- Email: [email protected]
Time-Between Control Charts for Monitoring Asthma Attacks
Joint Commission
Journal on Quality and Safety
Tools, Methods, and Strategies
Time-Between Control Charts for Monitoring Asthma Attacks
Farrokh Alemi, Ph.D. Duncan Neuhauser, Ph.D.
he monitoring of peak expiratory flow rate (PEFR) is crucial for effective management of asthma. Recent national and international guidelines for care of patients recommend daily monitoring of PEFR.1,2 However, the collected data are rarely used by patients to help them understand their progress or by clinicians to modify treatment plans. Because neither the patient nor the clinician makes 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 to understand PEFR data.3–8 A 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 changes 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. Boggs and colleagues have described in a step-by-step fashion how to construct an XmR chart* for PEFR data.3,8 They provide examples of how PEFR can be charted by displaying data from three patients. We suggest an alternative method known as time-between charts, which have been shown to be especially suited for monitoring rare events.9,10 This method is based on the assumption of recurrent events in repeated trials.11 Every day is considered a new trial. Asthma attacks are assumed to be of different lengths, but when one ends, a recurrent event has
T
* In an XmR control chart, the variable (X-portion)—PEFR—is plotted on one control chart, and the moving range differences between serial variables (mR portion) are plotted on a second chart beneath the first.
February 2004
Article-at-a-Glance Background: The monitoring of peak expiratory flow rate (PEFR) is crucial for effective management of asthma. Daily PEFR monitoring is recommended, yet the data are rarely used by patients to help them understand their progress or by clinicians to modify treatment plans. Time-between control charts, which have been shown to be specially suited for monitoring rare events, can be used to monitor asthma attacks. Methods: Each patient is asked to record his or her PEFR value once a day, and these data are used to construct the control chart. PEFR data for three previously reported cases are presented and used to illustrate the control chart methodology. If duration of consecutive attacks is plotted and the observed duration exceeds the upper control limit (UCL), the patient is getting worse. If length of consecutive symptom-free days is plotted and the observed duration exceeds the UCL, the patient is getting better. In both circumstances, the clinician and the patient explore what brought about the prolonged recovery or periods of deterioration. The object is to increase time until the next attack. Discussion: Using time-between control charts in monitoring asthma attacks has the advantage of providing a visual display of data that, unlike eyeballing of trends, clarifies when patients should seek additional clinical advice. The control limit allows clinicians and patients to ignore random variations and focus on real changes in underlying patterns of asthma attacks.
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Journal on Quality and Safety
occurred, and we are back to the start of the process. Because control limits can be calculated for recurrent events, the duration of asthma attacks can be monitored and compared with the limit. In this approach, instead of directly displaying PEFR values, one measures and plots the time between attacks. The clinician’s and the patient’s objective is to increase time until the next attack. On the basis of the data provided by Boggs and colleagues, this article shows how new insights can be gained from patients’ use of time-between charts for asthma attacks.
Methods Each patient is asked to record his or her PEFR value once a day. These data are used to construct the control chart. For the purposes of our study and in accordance with the National Heart, Lung, and Blood Institute’s (NHLBI’s) suggestions,1,2 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, in accordance with NHLBI suggestions, he or she may define an attack as a value less than 60% of personal best or predicted PEFR value.
Steps* The steps in constructing the chart are now described. 1. Select What to Chart. One can chart whether the patient is getting better or worse. For a patient who is typically experiencing attacks and rarely having symptom-free days, duration of symptom-free days should be plotted. This chart can tell if the patient is getting better. For a patient who is typically well but occasionally experiencing attacks, duration of attacks should be plotted. This chart can tell if the patient is getting worse. In either case, one should chart the duration of whichever event is rare. 2. Verify the Chart Assumptions. We assume that attacks do not last more than a day and that attacks on separate days are different attacks, as opposed to a prolonged episodes of the same attack. If two attacks occur on the same day, we consider it one day of attack. We * Two forms for data collection and charting—one for patients with infrequent asthma attacks and one for patients with frequent asthma attacks—are in the public domain and are available as e-mail attachments on request from Dr. Farrokh Alemi.
