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Table 2 Criterion validity assessment: Lorenz-1 status and inpatient hospital use

From: Use of power-law analysis to predict abuse or diversion of prescribed medications: proof-of-concept mathematical exploration

Power law zone

Alprazolam (n = 463,203)

Gabapentin (n = 267,693)

Opioid (n = 2,077,393)

 

PLG1

PLG2

PLG3

PLG4

PLG1

PLG2

PLG3

 

PLG1

PLG2

PLG3

 

N of cases

241,992

161,677

49,603

9931

174,989

90,590

2114

 

1,833,724

186,258

57,411

 

Lorenz-1 in follow-up

0.0

0.0

1.6

45.3

0.0

1.4

58.5

 

0.0

0.5

34.5

 

Lorenz-1 sensitivity, specificity, PPV, NPVa (%)

83.5, 98.8, 45.3, 99.8

48.9, 99.7, 58.5, 99.5

95.4, 98.2, 34.5, 100.0

 Incident Lorenz-1 in follow-up

0.0

0.0

1.6

20.7

0.0

1.1

0.0

 

0.0

0.5

9.9

 

Incident Lorenz-1 sensitivity, specificity, PPV, NPVa (%)

69.9, 98.3, 20.7, 99.8

0.0, 99.2, 0.0, 99.6

85.5, 97.5, 9.9, 100.0

 IPH observation year

3.5

5.0

6.6

6.3

7.0

8.7

9.5

 

5.7

9.3

8.4

 

 IPH follow-up

3.6

5.0

6.6

7.3

6.7

8.4

9.4

 

4.5

8.1

8.2

 

 IPH % change

2.9

0.0

0.0

15.9

− 4.3

− 3.4

− 1.1

 

− 21.1

− 12.9

− 2.4

 

IPH sensitivity, specificity, PPV, NPV (%)

3.5, 97.9, 7.3, 95.6

1.0, 99.2, 9.4, 92.7

4.6, 97.3, 8.2, 95.2

 SUDb IPH observation year

0.6

1.2

2.0

2.0

1.4

1.7

2.6

 

0.7

2.3

2.6

 

 SUDb IPH follow-up

0.6

1.2

2.2

2.8

1.3

1.6

2.5

 

0.7

2.2

2.9

 

 SUDb IPH % change

0.0

0.0

10.0

40.0

− 7.1

− 5.9

− 3.8

 

0.0

− 4.3

11.5

 

SUD IPH sensitivity, specificity, PPV, NPVa (%)

5.7, 97.9, 2.8, 99.0

1.4, 99.2, 2.5, 98.6

9.4, 97.3, 2.9, 99.2

Utilization quartile

Q1

Q2

Q3

Q4

Q1

Q2

Q3

Q4

Q1

Q2

Q3

Q4

N of cases

133,446

108,543

103,532

117,680

71,889

60,802

65,223

69,779

486,760

537,304

528,704

524,625

Lorenz-1 in follow-up

0.0

0.0

0.0

4.6

0.0

0.0

0.0

3.6

0.0

0.0

0.0

4.0

Lorenz-1 sensitivity, specificity, PPV, NPVa (%)

99.5, 75.5, 4.6, 100.0

99.6, 74.6, 3.6, 100.0

99.9, 75.5, 4.0, 100.0

 Incident Lorenz-1 in follow-up

0.0

0.0

0.0

2.5

0.0

0.0

0.0

1.4

0.0

0.0

0.0

1.3

Incident Lorenz-1 sensitivity, specificity, PPV, NPVa (%)

99.2, 75.1, 2.5, 100.0

99.1, 74.2, 1.4, 100.0

99.7, 75.0, 1.3, 100.0

 IPH observation year

3.2

4.0

4.7

6.0

6.4

7.1

8.2

8.9

2.8

4.7

7.3

9.3

 IPH follow-up

3.4

3.9

4.7

6.1

6.1

6.9

7.7

8.5

3.2

3.8

5.2

7.4

 IPH % change

6.2

− 2.5

0.0

1.7

− 4.7

− 2.8

− 6.1

− 4.5

14.3

− 19.1

− 28.8

− 20.4

IPH sensitivity, specificity, PPV, NPVa (%)

34.6, 75.0, 6.1, 96.1

30.5, 74.3, 8.5, 93.1

38.0, 75.4, 7.4, 95.9

 SUDb IPH observation year

0.5

0.8

1.1

1.7

1.2

1.4

1.5

1.7

0.3

0.5

0.8

1.8

 SUDb IPH follow-up

0.5

0.8

1.1

1.9

1.2

1.3

1.4

1.7

0.4

0.5

0.7

1.8

 SUDb IPH % change

0.0

0.0

0.0

11.8

0.0

− 7.1

− 6.7

0.0

33.3

0.0

− 12.5

0.0

SUD IPH sensitivity, specificity, PPV, NPVa (%)

45.9, 74.8, 1.9, 99.2

31.6, 74.0, 1.7, 98.7

52.4, 75.0, 1.8, 99.4

  1. Earliest baseline year from January 1, 2013, through December 31, 2013, with follow-up from January 1, 2014, through June 30, 2014. Latest baseline year from July 1, 2014, through June 30, 2015, with follow-up from July 1, 2015, through December 31, 2015
  2. IPH inpatient hospital, NPV negative predictive value, PLG power-law group, PPV positive predictive value, Q quartile, SUD substance use disorder
  3. aAssuming that top PLG category and fourth quartile are predicted as at risk
  4. bDiagnosis codes in Additional file 1: Appendix S4