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Table 3 Results of our prediction models based on hospitalizations in 2018, considering the validation set (1/3 of the sample)

From: Neural networks and hospital length of stay: an application to support healthcare management with national benchmarks and thresholds

Outcome

Index

DIEM

Internal medicine

Cardiology

Emergency medicine

Geriatrics

Respiratory diseases

Neurology

Oncology

Long hospitalizations (> national average)

Incorrect classification

42.96%

47.66%

42.09%

42.09%

36.82%

41.67%

42.67%

39.16%

Sensitivity

69.34%

68.98%

77.50%

63.51%

70.86%

62.07%

70.45%

67.21%

Std. Err.

0.014

0.034

0.0.7

0.04

0.034

0.045

0.049

0.06

[95% Conf. interval]

(0.666–0.72)

(0.618–0.755)

(0.668–0.861)

(0.552–0.713)

(0.635–0.775)

(0.523–0.709)

(0.598–0.797)

(0.54–0.787)

Specificity

48.59%

40.46%

53.17%

54.22%

52.07%

54.84%

49.31%

57.14%

Std. Err.

0.012

0.03

0.027

0.033

0.045

0.044

0.042

0.048

[95% Conf. interval]

(0.462–0.51)

(0.345–0.467)

(0.476–0.506)

(0.475–0.609)

(0.428–0.612)

(0.456–0.638)

(0.409–0.578)

(0.471–0.667)

False positive rate (type I error)

51.41%

59.54%

46.83%

45.78%

47.93%

45.16%

50.69%

42.86%

False negative rate (type II error)

30.66%

31.02%

22.50%

36.49%

29.14%

37.93%

29.55%

32.79%

Positive likelihood ratio

1.35

1.16

1.66

1.39

1.48

1.37

1.39

1.57

Negative likelihood ratio

0.63

0.77

0.42

0.67

0.56

0.69

0.60

0.57

Area under the curve

0.59

0.55

0.65

0.59

0.61

0.58

0.60

0.62

Occurrence (outcome = 1)

1148

187

80

148

175

116

88

61

Number of obs. (hospitalizations)

2819

449

411

373

296

240

232

166

Outlier hospitalizations (> national threshold)

Incorrect classification

47.85%

46.67%

18.49%

37.80%

40.54%

33.33%

44.40%

34.94%

Sensitivity

62.73%

73.68%

71.43%

77.78%

77.78%

66.67%

85.71%

75.00%

Std. Err.

0.046

0.101

0.171

0.098

0.098

0.192

0.132

0.216

[95% Conf. interval]

(0.53–0.72)

(0.488–0.908)

(0.29–0.963)

(0.523–0.924)

(0.523–0.924)

(0.223–0.956)

(0.421–0.996)

(0.194–0.994)

Specificity

51.72%

52.44%

81.68%

61.41%

58.27%

66.67%

54.67%

64.81%

Std. Err.

0.01

0.024

0.019

0.026

0.029

0.031

0.033

0.037

[95% Conf. interval]

(0.498–0.536)

(0.476–0.572)

(0.776–0.853)

(0.597–0.702)

(0.522–0.641)

(0.602–0.727)

(0.479–0.613)

(0.569–0.721)

False positive rate (type I error)

48.28%

47.56%

18.32%

38.59%

41.73%

33.33%

45.33%

35.19%

False negative rate (type II error)

37.27%

26.32%

28.57%

22.22%

22.22%

33.33%

14.29%

25.00%

Positive likelihood ratio

1.30

1.55

3.90

2.02

1.86

2.00

1.89

2.13

Negative likelihood ratio

0.72

0.50

0.35

0.36

0.38

0.50

0.26

0.39

Area under the curve

0.57

0.63

0.77

0.70

0.68

0.67

0.70

0.70

Occurrence (outcome = 1)

110

19

7

18

18

6

7

4

Number of obs. (hospitalizations)

2,819

449

411

373

296

240

232

166

  1. See “Empirical strategy” section for a clear explanation of these indexes