- Email: [email protected]
Improving the ability of peak expiratory flow rates to predict asthma
Hudson
et al.
3. Burge PS: Occupational asthma in electronics workers caused by colophony fumes: follow-up of affected workers. Thorax 37:348, 1982 4. Paggiaro PL, Loi AM, Rosai 0, Ferrante B. Pardi F, Roaseli MG. Baschieri L: Follow-up study of patients with respiratory disease due to toluene diisocyanate (TDI). Clin Allergy 14:463. IO84 5. Moller DR, McKay RT, Bernstein IL, Brooks SM: Long-term follow-up of workers with TDI asthma. Am Rev Respir Dis 129:A159, 1984 (abst) 6. Cartier A, Malo J-L. Forest F, Lafrance M, Pincau L, St-Aubin J-J, Dubois J-Y: Occupational asthma in snow crab-processing workers. J ALLERGYCLIN IMMUNOL 74:26 I . 1984 7. Dehaut P, Rachiele A, Martin RR, Malo JL: Histamine doseresponse curves in asthma: reproducibility and sensitivity of different indices to assess response. Thorax 38:516. 1983 8. ATS statement. Snowbird workshop on standardizatron of spirometry Am Rev Respir Dis 119:83 I. I979 9. Knudson RJ. Siatin RC, Lebowitz MD, Burrows B: The maximal expiratory flow-volume curves Am Rev Respir Dis 113587, 1976 10. Cockcroft DW, Killian DN, Mellon JJA, Hargreave FE: Bronchial reactivity to inhaled histamine: a method and clinical survey. Clin Allergy 7:235, 1977
1 I. Malo JL. Pineau L. Cattier A, Martm RR: Krierence valuch of the provocative concentrattons of methachoimc mar ciju~-~ 6% and 20% changes in forced expiratory voiumt. :I-,one ‘VC~V& in a normal population. Am Rev Respir Dis I?,: ,i !‘I? \ 12. Lam S, Wong R. Yeung M: Nonspecific broncht:ti rc:~~%vrt) in occupational asthma. J ALI~RGY CLIN Ibtiw:~.:a~ ki.18 ! Y7Q 13. Butcher BT, O’Neil CE. Reed MA. Calvagg~i, i) i’~:ictl) !i Development and loss of toluene diisocyanatc ~r‘acttv I?> I:>‘ munologic. pharmdcoh~ic. and provocative chdlh’ngr ~tudl? J AL.LERW CI.IN hlMLlNOl ?o,‘.; I, I’?82 14. Cartier A, Thomson NC. Froth PA. Roberta Ii. Iiargrea\c Iii:. Allergen-induced increase in bronchial respon~!vencss to ht; tamine: relationship to the late asthmatic response and changin auway caliber. J A1.i tKo~ Cl IN I~~Mu?IO!?) 170. 1982 15. Malo JL, Ouimet G, Cartier A. Levitz D. &is\ <‘K Comhincd alveolitis and asthma due tcr hexamethylcnc c!!tso,:y,mare (HDI). with dcmonstrdtion ot crossed respirator! and lmmu nologic reactivitics to diphenylmethane diisoc! .tnarc t MDI) .i AILERW CI.IN IMWNOI 72:31X 19X3 16. Yeung M. Grzybowski S. Prcgncisik in ~wup.tt~~mi;asthma Thorax JO:24 1. 1985
Improving the abiiity of peak rates to predict asthma Deborah L. Harm, Ph.D., Harry Kotses, Ph.D., and Thomas L. Creer, Ph.D. Athens, Ohio A major problem in the behavioral management of childhood usthma concerns recognition of the early signs of an impending episode. An objective measure commonly used to aid recognition rrf early warning signs is the peak expiratov flow rate (PEFR). This study examined the abilit\ of PEFRs to predict asthma within a I’-hour period; the prediction method used was based on prior and conditional posterior probabilities. Twenty$ve children with asthma recorded their PEFR twice daily, and also recorded the date and time of their asthma episodes. Conditional posterior probabilities and the ratio of hits to misses were computed for each subject at successively 1owerJlow rates. The average improvement in predictabilifi from the prior probability to the highest posterior probability was 491%. The ratio of hits to misses and the number of episodes predicted, however, decreased as the posterior probability increased. Selection of thr PEFR ut lower posterior probabilities resulted in fewer prediction errors and led to prediction of a higher number of episodes than selection of the PEFR at the highest posterior probability.