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assume that the probability of an attack or a symptomfree day is (1) independent, (2) constant from day to day, and (3) relatively small. Under these assumptions, the duration of either an attack or symptom-free days has a geometric distribution.* A geometric distribution can be verified by examining the frequency of duration of the event of interest. 3. Calculate the Duration. One can score the length of attack-free periods or the duration of attacks using the scoring procedure in Table 1 (page 97). The table shows how the number of continuous days with or without asthma is estimated based on the values of two subsequent PEFR measurements. For example, during a week starting from Monday a client had values less than 80% of his 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 it was the first symptom-free day. The count for Tuesday is 2 because it is two days without attack. The counts for Wednesday and Thursday are both zero because of the asthma attacks. The counts for Friday, Saturday, and Sunday are, respectively, 1, 2, and 3. Note that for each day of success, the number of attack-free days 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 starts. Strictly speaking, the proposed method of displaying the chart is not accurate. Time-between charts are based on the assumption of recurrent events in repeated trials. At the last day of a series of attacks, we are back to a recurrent event, and thus the statistical test is conducted for that day (which is always the length of the series). However, we plot the last day and all days leading to it on the control chart to better represent the * If you are charting duration of attacks, the probability of having n–1 days of attack and a symptom-free day on the nth day is calculated as: P(X = n) = (1–p)n–1p. Each time the duration of asthma attacks increases by one day, the probability of observing that duration should decrease by 1–p times. Thus, an asthma attack of 2 days has 1–p times lower probability than an asthma attack of 1 day. Suppose you have collected data on 100 durations of attacks until a symptom-free day occurs. If the probability of symptom-free day is 75%, then in a geometric distribution there will be 75 durations of length of zero days, 19 durations of length of one day, 5 durations of length of two days, and 1 case in which the duration of attack is more than two days. Note that as the length of the duration increases, the probability of observing it becomes more rare by a constant factor of 1–p.
Volume 30 Number 2
Copyright 2004 Joint Commission on Accreditation of Healthcare Organizations
Joint Commission
Journal on Quality and Safety
Table 1. Rules for Counting Days with No Asthma Attacks* Yesterday
Today
No data at start No data at start Symptom-free
Symptom-free Attack Attack
Number of Days with no Asthma Attack 1 day 0 day 0 day
Attack
Attack
0 day
Attack
Symptom-free
Symptom-free
Symptom-free
1 day 1 + yesterday’s length of symptom-free days
patient’s progression over time. Although the progression is plotted, the statistical test is performed only for the last day. 4. Plot the Duration Against Time. The y-axis is the duration. The x-axis is the time since the last visit. For the data in Table 2 (below), because attacks are rare, the control chart will plot duration of attacks on the yaxis and time on the x-axis. 5. Calculate the Upper Control Limit (UCL).9,10 A patient’s lung function has improved if the number of days with no asthma attacks is higher than a UCL. To calculate the UCL for duration of attack-free days, we need R, the ratio of days without an attack to days with an attack: Number of symptom-free days R= Number of days with asthma attack Then the UCL can be calculated as follows: UCL = R + 3 [R ⫻ (1+R)]0.5
Number of Days with Asthma Attack 0 day 1 day 1 day 1 + yesterday’s duration of attack days 0 day 0 day
If we are plotting duration of attacks and the observed duration exceeds the UCL, the patient is getting worse. If we are plotting length of symptomfree days and the observed duration exceeds the UCL, the patient is getting better. In both circumstances, the duration that exceeds the UCL is beyond what can be expected from chance alone. The clinician and the patient explore what brought about these prolonged periods of recovery or deterioration.
Case Studies Data were collected from three illustrative cases reported by Boggs and colleagues.8
Patient 1 The first patient was a “36-year-old female who has had asthma since age 10 years as a result of
Table 2. Sample Assignment of Duration of Attacks or Symptom-Free Days Day of the week
Was There an Attack?
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Symptom-free Symptom-free Attack Attack Symptom-free Symptom-free Symptom-free
February 2004
Duration of SymptomFree Days 1 day 2 days 0 day 0 day 1 day 2 days 3 days
Duration of Attacks
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0 day 0 day 1 day 2 days 0 day 0 day 0 day
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Table 3. Data for Three Case Study Patients* Patient 1 Day 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 28 Personal best 80% of the best
PEFR 430 380 410 400 420 410 460 420 460 440 420 460 470 460
Patient 2
Asthma Attack? No No No No No No No No No No No No No No
PEFR
468
314 411 426 432 411 401 371 346 361 391 371 356 450 396 529 516 536 543 543 536 550 520 516 521 557 550 506 529 554
374
443
Patient 3 Asthma Attack? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes
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
310 248
* PEFR, peak expiratory flow rate. Asthma attack is defined as 80% of best personal value. Care for Patient 2 was changed after the 14th day.
both allergic and nonallergic causal and trigger agents.”8(p. 555) Her care included avoiding dust mites and cigarette smoke. She was asthmatic only once in the past 3 months, and that was secondary to
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exertion. Table 3 (above) provides PEFR data for 14 consecutive observation days for Patient 1. Her personal best was 468 liters/minute during this period.
