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Hybrid Regression Models for Predicting Hydration: A Case Study in Pediatric Hemodialysis

Suzana Djordjevic

Suzana Djordjevic

Faculty of Education, University of KragujevacJagodina, Serbia
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Djordjevic, Suzana
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Mirjana Kostic

Mirjana Kostic

Department of Nephrology, University Children HospitalBelgrade, Serbia
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Kostic, Mirjana
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Blerina Zanaj

Blerina Zanaj

Faculty of Economics and Agribusiness, Agriculture University of TiranaTirana, Albania
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Zanaj, Blerina
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Danijela Milosevic

Danijela Milosevic

Faculty of Technical Sciences Cacak, University of KragujevacCacak, Serbia
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Milosevic, Danijela
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Vladimir Mladenovic

Vladimir Mladenovic

Faculty of Technical Sciences Cacak, University of KragujevacCacak, Serbia
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Mladenovic, Vladimir
  
10 set 2025
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Pubblicato online: 10 set 2025
Pagine: 212 - 222
Ricevuto: 21 lug 2024
Accettato: 14 lug 2025
DOI: https://doi.org/10.2478/msr-2025-0025
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© 2025 Suzana Djordjevic et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1.

Matrix representation of a dataset with n input parameters xij (j = 1, … , n) and output parameter yi, measured over m time moments (i = 1,..,m).
Matrix representation of a dataset with n input parameters xij (j = 1, … , n) and output parameter yi, measured over m time moments (i = 1,..,m).

Fig. 2.

EN-GBR hybrid model hydration predictions vs. real hydration values.
EN-GBR hybrid model hydration predictions vs. real hydration values.

Fig. 3.

EN-SVR hybrid model hydration predictions vs. real hydration values.
EN-SVR hybrid model hydration predictions vs. real hydration values.

Fig. 4.

Comparison between the models’ metrics.
Comparison between the models’ metrics.

Fig. 5.

Comparison between the EN, GBR, and EN-GBR hydration prediction vs. real hydration values.
Comparison between the EN, GBR, and EN-GBR hydration prediction vs. real hydration values.

Fig. 6.

Comparison between the EN, SVR, and EN-SVR hydration prediction vs. real hydration values.
Comparison between the EN, SVR, and EN-SVR hydration prediction vs. real hydration values.

Results achieved with the EN, GBR, SVR, hybrid EN-GBR and hybrid EN-SVR models_

Real values EN values GBR values SVR values EN-GBR values EN-SVR values
Patient A −0.3 −0.48129796 −0.18628015 −0.81704017 −0.3527895 −0.46503815
−0.8 −0.91890762 −0.80598051 −1.27369152 −0.80427712 −0.90426637
0.2 0.50873695 0.23782386 0.39220703 0.20545681 0.46932447
−1.2 −1.11180823 −1.16581552 −1.27910948 −1.18921171 −1.13263351
−2.1 −2.2058463 −2.09972043 −1.83435081 −2.09690962 −2.19735346
−2.2 −2.30081989 −2.18690249 −1.91096666 −2.1958786, −2.30016087
−5.6 −5.05723497 −5.59310215 −3.86500347 −5.59597978 −5.12703839
−2.8 −2.83149824 −2.79700751 −2.38790569 −2.79852713 −2.84700099
−3.1 −3.28661257 −3.10436425 −2.90010456 −3.08728966 −3.21576016
1.1 1.13724622 1.08674662 0.91430495 1.08914686 1.13514346
Patient B 2.3 2.05498245 2.30474957 2.07372147 2.30325372 2.32446905
0.6 0.67973341 0.62278249 0.72046415 0.61362807 0.70735133
−1.1 −0.98525658 −1.16755784 −1.07055426 −1.10503825 −1.14305158
−1.3 −1.19201570 −1.40885596 −1.32889134 −1.32276658 −1.37031130
−1.8 −1.72955661 −1.73768376 −1.84493265 −1.80881611 −1.86989233
−1.7 −1.66446912 −1.69278792 −1.80055228 −1.73364828 −1.81502659
0.9 0.85001765 0.93925670 0.88927059 0.91509444 0.92993130
−3.8 −3.84511421 −3.89311761 −3.89983185 −3.79272144 −3.84172986
−4.7 −4.97572847 −4.68874558 −4.75482693 −4.72968422 −4.79968123
−2.2 −2.16571580 −2.17217104 −2.26907722 −2.20450492 −2.20647985

Performance metrics_

R2 RMSE MAPE
1−∑i=1mYι^−Yi2∑i=1mY¯−Yi2 1 - {{\sum\nolimits_{i = 1}^m {{{\left( {\widehat {{Y_\iota }} - {Y_i}} \right)}^2}} } \over {\sum\nolimits_{i = 1}^m {{{\left( {\bar Y - {Y_i}} \right)}^2}} }} 1m∑i=1mYi−Yι^2 \sqrt {{1 \over m}\sum\limits_{i = 1}^m {{{\left( {{Y_i} - \widehat {{Y_\iota }}} \right)}^2}} } 1m∑i=1mYi−Yι^Yi⋅100 {1 \over m}\sum\limits_{i = 1}^m {\left| {{{{Y_i} - \widehat {{Y_\iota }}} \over {{Y_i}}}} \right| \cdot 100}

Model comparisons_

Model R2 RMSE MAPE
Patient A EN 0.97770 0.33319 0.103
GBR 0.99969 0.50409 0.012
SVR 0.92285 0.53131 0.095
EN-GBR 0.99960 0.16218 0.007
EN-SVR 0.98259 0.30489 0.092
Ridge regression 0.91005 0.44157 0.243
Kernel Ridge 0.90765 0.43811 0.257
Bayesian Ridge 0.89345 0.45118 0.256
RF 0.68556 0.46803 0.433
LSTM 0.95325 0.38197 0.136
Patient B EN 0.97998 0.28097 0.055
GBR 0.99802 0.27370 0.015
SVR 0.97227 0.54102 0.141
EN-GBR 0.99919 0.10223 0.011
EN-SVR 0.96178 0.37549 0.053
Ridge regression 0.97089 0.34216 0.062
Kernel Ridge 0.96991 0.34059 0.063
Bayesian Ridge 0.89360 0.46269 0.055
RF 0.93517 0.35403 0.789
LSTM 0.84637 0.32715 0.408
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Ingegneria, Elettrotecnica, Ingegneria dell'automazione, metrologia e collaudo
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