985 | 29.01 | 52.84 | 1.82 | 16,847.73 | 3 | 16,847.73 | - |
1 (Root node) | Gender | Male | 933 | 26.59 | 44.06 | 1.66 | 7736.85 | 2 | 16,845.79 | 1.94 |
Female | 1052 | 31.15 | 59.47 | 1.91 | 9108.94 | 3 | ||||
Age | Young | 624 | 19.26 | 39.15 | 2.03 | 4650.09 | 2 | 16,729 | 118.73 | |
Old | 1361 | 33.48 | 57.49 | 1.72 | 12,078.9 | 3 | ||||
Diagnosis | Hemorrhagic | 154 | 33.6 | 56.45 | 1.68 | 1338.96 | 3 | 16,567.05 | 280.68 | |
Cerebral | 655 | 36.66 | 47.68 | 1.3 | 5978.78 | 2 | ||||
TIA | 425 | 9.31 | 19.95 | 2.14 | 2612.38 | 2 | ||||
Other | 751 | 32.54 | 65.05 | 2 | 6636.92 | 2 | ||||
2 Hemorrhagic | Gender | Male | 80 | 28.2 | 52.1 | 1.85 | 660.85 | 4 | 1332.41 | 6.55 |
Female | 74 | 39.45 | 60.25 | 1.53 | 671.56 | 2 | ||||
Age | Young | 50 | 24.56 | 55.12 | 2.24 | 370.13 | 4 | 1324.75 | 14.21 | |
Old | 104 | 37.95 | 56.56 | 1.49 | 954.63 | 2 | ||||
3 Cerebral | Gender | Male | 302 | 33.71 | 49.88 | 1.48 | 2694.19 | 2 | 5981.96 | −3.18 |
Female | 353 | 39.19 | 45.55 | 1.16 | 3287.78 | 2 | ||||
Age | Young | 194 | 24.07 | 42.45 | 1.76 | 1586.02 | 2 | 5949.18 | 29.61 | |
Old | 461 | 41.96 | 48.79 | 1.16 | 4363.16 | 2 | ||||
4 TIA | Gender | Male | 207 | 8.7 | 22.68 | 2.61 | 1229.17 | 2 | 2619.64 | −7.26 |
Female | 218 | 9.89 | 16.94 | 1.71 | 1390.47 | 2 | ||||
Age | Young | 176 | 5.84 | 11.16 | 1.91 | 924.58 | 2 | 2593.06 | 19.32 | |
Old | 249 | 11.77 | 24.02 | 2.04 | 1668.48 | 2 | ||||
5 Other strokes | Gender | Male | 344 | 30.74 | 43.41 | 1.41 | 3014.02 | 2 | 6645.27 | −8.35 |
Female | 407 | 34.07 | 78.8 | 2.31 | 3631.25 | 2 | ||||
Age | Young | 204 | 24.96 | 43.76 | 1.75 | 1662.38 | 2 | 6611.95 | 24.97 | |
Old | 547 | 35.37 | 71.17 | 2.01 | 4949.57 | 2 | ||||
6 Hemorrhagic Young | Gender | Male | 29 | 30.52 | 69.11 | 2.26 | 226.49 | 2 | 375.19 | −5.07 |
Female | 21 | 16.33 | 22.81 | 1.4 | 148.71 | 2 | ||||
7 Hemorrhagic Old | Gender | Male | 51 | 26.88 | 39.2 | 1.46 | 437.87 | 2 | 954.43 | 0.19 |
Female | 53 | 48.6 | 67.58 | 1.39 | 516.56 | 2 | ||||
8 Cerebral Young | Gender | Male | 104 | 24.67 | 49.27 | 2 | 853.33 | 2 | 1591.24 | −5.22 |
Female | 90 | 23.37 | 32.94 | 1.41 | 737.91 | 2 | ||||
9 Cerebral Old | Gender | Male | 198 | 38.45 | 49.67 | 1.29 | 1836.51 | 2 | 4369.07 | −5.92 |
Female | 263 | 44.6 | 47.94 | 1.07 | 2532.56 | 2 | ||||
10 TIA Young | Gender | Male | 88 | 5.74 | 11.33 | 1.97 | 460.65 | 2 | 933.56 | −8.98 |
Female | 88 | 5.93 | 11 | 1.85 | 472.91 | 2 | ||||
11 TIA Old | Gender | Male | 119 | 10.89 | 28.08 | 2.58 | 767.35 | 2 | 1674.19 | −5.71 |
Female | 130 | 12.58 | 19.53 | 1.55 | 906.85 | 2 | ||||
12 Other strokes Young | Gender | Male | 119 | 30.11 | 52.77 | 1.75 | 1006.47 | 3 | 1665.64 | −3.26 |
Female | 85 | 17.75 | 24.66 | 1.75 | 659.17 | 2 | ||||
13 Other strokes Old | Gender | Male | 225 | 31.08 | 37.52 | 1.21 | 2000.22 | 2 | 4955.54 | −5.97 |
Female | 322 | 38.37 | 87.17 | 2.27 | 2955.32 | 2 |
Node | Destination | Number of Patients | Mean LOS | Standard Deviation (LOS) | Coefficient of Variation | WIC | Number of Phases | Degrees of Freedom () | Total WIC | Gain in WIC |
---|---|---|---|---|---|---|---|---|---|---|
6 Hemorrhagic Young | All | 50 | 24.56 | 55.12 | 2.24 | 370.13 | 4 | 7 | - | - |