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Journal on Quality and Safety
Patient 2 The second patient was a 22-year-old female with a history of “chronic, severe, life-threatening asthma since early childhood.”8(p. 556) She had a wide range of allergies. Table 3 shows 14 consecutive observation days for the second patient. Her personal best was 554 liters/minute. After these 14 days, the patient’s medication and care changed. An additional 14 days were observed posttreatment change.
Patient 3 The third patient was an 11-year-old child who was seen for the first time. She had had asthma for 8 years and had required hospitalization 3 times in the past 12 months. Her personal best was 310 liters/minute.8
Results Table 4 (page 100) shows the calculation of the attackfree periods for Patients 1 and 2. The calculation for Patient 1 is trivial because the patient was always attack free. For Patient 1, 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 the patient’s care is indicated. Because attack days are more rare than symptom-free days, one would plot the number of consecutive asthma-attack days. Patient 2 is a different story. During the first 14 days, the patient had numerous days on which her PEFR was below 80% of personal best. For this patient, an attackfree day is quite rare. Therefore, we plot the number of attack-free days against days since office visit. Figure 1 (page 101) provides the findings. 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 Patient 2’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 statistically significant event. The clinician and the patient need to review why on this day the patient did not have an attack. After 14 observation days, the second patient’s care was modified significantly. Figure 2 (page 101) shows the patient’s resulting recovery. As can be seen, the
February 2004
patient was symptom-free for the next 15 days posttreatment. Throughout the 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. In Figure 2, note that we have separated the plot into two periods: before and after the intervention. For calculating the UCL, one should use only the data from before the intervention. In this fashion, the patient and the clinicians can decipher if the postintervention data exceeds their expectations from historical patterns. If there is no planned intervention, as in Figure 1, UCL is calculated based on the entire data set. In these circumstances, each day is compared to the pattern of all days. Patient 3 illustrates a mix of symptom-free days and asthma attacks. As shown in Figure 3 (page 101), the patient had asthma attacks for 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 the 9th through the 13th days. 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 returned home-and so did the asthma attacks.
Discussion Using time-between control charts in monitoring asthma attacks provides a viable method of analyzing PEFR values. It has the advantage of providing a visual display of data. Some may argue that significant changes in peak flow should be self-evident to patients and physicians alike simply by “eyeballing” the trends. However, control charts facilitate going beyond understanding trends and clarify when patients should seek additional clinical advice. Eyeballing trends is helpful but may not be conducive to action because it provides no concise guidelines for when the patient is deteriorating. The control limit allows clinicians and patients to ignore random variations and focus on real changes in underlying patterns of asthma attacks. The rules for constructing the control chart are relatively simple and can
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Table 4. Calculation of Attack-Free Periods* Patient 2 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 28 Personal best 80% of the best
PEFR 314 411 426 432 411 401 371 346 361 391 371 356 450 396 529 516 536 543 543 536 550 520 516 521 557 550 506 529 554
Asthma Attack? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes No No No No No No No No No No No No No No
Patient 3 Attack-Free Period 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
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
310
443
248
* PEFR, peak expiratory flow rate.
be taught to patients. In addition, clinical laboratories and Web-based and medical-record-based tools are available resources for help in constructing control chart for patients with asthma.
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The only rule used for detecting special-cause variation in the time-between control chart method described in this article was whether the duration of the event plotted exceeded the UCL.
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Journal on Quality and Safety
Observation of Second Patient for 14 Days
Figure 1. Until the 13th day there were no days in which the patient did not have a mild asthma attack.
Other rules that focus on the pattern of data around the center line may also be used. Benneyan provides a formula for estimating the center line.9,10 Run-chart rules (for example, 8 points in a row anywhere on one side of the center line, 6 points in a row increasing or decreasing, 14 points in a row alternating up and down) can be used to detect unique patterns around the center line. Additional research is needed to compare the proposed approach to other control charts, especially XmR charts.12 XmR charts may be more accurate because they use the PEFR values instead of dichotomizing these values into attack or symptomfree days. On the other hand, time-between charts are especially suited for tracking events that are rare and may be easier for a patient or layperson to use and maintain. Comparative studies should establish both the accuracy of detecting changes in patient conditions and the patients’ ease of daily PEFRvalue reporting and understanding of the resulting chart. It would also be important to investigate whether patients who are shown their own control charts have more effective communications with their clinicians and can more easily get to root environmental causes of their asthma. Perhaps most importantly, research is needed to verify that patients who are shown control charts obtain greater relief from asthma attacks. A time-between chart, described here for patients, is also applicable for monitoring the performance of organizations. For example, in 2002 the Joint Commission on
February 2004
Recovery of Second Patient After Intervention
Figure 2. The patient was symptom-free for the next 15 days posttreatment.
