Control charts for time to asthma attack

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Control Charts for Time In Between Asthma Events
Control Charts for Time in Between Asthma Attacks
By
Farrokh Alemi, Ph.D.
George Mason University
College of Nursing and Health Science
Tel: 703-993-4226
Fax: 509-756-1991
Email: [email protected]
Version of Wednesday, November 06, 2002
Page 1
Control Charts for Time In Between Asthma Events
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Abstract
This paper provides a tutorial on use of time-in-between control charts for
management of asthma. We provide the formulas needed for calculation and display of
the chart. We also apply the method to 3 illustrative examples previously provided in the
literature. Data show that the proposed chart describes patient conditions well and can
detect important changes in patient environments. Additional research is needed to test
the viability of the proposed tool in assisting asthmatic patients.
Control Charts for Time In Between Asthma Events
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Introduction
The monitoring of Peak Expiratory Flow Rate (PEFR) is crucial to effective
management of asthma. Recent national and international guidelines for care of patients
recommend daily monitoring of PEFR.1 But the data collected, is rarely used by patients
to help them understand their progress or by clinicians to modify treatment plans. Since
neither the patient nor the clinician make extensive use of the data, it is not surprising that
the effort to collect PEFR is often abandoned by the patients. To remedy this situation, a
number of investigators have called for use of control charts in understanding PEFR data.
2, 3, 4, 5, 6
In a recent paper, Boggs and colleagues provide the steps for constructing an
XmR chart for PEFR data.7 They provide examples of how PEFR can be charted by
displaying data from three patients. We suggest an alternative method known as Timein-Between charts and which has been shown to be specially suited for monitoring rare
events.8,9 In this approach, instead of directly displaying PEFR values, one measures and
plots the time in between attacks. The clinician’s and the patient’s objective is to
increase time until the next attack. Using the data provided by Boggs and colleagues, this
paper shows how new insights is gained from patients’ management of asthma.
Patient’s PEFR varies a great deal over time. Some of this variability is due to
measurement errors and chance events that do not mark a change in the underlying lung
function. Occasionally however, the PEFR values indicate a radical departure from usual
patterns. In these circumstances, it is important to examine what might have caused the
change. Control charts allow us to focus on occasions when changes in PEFR values
indicate new disease patterns.
Methods
Patients are asked to record their PEFR value once a day. These data are used to
construct the control chart. For the purposes of our study and in accordance with NHLBI
suggestions, we define an asthma attack as a PEFR value that is lower than 80% of the
personal best or predicted PEFR value. If the clinician wishes to monitor time to next
severe attack, and in accordance with NHLBI suggestions they may define an attack as a
value less than 60% of personal best or predicted PEFR value.
In the control chart, we have a choice of either plotting length of well days or
length of asthma attacks. The choice depends on which event is more rare. If the patient
tends to have asthma attacks, then analyzing and plotting length of attack free days is
best. In contrast, if patient has infrequent attacks, then analyzing and plotting length of
asthma attacks is best. In either case, we are plotting the duration of the event which is
relatively rare.
We demonstrate the construction of the chart by examining the number of attack
free days. In these charts, we plot the number of continuous days with no asthma attack
against days since last visit. The steps in constructing the chart for number of attack free
days are as follows:
1. Verify the chart assumptions. Check to see that attack free days are less common
than asthma attack days. Check that length of attack free periods has a geometric
distribution, meaning that longer periods are increasingly rare.
Control Charts for Time In Between Asthma Events
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2. Calculate the length of attack free periods. Score the length of attack free period.
Table 1 shows how the number of continuous days with no asthma is estimated
based on the values of two subsequent PEFR measurements.