Death | 17 | 16.41 | 40.62 | 2.48 | 98.52 | 2 | 10 | 369.19 | 0.94 | |
Other | 33 | 28.76 | 60.83 | 2.12 | 270.67 | 4 | ||||
14 Hemorrhagic Old Male | All | 51 | 26.88 | 39.2 | 1.46 | 437.87 | 2 | 3 | - | - |
Death | 21 | 10.9 | 14.73 | 1.35 | 141.1 | 2 | 7 | 395.23 | 42.64 | |
Other | 27 | 31.89 | 38.85 | 1.22 | 243.81 | 1 | ||||
PNH | 3 | 93.67 | 67.48 | 0.72 | 10.32 | 2 | ||||
15 Hemorrhagic Female | All | 53 | 48.6 | 67.58 | 1.39 | 516.56 | 2 | 3 | - | - |
Death | 27 | 24.15 | 35.47 | 1.47 | 223.82 | 2 | 7 | 490.63 | 25.93 | |
Other | 24 | 74.17 | 85.36 | 1.15 | 257.48 | 1 | ||||
PNH | 2 | 74.17 | 85.36 | 1.15 | 9.33 | 2 | ||||
8 Cerebral Young | All | 194 | 24.07 | 42.45 | 1.76 | 1586.02 | 2 | 3 | - | - |
Death | 14 | 21.29 | 35.22 | 1.65 | 112.65 | 2 | 7 | 1585.46 | 0.56 | |
Other | 174 | 22.28 | 40.5 | 1.82 | 1405.34 | 2 | ||||
PNH | 6 | 82.33 | 63.22 | 0.77 | 67.48 | 1 | ||||
9 Cerebral Old | All | 461 | 41.96 | 48.79 | 1.16 | 4363.16 | 2 | 3 | - | - |
Death | 112 | 35.66 | 46.4 | 1.3 | 1028.5 | 1 | 5 | 4339.19 | 23.97 | |
Other | 296 | 36.94 | 43.09 | 1.17 | 2732.54 | 2 | ||||
PNH | 53 | 83.34 | 62.02 | 0.74 | 578.15 | 1 | ||||
10 TIA Young | All | 176 | 5.84 | 11.16 | 1.91 | 924.58 | 2 | 3 | - | - |
Death | 2 | 57.5 | 12.5 | 0.22 | 8.47 | 2 | 7 | 890.83 | 33.75 | |
Other | 173 | 4.8 | 7.77 | 1.62 | 873.57 | 2 | ||||
PNH | 1 | 81 | 0 | 0 | 8.79 | 1 | ||||
11 TIA Old | All | 249 | 11.77 | 24.02 | 2.04 | 1668.48 | 2 | 3 | - | - |
Death | 11 | 33.27 | 30.31 | 0.91 | 101.53 | 1 | 5 | 1655.42 | 13.06 | |
Other | 231 | 10.58 | 23.32 | 2.2 | 1497.54 | 2 | ||||
PNH | 7 | 17.29 | 18.01 | 1.04 | 56.35 | 1 | ||||
12 Other strokes Young | All | 204 | 24.96 | 43.76 | 1.75 | 1662.38 | 2 | 3 | - | - |
Death | 22 | 20.27 | 27.84 | 1.37 | 179.13 | 1 | 7 | 1638.66 | 23.72 | |
Other | 179 | 25.13 | 45.48 | 1.81 | 1454.59 | 2 | ||||
PNH | 3 | 49.33 | 19.48 | 0.39 | 4.94 | 2 | ||||
13 Other strokes Old | All | 547 | 35.37 | 71.17 | 2.01 | 4949.57 | 2 | 3 | - | - |
Death | 142 | 41.82 | 123.73 | 2.96 | 1295.56 | 2 | 11 | 4895.2 | 54.37 | |
Other | 358 | 28.27 | 33.35 | 1.18 | 3104.34 | 3 | ||||
PNH | 47 | 70.02 | 50.18 | 0.72 | 495.31 | 2 |
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Garg, L.; McClean, S.; Meenan, B.; Barton, M.; Fullerton, K.; Buttigieg, S.C.; Micallef, A. Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit. Algorithms 2022, 15, 414. https://doi.org/10.3390/a15110414
Garg L, McClean S, Meenan B, Barton M, Fullerton K, Buttigieg SC, Micallef A. Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit. Algorithms. 2022; 15(11):414. https://doi.org/10.3390/a15110414
Chicago/Turabian StyleGarg, Lalit, Sally McClean, Brian Meenan, Maria Barton, Ken Fullerton, Sandra C. Buttigieg, and Alexander Micallef. 2022. "Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit" Algorithms 15, no. 11: 414. https://doi.org/10.3390/a15110414
APA StyleGarg, L., McClean, S., Meenan, B., Barton, M., Fullerton, K., Buttigieg, S. C., & Micallef, A. (2022). Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit. Algorithms, 15(11), 414. https://doi.org/10.3390/a15110414