Accreditation of Healthcare Organizations (JCAHO) posted on its Web site 10 candidate measures for monitoring quality of asthma care, including education on peak flow meter use, education on asthma triggers and avoidance, asthma patients with self-management plans, asthma patients with severity assessment, and symptomfree days.13 Time-between charts can be used to measure an organization’s progress in meeting any one of these 10 criteria. For example, one could examine time-between for patients showing up at a clinic who do not get smoking cessation advice. The organization’s goal would be to increase the time-between missed criteria. A succinct example of application of time-between charts to evaluation of organizations can be found in the work of Pierce-Bulger and Nighswander,14 who used timebetween charts to monitor infant mortality.
Recovery of Third Patient
Figure 3. The patient had asthma attacks for the first four days, and recovery started on the fifth day.
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Conclusions The use of time-between control charts in monitoring asthma appears to highlight the inherent value of peak flow trends and may ultimately help clinicians and patients find a common language with which to express changes in airway behavior. J
Farrokh Alemi, Ph.D., is Acting Assistant Dean of Graduate Health Science, College of Nursing and Health Science, George Mason University, Fairfax, Virginia. Duncan Neuhauser, Ph.D., is Professor, Department of Epidemiology and Biostatistics, School of Medicine, Case Western Reserve University, Cleveland. Please address correspondence to Farrokh Alemi, Ph.D., [email protected].
References 1. Guidelines for the diagnosis and management of asthma. National Heart, Lung, and Blood Institute. National Asthma Education Program. Expert Panel Report. J Allergy Clin Immunol 88(3 Pt. 2):425–534, Sep. 1992. 2. National Heart, Lung, and Blood Institute, National Institutes of Health: International Consensus Report on Diagnosis and Treatment of Asthma. Bethesda, MD. Publication No. 92-3091. March 1992. Eur Respir J 5(5):601–41, May 1992. 3. Boggs P.B.: Using statistical process control charts for the continual improvement of asthma care. Jt Comm J Qual Improv 25:163–181, Apr. 1999. 4. Gibson P.G., et al.: Using quality-control analysis of peak expiratory flow readings to guide therapy for asthma. Ann Intern Med 123:488–492, Oct. 1995. 5. Headrick L., Neuhauser D., Melnikow J.: Asthma health status: Ongoing measurement in the context of continuous quality improvement. Med Care 31(3 suppl.):MS97–MS105, Mar. 1993. 6. Solodky C., et al.: Patients as partners in clinical research: A proposal for applying quality improvement methods to patient care. Med Care 36(8 suppl.):AS13–AS20, Aug. 1998. 7. Neuhauser D.V., Jean-Baptiste R., Solodky C.: Neighborhood care partners (NCP): A teaching case. Qual Manag Health Care 9:66–70, spring 2001.
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8. Boggs P., et al.: The peak expiratory flow rate control chart in asthma care: Chart construction and use in asthma care. Ann Allergy Asthma Immunol 81:552–562, Dec. 1998. 9. Benneyan J.C.: Number-between g-type statistical quality control charts for monitoring adverse events. Health Care Management Science 4:305–318, Dec. 2001. 10. Benneyan J.C.: Performance of number-between g-type statistical control charts for monitoring adverse events. Health Care Management Science 4:319–336, Dec. 2001. 11. Feller W.: An Introduction to Probability Theory and Its Applications, vol. 1, 3rd ed. New York: John Wiley & Sons, 1968. 12. Wheeler D.J.: Advanced Topics in Statistical Process Control: The Power of Shewhart’s Charts. Knoxville, TN: SPC Press, 1995. 13. Joint Commission on Accreditation of Healthcare Organizations: Request for Public Comment on Disease-Specific Care Standardized Asthma Measure Set. http://www.jcaho.org/ dscc/performance+measures/asthma+measure+set.htm (accessed Nov. 26, 2003). 14. Pierce-Bulger M., Nighswander T.: Nutaqsiivik: An approach to reducing infant mortality using quality improvement principles. Qual Manag Health Care 9:40–46, spring 2001.
