### Description

Holleman et al developed a nomogram for predicting the probability of obstructive airway disease based on a limited amount of clinical data available at the bedside. The authors were at Duke University.

Parameters:

(1) smoking history in years of smoking

(2) presence or absence of wheezing

(3) peak expiratory flow (PEF) in liters per minute, using the best of 3 trials

The central line in the nomogram is the output for the nomogram, giving the percent probability of airway obstruction. With the line enlarged twofold, the following readings are measured:

Per Cent Probability

Millimeters

1

0

3

8

5

13.5

10

18.8

25

27.7

50

35

75

42.5

90

50.3

95

56

97

61.25

99

65.5

When this is graphed, a characteristic logistic regression curve is generated. This can be approximated by the following equation.

X =

= (0.136228 * (millimeters)) – 4.667595

probability =

= 1 / (1 + EXP((-1) * (X)))

To simplify the evaluation of the nomogram:

(1) only peak expiratory flow on the right vertical line is implemented and not wheezing. This would be easy to include since wheezing is set to 240 L/min PEF and no wheezing is about 401 L/min.

(2) the entries on the left line for wheezing (B) are assumed to overlap the no wheezing side (A) as follows:

A side

B side

0

12.5

25

37.5

0

50

12.5

62.5

25

75

37.5

50

62.5

75

If lines are then drawn between the smoking history line and the peak expiratory flow line, the following measurements along the middle line can be made.

No Wheezing (Side A) with data in mm along middle line

Years of Smoking

PEF

0

12.5

25

37.5

50

62.5

75

720

-7.5

-5

-2.5

0

3

6

8.1

660

-2.3

0.5

3

6

8.3

12

14

600

2.8

5

8

10.8

13

16.8

19

540

8

10.5

13.5

16.5

18.5

22

24.1

480

13.5

16

19

21.8

24

27.2

30

420

19

21.2

24.5

27.2

30

33

35.2

401

21

23.5

26.2

29

32

34.6

37.2

360

24.5

27

29.8

32.8

35

38

40.8

300

29

31.2

34

37

40

42.5

45

240

35

37.1

40.5

42.5

46

48.2

51

180

39.2

42

45

47.5

50.5

53

55.7

120

44.5

47

50

52.5

55.5

58.2

61

60

50

52.2

55.5

58

61

63.2

66

0

54

58

61

64

65.5

69

71.5

Wheezing (Side B) with data in mm along middle line

Years of Smoking

PEF

0

12.5

25

37.5

50

62.5

75

720

0

3

6

8.1

11

14.5

16.5

660

6

8.3

12

14

17

20

22.2

600

10.8

13

16.8

19

22

24.8

27.7

540

16.5

18.5

22

24.1

27.2

30.5

32.7

480

21.8

24

27.2

30

33

35.5

38.2

420

27.2

30

33

35.2

38.3

41

43.8

401

29

32

34.6

37.2

40

43

45.1

360

32.8

35

38

40.8

43.6

46.2

49

300

37

40

42.5

45

48

50.5

53

240

42.5

46

48.2

51

54

56.8

59.2

180

47.5

50.5

53

55.7

58.5

61.2

64

120

52.5

55.5

58.2

61

63.8

67

69

60

58

61

63.2

66

69

72

74.5

0

64

65.5

69

71.5

74.5

77

80

When this data is converted to probability, the corresponding data is calculated.

No Wheezing (Side A) with data in percentage probability

Years of Smoking

PEF

0

12.5

25

37.5

50

62.5

75

720

0.000

0.005

0.008

0.010

0.014

0.021

0.030

660

0.005

0.010

0.014

0.021

0.032

0.046

0.060

600

0.014

0.018

0.030

0.039

0.050

0.085

0.111

540

0.030

0.038

0.050

0.082

0.100

0.158

0.200

480

0.050

0.077

0.100

0.155

0.198

0.250

0.359

420

0.100

0.144

0.209

0.250

0.359

0.457

0.500

401

0.141

0.188

0.250

0.328

0.424

0.500

0.599

360

0.209

0.271

0.353

0.450

0.500

0.625

0.709

300

0.328

0.397

0.491

0.592

0.686

0.754

0.812

240

0.500

0.595

0.700

0.754

0.832

0.870

0.907

180

0.662

0.750

0.812

0.859

0.900

0.963

0.950

120

0.801

0.850

0.900

0.923

0.950

0.960

0.970

60

0.895

0.920

0.948

0.962

0.970

0.980

0.990

0

0.936

0.962

0.970

0.983

0.991

1.000

1.000

Wheezing (Side B) with data in percentage probability

Years of Smoking

PEF

0

12.5

25

37.5

50

62.5

75

720

0.010

0.014

0.021

0.030

0.040

0.063

0.082

660

0.021

0.032

0.046

0.060

0.087

0.125

0.162

600

0.039

0.050

0.085

0.111

0.158

0.216

0.250

540

0.082

0.100

0.158

0.200

0.250

0.375

0.447

480

0.155

0.198

0.250

0.359

0.457

0.500

0.631

420

0.250

0.359

0.457

0.500

0.634

0.715

0.786

401

0.328

0.424

0.500

0.599

0.686

0.750

0.814

360

0.450

0.500

0.625

0.709

0.781

0.836

0.882

300

0.592

0.686

0.754

0.812

0.867

0.900

0.928

240

0.754

0.832

0.870

0.907

0.936

0.952

0.968

180

0.859

0.900

0.963

0.950

0.964

0.970

0.982

120

0.923

0.950

0.960

0.970

0.982

0.992

0.995

60

0.962

0.970

0.980

0.990

0.995

1.000

1.000

0

0.983

0.991

1.000

1.000

1.000

1.000

1.000

The graph of the data in the middle line in mm vs the PEF is linear.

Set of Lines

Set of Lines

slope to line

intercept

A 0

-0.086396

54.98

A 12.5

-0.087065

57.76

A 25

-0.087748

60.95

A 37.5

B 0

-0.087423

63.56

A 50

B 12.5

-0.087719

66.29

A 62.5

B 25

-0.086426

68.77

A 75

B 37.5

-0.087415

71.63

B 50

-0.087315

74.54

B 62.5

-0.086776

77.21

B 75

-0.087239

79.87

The average slope is about -0.08715

If the intercept values are collected and graphed vs years of smoking:

Years of Smoking

A (no wheezing)

B (wheezing)

0

54.98

63.56

12.5

57.76

66.29

25

60.95

68.77

37.5

63.56

71.63

50

66.29

74.54

62.5

68.77

77.21

75

71.63

79.87

intercept for no wheezing =

= (0.2208857 * (years of smoking)) + 55.136786

intercept for wheezing =

= (0.2186857 * (years of smoking)) + 63.495

Putting It All Together

millimeters along middle line for probability with not wheezing =

= (–0.08715 * (PEF in L/min)) + (0.2208857 * (years of smoking)) + 55.136786

millimeters along middle line for probability with wheezing =

= (–0.08715 * (PEF in L/min)) + (0.2186857 * (years of smoking)) + 63.495

X =

= (0.136228 * (millimeters)) – 4.667595

probability of airway obstruction =

= 1 / (1 + EXP((-1) * (X)))

Using the Data

odds of any airflow obstruction =

= (probability) / (1 – (probability)

odds of at least moderate airflow obstruction =

= 0.95 * (odds of any airflow obstruction)

odds of at least severe airflow obstruction =

= 0.35 * (odds of any airflow obstruction)

probability of at least moderate airflow obstruction =

= (odds for moderate) / (1 + (odds for moderate))

probability of at least severe airflow obstruction =

= (odds for severe) / (1 + (odds for severe))