Diagnosis Obstructive Lung Disease - Medical Algorithm

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))

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Description

Specialty

Objective

ICD-10

Nomogram of Holleman et al for Diagnosis of Obstructive Airway Disease at the Bedside

Purpose: To evaluate a patient for obstructive airway disease based on limited clinical data using the nomogram of Holleman et al.

Description

Specialty

Objective

ICD-10