Volume 30 Number 2
Copyright 2004 Joint Commission on Accreditation of Healthcare Organizations
Journal on Quality and Safety
Tools, Methods, and Strategies
Time-Between Control Charts for Monitoring Asthma Attacks
Farrokh Alemi, Ph.D. Duncan Neuhauser, Ph.D.
he monitoring of peak expiratory flow rate (PEFR) is crucial for effective management of asthma. Recent national and international guidelines for care of patients recommend daily monitoring of PEFR.1,2 However, the collected data are rarely used by patients to help them understand their progress or by clinicians to modify treatment plans. Because neither the patient nor the clinician makes 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 to understand PEFR data.3–8 A 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 changes 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. Boggs and colleagues have described in a step-by-step fashion how to construct an XmR chart* for PEFR data.3,8 They provide examples of how PEFR can be charted by displaying data from three patients. We suggest an alternative method known as time-between charts, which have been shown to be especially suited for monitoring rare events.9,10 This method is based on the assumption of recurrent events in repeated trials.11 Every day is considered a new trial. Asthma attacks are assumed to be of different lengths, but when one ends, a recurrent event has
T
* In an XmR control chart, the variable (X-portion)—PEFR—is plotted on one control chart, and the moving range differences between serial variables (mR portion) are plotted on a second chart beneath the first.
February 2004
Article-at-a-Glance Background: The monitoring of peak expiratory flow rate (PEFR) is crucial for effective management of asthma. Daily PEFR monitoring is recommended, yet the data are rarely used by patients to help them understand their progress or by clinicians to modify treatment plans. Time-between control charts, which have been shown to be specially suited for monitoring rare events, can be used to monitor asthma attacks. Methods: Each patient is asked to record his or her PEFR value once a day, and these data are used to construct the control chart. PEFR data for three previously reported cases are presented and used to illustrate the control chart methodology. If duration of consecutive attacks is plotted and the observed duration exceeds the upper control limit (UCL), the patient is getting worse. If length of consecutive symptom-free days is plotted and the observed duration exceeds the UCL, the patient is getting better. In both circumstances, the clinician and the patient explore what brought about the prolonged recovery or periods of deterioration. The object is to increase time until the next attack. Discussion: Using time-between control charts in monitoring asthma attacks has the advantage of providing a visual display of data that, unlike eyeballing of trends, clarifies when patients should seek additional clinical advice. The control limit allows clinicians and patients to ignore random variations and focus on real changes in underlying patterns of asthma attacks.
Volume 30 Number 2
Copyright 2004 Joint Commission on Accreditation of Healthcare Organizations
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Joint Commission
Journal on Quality and Safety
occurred, and we are back to the start of the process. Because control limits can be calculated for recurrent events, the duration of asthma attacks can be monitored and compared with the limit. In this approach, instead of directly displaying PEFR values, one measures and plots the time between attacks. The clinician’s and the patient’s objective is to increase time until the next attack. On the basis of the data provided by Boggs and colleagues, this article shows how new insights can be gained from patients’ use of time-between charts for asthma attacks.
Methods Each patient is asked to record his or her PEFR value once a day. These data are used to construct the control chart. For the purposes of our study and in accordance with the National Heart, Lung, and Blood Institute’s (NHLBI’s) suggestions,1,2 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, in accordance with NHLBI suggestions, he or she may define an attack as a value less than 60% of personal best or predicted PEFR value.
Steps* The steps in constructing the chart are now described. 1. Select What to Chart. One can chart whether the patient is getting better or worse. For a patient who is typically experiencing attacks and rarely having symptom-free days, duration of symptom-free days should be plotted. This chart can tell if the patient is getting better. For a patient who is typically well but occasionally experiencing attacks, duration of attacks should be plotted. This chart can tell if the patient is getting worse. In either case, one should chart the duration of whichever event is rare. 2. Verify the Chart Assumptions. We assume that attacks do not last more than a day and that attacks on separate days are different attacks, as opposed to a prolonged episodes of the same attack. If two attacks occur on the same day, we consider it one day of attack. We * Two forms for data collection and charting—one for patients with infrequent asthma attacks and one for patients with frequent asthma attacks—are in the public domain and are available as e-mail attachments on request from Dr. Farrokh Alemi.