Table 1: Rules for counting days with no asthma attacks
PEFR measure
Number of days with
Yesterday
Today
no asthma attack
Start of data collection
PEFR>=80% of best value
1 day
Start of data collection
PEFR<80% of best value
0 day
PEFR>=80% of best value
PEFR<80% of best value
0 day
PEFR<80% of best value
PEFR<80% of best value
0 day
PEFR<80% of best value
PEFR>80% of best value
1 day
PEFR>=80% of best value
PEFR>=80% of best value
1 + yesterday’s length
of attack free days
For example, during a week starting from Monday the client had values less than
80% of their best value on Wednesday and Thursday. In all other days, the client
had normal values. In these circumstances, the count for Monday is 1 because
there was no attack on this day. The count for Tuesday is 2 because it is two days
without attack. The count for Wednesday and Thursday are both zero because of
the attacks. The count for Friday, Saturday and Sunday are respectively 1, 2, and
3. Note that for each day of success, the number of attack free day increases until
a day with an asthma attack occurs and returns the count to zero. The count
remains at zero until another consecutive sequence of attack free days start.
3. Plot length of attack free periods against time. The Y-axis is the length of attack
free periods. The x-axis is the time since last visit.
4. Calculate the Upper Control Limit. A patient’s lung function has improved, if
number of days with no asthma attacks is higher than an upper control limit
(UCL). To calculate the UCL, we need R, the ratio of days without an attack to
days with an attack
R=
Number of days without asthma attack
Number of days with asthma attack
If we assume that time to the next attack has a geometric distribution (meaning
that most attacks are short and longer attacks are increasingly rare), then the UCL
can be calculated as:
UCL = R + 3 [R * (1+R)] 0.5
5. If the duration of attack free days exceed the UCL, then the patient is getting
better. The duration is beyond what can be expected from chance alone. The
clinician and the patient explore what brought about these prolonged recovery
with the objective of finding the cause and repeating the success.
Control Charts for Time In Between Asthma Events
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Source of data
Data were collected from three illustrative cases reported by Boggs and
colleagues. The first patient was a “36 year old female who had asthma since age 10 as a
result of both allergic and non allergic causal and trigger agents.” Her care included
avoiding dust mite, and cigarette smoke. She was asthmatic only once in the last 3
months and that was secondary to exertion. Table 2 provides PEFR data for 14
consecutive observation days for patient one. Her personal best was 468 L/minute during
this period.
Table 2: Data for Three Illustrative Patients
First patient
Second patient
Third patient
Asthma
Asthma
Asthma
Day since visit PEFR
attack?
PEFR
attack?
PEFR
attack?
1
430
No
314
Yes
120
Yes
2
380
No
411
Yes
140
Yes
3
410
No
426
Yes
100
Yes
4
400
No
432
Yes
150
Yes
5
420
No
411
Yes
260
No
6
410
No
401
Yes
150
Yes
7
460
No
371
Yes
100
Yes
8
420
No
346
Yes
120
Yes
9
460
No
361
Yes
160
Yes
10
440
No
391
Yes
300
No
11
420
No
371
Yes
300
No
12
460
No
356
Yes
275
No
13
470
No
450
No
300
No
14
460
No
396
Yes
200
No
15
529
140
Yes
16
516
170
Yes
17
536
150
Yes
18
543
150
Yes
19
543
190
No
20
536
21
550
22
520
23
516
24
521
25
557
26
550
27
506
28
529
Personal best
468
554
310
80% of the best
374
443
248
Asthma attack is defined as 80% of best personal value. Second patient care
was changed after 14th day.
Control Charts for Time In Between Asthma Events
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The second patient was “22 years old female with a history of chronic, severe, life
threatening asthma since early childhood.” She had a wide range of allergies. Table 2
shows 14 consecutive observation days for the second patient. Her personal best was 554
L/minute. After these 14 days, the patient’s medication and care changed. An additional
14 days were observed post treatment change.
The third patient was 11 years old and being seen for the first time. She had
asthma for 8 years and had required hospitalization 3 times in the past 12 months. Her
personal best was 310 L/minute.
Results
Table 3 shows the calculation of the attack free periods for second and third patient. The
calculation for the first patient is trivial as the patient was always attack free.
Table 3: Calculation of attack free periods
Days since
visit
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Second Patient
Attack
Asthma
free
PEFR
attack?
period
314
Yes
0
411
Yes
0
426
Yes
0
432
Yes
0
411
Yes
0
401
Yes
0
371
Yes
0
346
Yes
0
361
Yes
0
391
Yes
0
371
Yes
0
356
Yes
0
450
No
1
396
Yes
0
529
No
1
516
No
2
536
No
3
543
No
4
543
No
5
536
No
6
550
No
7
520
No
8
516
No
9
521
No
10
557
No
11
550
No
12
506
No
13
Third Patient
PEFR
120
140
100
150
260
150
100
120
160
300
300
275
300
200
140
170
150
150
190
Asthma
attack?
