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Table 4 Evaluation performance of all considered ML and PopPK models

From: Development and evaluation of uncertainty quantifying machine learning models to predict piperacillin plasma concentrations in critically ill patients

Model

RMSE

MAE

ME

\({R^2}\)

MdAPE

MdPE

GUH evaluation: a priori

GBT new

34.27 (0.38)

21.55 (0.25)

− 4.09 (0.00)

0.58 (0.57)

17.29% (3.83%)

0.06% (0.01%)

GP new

37.41 (0.43)

23.54 (0.28)

2.04 (0.07)

0.50 (0.46)

21.39% (4.79%)

− 3.83% (− 0.84%)

MLP

38.56 (0.47)

27.35 (0.34)

2.58 (0.05)

0.47 (0.36)

23.09% (5.29%)

− 5.34% (− 1.26%)

PopPK

57.97 (0.64)

39.67 (0.54)

− 30.27 (− 0.45)

− 0.19 (− 0.21)

40.79% (11.60%)

38.33% (11.41%)

GUH evaluation: a posteriori

GBT prev

32.93 (0.27)

18.22 (0.19)

− 6.55 (− 0.02)

0.62 (0.73)

12.75% (3.09%)

1.77% (0.43%)

GP prev

34.03 (0.28)

19.41 (0.21)

− 3.83 (− 0.01)

0.59 (0.71)

16.48% (3.79%)

− 3.76% (− 0.92%)

MLP

37.20 (0.36)

23.64 (0.26)

− 4.87 (− 0.03)

0.51 (0.51)

17.06% (4.14%)

0.73% (0.17%)

PopPK

49.58 (0.43)

31.28 (0.32)

4.91 (0.03)

0.14 (0.32)

26.09% (6.69%)

− 1.85% (− 0.43%)

UMCG evaluation: a priori

GBT new

43.92 (0.78)

38.67 (0.62)

30.67 (0.58)

0.36 (− 0.12)

68.38% (12.89%)

− 68.38% (− 12.89%)

GP new

64.99 (0.89)

55.31 (0.74)

50.90 (0.72)

− 0.39 (− 0.45)

84.88% (15.33%)

− 84.88% (− 15.33%)

MLP

62.28 (0.85)

51.47 (0.71)

38.52 (0.63)

− 0.28 (− 0.33)

83.09% (14.97%)

− 83.09% (− 14.97%)

PopPK

50.46 (0.67)

31.50 (0.55)

− 23.97 (− 0.30)

0.16 (0.18)

39.84% (12.31%)

33.88 % (9.85%)

UMCG evaluation: a posteriori

GBT prev

28.12 (0.57)

21.11(0.40)

15.01 (0.37)

0.68 (0.25)

37.20% (8.46%)

− 37.20% (− 8.46%)

GP prev

31.58 (0.57)

22.73 (0.39)

18.05 (0.35)

0.60 (0.26)

25.15% (6.90%)

− 25.15% (− 6.9%)

MLP

30.35 (0.64)

26.55 (0.50)

22.45 (0.47)

0.63 (0.06)

54.16% (10.48 %)

− 54.16% (− 10.48%)

PopPK

25.89 (0.62)

19.95 (0.45)

2.15 (− 0.00)

0.73 (0.13)

26.69% (7.31%)

3.31% (0.87%)

  1. All RMSE, MAE, and ME values are in mg/L. The values in parenthesises are in log scale. Bold indicates the best model for that metric and case