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February 2004
assume that the probability of an attack or a symptomfree day is (1) independent, (2) constant from day to day, and (3) relatively small. Under these assumptions, the duration of either an attack or symptom-free days has a geometric distribution.* A geometric distribution can be verified by examining the frequency of duration of the event of interest. 3. Calculate the Duration. One can score the length of attack-free periods or the duration of attacks using the scoring procedure in Table 1 (page 97). The table shows how the number of continuous days with or without asthma is estimated based on the values of two subsequent PEFR measurements. For example, during a week starting from Monday a client had values less than 80% of his 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 it was the first symptom-free day. The count for Tuesday is 2 because it is two days without attack. The counts for Wednesday and Thursday are both zero because of the asthma attacks. The counts for Friday, Saturday, and Sunday are, respectively, 1, 2, and 3. Note that for each day of success, the number of attack-free days 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 starts. Strictly speaking, the proposed method of displaying the chart is not accurate. Time-between charts are based on the assumption of recurrent events in repeated trials. At the last day of a series of attacks, we are back to a recurrent event, and thus the statistical test is conducted for that day (which is always the length of the series). However, we plot the last day and all days leading to it on the control chart to better represent the * If you are charting duration of attacks, the probability of having n–1 days of attack and a symptom-free day on the nth day is calculated as: P(X = n) = (1–p)n–1p. Each time the duration of asthma attacks increases by one day, the probability of observing that duration should decrease by 1–p times. Thus, an asthma attack of 2 days has 1–p times lower probability than an asthma attack of 1 day. Suppose you have collected data on 100 durations of attacks until a symptom-free day occurs. If the probability of symptom-free day is 75%, then in a geometric distribution there will be 75 durations of length of zero days, 19 durations of length of one day, 5 durations of length of two days, and 1 case in which the duration of attack is more than two days. Note that as the length of the duration increases, the probability of observing it becomes more rare by a constant factor of 1–p.
Volume 30 Number 2
Copyright 2004 Joint Commission on Accreditation of Healthcare Organizations
Joint Commission
Journal on Quality and Safety
Table 1. Rules for Counting Days with No Asthma Attacks* Yesterday
Today
No data at start No data at start Symptom-free
Symptom-free Attack Attack
Number of Days with no Asthma Attack 1 day 0 day 0 day
Attack
Attack
0 day
Attack
Symptom-free
Symptom-free
Symptom-free
1 day 1 + yesterday’s length of symptom-free days
patient’s progression over time. Although the progression is plotted, the statistical test is performed only for the last day. 4. Plot the Duration Against Time. The y-axis is the duration. The x-axis is the time since the last visit. For the data in Table 2 (below), because attacks are rare, the control chart will plot duration of attacks on the yaxis and time on the x-axis. 5. Calculate the Upper Control Limit (UCL).9,10 A patient’s lung function has improved if the number of days with no asthma attacks is higher than a UCL. To calculate the UCL for duration of attack-free days, we need R, the ratio of days without an attack to days with an attack: Number of symptom-free days R= Number of days with asthma attack Then the UCL can be calculated as follows: UCL = R + 3 [R ⫻ (1+R)]0.5
Number of Days with Asthma Attack 0 day 1 day 1 day 1 + yesterday’s duration of attack days 0 day 0 day
If we are plotting duration of attacks and the observed duration exceeds the UCL, the patient is getting worse. If we are plotting length of symptomfree days and the observed duration exceeds the UCL, the patient is getting better. In both circumstances, the duration that exceeds the UCL is beyond what can be expected from chance alone. The clinician and the patient explore what brought about these prolonged periods of recovery or deterioration.
Case Studies Data were collected from three illustrative cases reported by Boggs and colleagues.8
Patient 1 The first patient was a “36-year-old female who has had asthma since age 10 years as a result of
Table 2. Sample Assignment of Duration of Attacks or Symptom-Free Days Day of the week
Was There an Attack?
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Symptom-free Symptom-free Attack Attack Symptom-free Symptom-free Symptom-free
February 2004
Duration of SymptomFree Days 1 day 2 days 0 day 0 day 1 day 2 days 3 days
Duration of Attacks
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0 day 0 day 1 day 2 days 0 day 0 day 0 day
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Table 3. Data for Three Case Study Patients* Patient 1 Day 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 28 Personal best 80% of the best
PEFR 430 380 410 400 420 410 460 420 460 440 420 460 470 460
Patient 2
Asthma Attack? No No No No No No No No No No No No No No
PEFR
468
314 411 426 432 411 401 371 346 361 391 371 356 450 396 529 516 536 543 543 536 550 520 516 521 557 550 506 529 554
374
443
Patient 3 Asthma Attack? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes
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
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* PEFR, peak expiratory flow rate. Asthma attack is defined as 80% of best personal value. Care for Patient 2 was changed after the 14th day.
both allergic and nonallergic causal and trigger agents.”8(p. 555) Her care included avoiding dust mites and cigarette smoke. She was asthmatic only once in the past 3 months, and that was secondary to
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exertion. Table 3 (above) provides PEFR data for 14 consecutive observation days for Patient 1. Her personal best was 468 liters/minute during this period.