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
No
No
No
No
Yes
Yes
Yes
Yes
No
Attack
free
period
0
0
0
0
1
0
0
0
0
1
2
3
4
5
0
0
0
0
1
Control Charts for Time In Between Asthma Events
28
Personal best
80% of the best
529
554
443
No
Page 7
14
310
248
For the first patient, all PEFR values were above 80% of her personal best. This
patient had no asthma attacks during this observation period and therefore no change in
patient’s care is indicated. For this patient because attack days are more rare than well
days, one would plot the number of consecutive asthma attack days.
The second patient is a different story. During the first 14 days, the patient had
numerous days where his PEFR was below 80% of personal best. For this patient an
attack free day is quite rare. Therefore we plot the number of attack free days against
days since office visit. Figure 1 provides the findings.
Consecutive
attack free days
Figure 1: Observation of Second
Patient for 14 days
2
1
Upper control limit
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Days since office visit
Consecutive attack free
days
Note that there are no days until the 13th day in which the patient does not have a mild
asthma attack. The control limit is calculated from the ratio of attack free days to attack
days. For the second patient’s first 14 days, this ratio is 1/13 = 0.08. The UCL is
calculated as 0.08 + 3 * (0.08*1.08)^0.5 = 0.94. Note that the single day in which the
client does not have an
attack is a statistical
Figure 2: Recovery of Second Patient
significant event. The
after intervention
clinician and the patient
need to review why on this
16
day the patient did not have
14
Before
an attack.
After
12
intervention
intervention
After 14
10
observation days, the
8
6
second patient’s care was
4
modified significantly.
2
Figure 2 shows the
UCL
0
resulting recovery of the
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
patient. As can be seen, the
Days since visit
patient had no attack for
Control Charts for Time In Between Asthma Events
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the next 15 days post treatment. Throughout the time period after the intervention, the
length of attack free days exceeded the UCL. Therefore, after the intervention that
patient had improved beyond what could be expected by mere chance.
The third patient illustrates a mix of well days and asthma attacks. The patient
had asthma attacks the first four days. Recovery started on the 5th day but the length of
recovery was not statistically significant and therefore could have been due to random
chance events. The recovery was statistically significant from 9th through the 13th day.
The patient and the clinician explored what brought about this success. During this
period the patient was visiting her aunt and was away from dog, mite and smoke irritants
in her home environment. After the 13th day, the patient returns home and so do the
asthma attacks.
5
4
3
Upper control
limit
2
1
19
17
15
13
11
9
7
5
3
0
1
Consecutive attack
free days
Figure 3: Recovery of Third Patient
Days since visit
Conclusions
This paper provides a brief tutorial on use of time-in-between control charts in
monitoring asthma attacks. The approach provided here provides a viable method of
analyzing PEFR values. It has the advantage of providing a visual display of data. The
control limit allows the clinicians and the patients to ignore random variations and focus
on periods of time when real changes in underlying patterns of asthma attacks are
occurring. The rules for construction of the control chart are relatively simple and can be
taught to patients. In addition, web based and medical record based tools are also
available for analyzing control charts (see for example
http://www.rapidimprovements.com). Finally, clinical laboratories can construct control
charts for patients. These possibilities encourage additional work on the use of control
chart for asthmatic patients.
Additional research is needed to compare the proposed approach to XmR charts
both in terms of accuracy in detecting changes in patient outcomes as well as ease of use
and understanding by patients. It is important to study whether patients who use control
Control Charts for Time In Between Asthma Events
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chart methodologies have more effective communications with their clinicians and can
more easily get to root environmental causes of their asthma. But perhaps most
important, research is needed to verify that patients who use control charts obtain greater
relief from asthma attacks than those who do not use control charts.
Appendix A: Data Collection Tool
Patients often need a well-structured task for collecting and charting the data. The
following are two forms for data collection and charting.
Control Charts for Time In Between Asthma Events
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Form for Patients with Infrequent Asthma Attacks
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mild
Attack?