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Patient 2 The second patient was a 22-year-old female with a history of “chronic, severe, life-threatening asthma since early childhood.”8(p. 556) She had a wide range of allergies. Table 3 shows 14 consecutive observation days for the second patient. Her personal best was 554 liters/minute. After these 14 days, the patient’s medication and care changed. An additional 14 days were observed posttreatment change.
Patient 3 The third patient was an 11-year-old child who was seen for the first time. She had had asthma for 8 years and had required hospitalization 3 times in the past 12 months. Her personal best was 310 liters/minute.8
Results Table 4 (page 100) shows the calculation of the attackfree periods for Patients 1 and 2. The calculation for Patient 1 is trivial because the patient was always attack free. For Patient 1, 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 the patient’s care is indicated. Because attack days are more rare than symptom-free days, one would plot the number of consecutive asthma-attack days. Patient 2 is a different story. During the first 14 days, the patient had numerous days on which her PEFR was below 80% of personal best. For this patient, an attackfree day is quite rare. Therefore, we plot the number of attack-free days against days since office visit. Figure 1 (page 101) provides the findings. 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 Patient 2’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 statistically significant event. The clinician and the patient need to review why on this day the patient did not have an attack. After 14 observation days, the second patient’s care was modified significantly. Figure 2 (page 101) shows the patient’s resulting recovery. As can be seen, the
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patient was symptom-free for the next 15 days posttreatment. Throughout the 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. In Figure 2, note that we have separated the plot into two periods: before and after the intervention. For calculating the UCL, one should use only the data from before the intervention. In this fashion, the patient and the clinicians can decipher if the postintervention data exceeds their expectations from historical patterns. If there is no planned intervention, as in Figure 1, UCL is calculated based on the entire data set. In these circumstances, each day is compared to the pattern of all days. Patient 3 illustrates a mix of symptom-free days and asthma attacks. As shown in Figure 3 (page 101), the patient had asthma attacks for 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 the 9th through the 13th days. 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 returned home-and so did the asthma attacks.
Discussion Using time-between control charts in monitoring asthma attacks provides a viable method of analyzing PEFR values. It has the advantage of providing a visual display of data. Some may argue that significant changes in peak flow should be self-evident to patients and physicians alike simply by “eyeballing” the trends. However, control charts facilitate going beyond understanding trends and clarify when patients should seek additional clinical advice. Eyeballing trends is helpful but may not be conducive to action because it provides no concise guidelines for when the patient is deteriorating. The control limit allows clinicians and patients to ignore random variations and focus on real changes in underlying patterns of asthma attacks. The rules for constructing the control chart are relatively simple and can
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Table 4. Calculation of Attack-Free Periods* Patient 2 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 28 Personal best 80% of the best
PEFR 314 411 426 432 411 401 371 346 361 391 371 356 450 396 529 516 536 543 543 536 550 520 516 521 557 550 506 529 554
Asthma Attack? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes No No No No No No No No No No No No No No
Patient 3 Attack-Free Period 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
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
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* PEFR, peak expiratory flow rate.
be taught to patients. In addition, clinical laboratories and Web-based and medical-record-based tools are available resources for help in constructing control chart for patients with asthma.
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The only rule used for detecting special-cause variation in the time-between control chart method described in this article was whether the duration of the event plotted exceeded the UCL.
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Observation of Second Patient for 14 Days
Figure 1. Until the 13th day there were no days in which the patient did not have a mild asthma attack.
Other rules that focus on the pattern of data around the center line may also be used. Benneyan provides a formula for estimating the center line.9,10 Run-chart rules (for example, 8 points in a row anywhere on one side of the center line, 6 points in a row increasing or decreasing, 14 points in a row alternating up and down) can be used to detect unique patterns around the center line. Additional research is needed to compare the proposed approach to other control charts, especially XmR charts.12 XmR charts may be more accurate because they use the PEFR values instead of dichotomizing these values into attack or symptomfree days. On the other hand, time-between charts are especially suited for tracking events that are rare and may be easier for a patient or layperson to use and maintain. Comparative studies should establish both the accuracy of detecting changes in patient conditions and the patients’ ease of daily PEFRvalue reporting and understanding of the resulting chart. It would also be important to investigate whether patients who are shown their own control charts have more effective communications with their clinicians and can more easily get to root environmental causes of their asthma. Perhaps most importantly, research is needed to verify that patients who are shown control charts obtain greater relief from asthma attacks. A time-between chart, described here for patients, is also applicable for monitoring the performance of organizations. For example, in 2002 the Joint Commission on
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Recovery of Second Patient After Intervention
Figure 2. The patient was symptom-free for the next 15 days posttreatment.
Accreditation of Healthcare Organizations (JCAHO) posted on its Web site 10 candidate measures for monitoring quality of asthma care, including education on peak flow meter use, education on asthma triggers and avoidance, asthma patients with self-management plans, asthma patients with severity assessment, and symptomfree days.13 Time-between charts can be used to measure an organization’s progress in meeting any one of these 10 criteria. For example, one could examine time-between for patients showing up at a clinic who do not get smoking cessation advice. The organization’s goal would be to increase the time-between missed criteria. A succinct example of application of time-between charts to evaluation of organizations can be found in the work of Pierce-Bulger and Nighswander,14 who used timebetween charts to monitor infant mortality.
Recovery of Third Patient
Figure 3. The patient had asthma attacks for the first four days, and recovery started on the fifth day.
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Conclusions The use of time-between control charts in monitoring asthma appears to highlight the inherent value of peak flow trends and may ultimately help clinicians and patients find a common language with which to express changes in airway behavior. J
Farrokh Alemi, Ph.D., is Acting Assistant Dean of Graduate Health Science, College of Nursing and Health Science, George Mason University, Fairfax, Virginia. Duncan Neuhauser, Ph.D., is Professor, Department of Epidemiology and Biostatistics, School of Medicine, Case Western Reserve University, Cleveland. Please address correspondence to Farrokh Alemi, Ph.D., [email protected].
References 1. Guidelines for the diagnosis and management of asthma. National Heart, Lung, and Blood Institute. National Asthma Education Program. Expert Panel Report. J Allergy Clin Immunol 88(3 Pt. 2):425–534, Sep. 1992. 2. National Heart, Lung, and Blood Institute, National Institutes of Health: International Consensus Report on Diagnosis and Treatment of Asthma. Bethesda, MD. Publication No. 92-3091. March 1992. Eur Respir J 5(5):601–41, May 1992. 3. Boggs P.B.: Using statistical process control charts for the continual improvement of asthma care. Jt Comm J Qual Improv 25:163–181, Apr. 1999. 4. Gibson P.G., et al.: Using quality-control analysis of peak expiratory flow readings to guide therapy for asthma. Ann Intern Med 123:488–492, Oct. 1995. 5. Headrick L., Neuhauser D., Melnikow J.: Asthma health status: Ongoing measurement in the context of continuous quality improvement. Med Care 31(3 suppl.):MS97–MS105, Mar. 1993. 6. Solodky C., et al.: Patients as partners in clinical research: A proposal for applying quality improvement methods to patient care. Med Care 36(8 suppl.):AS13–AS20, Aug. 1998. 7. Neuhauser D.V., Jean-Baptiste R., Solodky C.: Neighborhood care partners (NCP): A teaching case. Qual Manag Health Care 9:66–70, spring 2001.
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8. Boggs P., et al.: The peak expiratory flow rate control chart in asthma care: Chart construction and use in asthma care. Ann Allergy Asthma Immunol 81:552–562, Dec. 1998. 9. Benneyan J.C.: Number-between g-type statistical quality control charts for monitoring adverse events. Health Care Management Science 4:305–318, Dec. 2001. 10. Benneyan J.C.: Performance of number-between g-type statistical control charts for monitoring adverse events. Health Care Management Science 4:319–336, Dec. 2001. 11. Feller W.: An Introduction to Probability Theory and Its Applications, vol. 1, 3rd ed. New York: John Wiley & Sons, 1968. 12. Wheeler D.J.: Advanced Topics in Statistical Process Control: The Power of Shewhart’s Charts. Knoxville, TN: SPC Press, 1995. 13. Joint Commission on Accreditation of Healthcare Organizations: Request for Public Comment on Disease-Specific Care Standardized Asthma Measure Set. http://www.jcaho.org/ dscc/performance+measures/asthma+measure+set.htm (accessed Nov. 26, 2003). 14. Pierce-Bulger M., Nighswander T.: Nutaqsiivik: An approach to reducing infant mortality using quality improvement principles. Qual Manag Health Care 9:40–46, spring 2001.
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