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
PEFR
Attack
length
Duration
of
asthma
attacks
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
1
2
Best PEFR =
80% of best PEFR =
3
4
5
6
7
8
9
1
0
Days since last office visit
1
1
1
2
Rules for scoring: Score each PEFR less than 80% of your best personal value or
predicted value as an attack. Put a zero for the length of attacks whenever a well day
occurs. When attacks occur over consecutive days, add “1” to previous day’s total until a
well day occurs, in which case you start the count back at zero. Following table shows
how to score the length of attacks:
Yesterday
No data
No data
No Attack
Attack
No Attack
Attack
Today
Attack
No Attack
No Attack
No Attack
Attack
Attack
Duration of attack
1 day
0 day
0 day
0 day
1 day
1 + yesterday’s length
of attack
Plot the duration of attack in the chart area to the right. To set your upper control limit,
calculate the ratio of attack days to well days. The control limit is calculated as:
Limit = Ratio + 3 * SQRT [Ratio *(1+ Ratio)]
Values that exceed the control limit indicate significant deterioration of your asthma.
When this occurs explore what may have caused this change. Bring this chart to your
next clinic visit. Bring this chart to your next clinic visit.
1
3
1
4
Control Charts for Time In Between Asthma Events
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Form for Patients with Frequent Asthma Attacks
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
PEFR
Mild
Attack?
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Yes | No
Consecutive
well days
# of
well
days
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
1
2
Personal best PEFR =
80% of personal best =
3
4
5
6
7
8
9
1
0
1
1
Days since last office visit
Rules for scoring: Score each PEFR less than 80% of your best personal value or
predicted value as an attack. Put a zero for the number of well days whenever an attack
occurs. When a well day occurs, add “1” to previous days number until an attack occurs,
in which case you start the count back at zero. Following table shows how to score the
number of days between attacks:
Yesterday
No data
No data
No Attack
Today
Attack
No Attack
No Attack
Attack
No Attack
Attack
No Attack
Attack
Attack
Number of well days
0 day
1 day
1 + yesterday’s length
of well days
1 day
0 day
0 day
Plot the number of days between attacks (well days), in the chart area to the right. To set
your limits, calculate the ratio of well days to attack days. The control limit is calculated
as:
Limit = Ratio + 3 * SQRT [Ratio *(1+ Ratio)]
Values that exceed the control limit indicate significant improvement in your asthma.
When this occurs explore what has changed to cause such an improvement.
1
2
1
3
1
4
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References
1
2
3
4
5
6
7
8
9
Expert Panel Report. Guidelines for the diagnosis and management of asthma.
National Insitute of Health, Publication number 92-3091, 1992.
Boggs P, Hayati, Washburne W, Wheeler D. Using statistical process control
charts for the continual improvement of asthma care. Jt Comm J Qual Improv
1999;25:163-81.
Gibson PG, Wlodarczyk J, Hensley MJ, et al. Using quality-control analysis of
peak expiratory flow readings to guide therapy for asthma. Ann Intern Med
1995;123:488-92.
Asthma health status. Ongoing measurement in the context of continuous quality
improvement. Med Care. 1993 Mar;31(3 Suppl):MS97-105.
Solodky C, Chen H, Jones PK, Katcher W, Neuhauser D. Patients as partners in
clinical research: a proposal for applying quality improvement methods to patient
care. Med Care. 1998 Aug;36(8 Suppl):AS13-20.
Neuhauser DV, Jean-Baptiste R, Solodky C. Neighborhood care partners (NCP):
a teaching case. Qual Manag Health Care. 2001 Spring; 9(3): 66-70.
Boggs P, Wheeler D, Washburne W, Hayati F. The peak expiratory flow rate
control chart in asthma care: chart construction and use in asthma care. Ann
Allergy Asthma Immunol 1998; 81:552-62
Benneyan JC. Number-between g-type statistical quality control charts for
monitoring adverse events. Health Care Management Science. 2001 Dec; 4(4):
305-18.
Benneyan JC. Performance of number-between g-type statistical control charts
for monitoring adverse events. Health Care Management Science. 2001 Dec;
4(4): 319-36.
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