(JALLERGYCLINIMMUNOL76:6%94, 1985.)
From the Department of Psychology, Ohio University, Athens, Ohio. Supported in part by Grants HL27402 and HL2972 from the Division of Lung Diseases, National Heart, Lung, and Blood Institute. Received for publication July 25, 1984. Accepted for publication March 12, 1985. Reprint requests: Thomas L. Creer, Ph.D., Ohio University, Dept. of Psychology, Porter Hall, Athens, Ohio 45701.
688
A major problem in the management of childhood asthma concerns recognition of the early signs of an impending asthma episode. The difficulty is that patients with asthma vary considerably in the degree of correspondence between subjective sensations and objective measures of airway obstruction. individual correlations bettieen children’s subjective ratings of the severity of asthma and their PEFR have been re-
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TABLE
Abbreviations used PEFR: Peak expiratory flow rate EMG: Electromyograph
expiratory
1. Descriptive
diction errors when regression equations are used. The results of the Taplin and Creels study found entering PEFR scores in a probability equation can be
rates to predict
statistics
asthma
689
on selected
variables
Age (yr) ported to range from 0.25 to 0.70.’ Similarly, large discrepancies between a patient’s subjective ratings of the severity of impaired pulmonary function and objective spirometric measures were reported in several clinical studies involving emergency room treatment of asthma.2-4These studies provide evidence of the problems in detectability and predictability of asthma episodes that could interfere with adequate management of the disorder. The importance of the use of objective pulmonary measures to improve the prediction and detection of asthma is unquestionable. PEFR has been used with some success in predicting relapse and the need for hospitalization for asthma.‘. 4 Furthermore, the use of PEFR scores in conditional probability equations predicts asthma episodes within a 12-hour period. Taplin and CreerSused PEFR in a probability equation to predict the occurrence of asthma in two children. The base rate, or prior probability, for the occurrence of asthma and a critical PEFR value that most increased the predictability of asthma were determined for each child. Two conditional probabilities were calculated for each subject. The first was the probability of asthma in a 12hour period after a PEFR less than or equal to the critical value. The second was the probability of asthma in a 1Zhour period after a PEFR greater than the critical value. The results yielded approximately a threefold increase over the base rate in the predictability of asthma for both subjects. This method is useful for two reasons. First, it provides a valuable objective component to self-management procedures. If an individual had an objective indicator that an asthma episode was likely to occur within the next 12-hour period, he would be alerted to attend to subjective signs of asthma and could institute early interventions that could either prevent the attack or reduce its severity. The use of these interventions should lead to better control of the child’s asthma and reduce medical costs. Second, use of conditional probabilities improves accuracy in predicting the occurrence of asthma for an individual. The two probabilities taken together provide a ratio of hits and misses in the prediction of asthma episodes. This method takes into account the prior probability of asthma in a single subject and removes the problem of between-subject variance that contributes to pre-
flow
PEFR No. episodes
Mean
Range
11.36 321.19 15.40
6.0 to 16.0 99.17 to 543.67 3.0 to 51 .o
applied to self-management programs for children with asthma. However, drawing general conclusions from these results was limited by the small sample of subjects. The purpose of the current study was to evaluate the use of a relatively simple method for predicting the occurrence of asthma in individual children. The study examined the ability of peak flow rates to predict asthma. The approach used was based on prior and conditional probabilities. The general hypothesis was that PEFRs can be used in a probability equation to improve the prediction of the occurrence of asthma over the prior probability. METHOD Subjects The participants were 25 children with asthma ranging in age from 6 to 16 years. There were 16 male and nine female children with mean ages of 11.9 and 10.3, respectively. A summary of descriptive statistics for age, PEFR, and number of episodes is presented in Table I. Twelve of the subjects and their parents were participants in an outpatient biofeedback treatment program* being conducted at Children’s Hospital in Columbus, Ohio. The other 13 subjects and their parents were participants in a self-manage-
ment training program conducted at the National Asthma Center in Denver, Colo. Subjects were referred to both programs by their physicians. An interview was conducted with each family to provide an explanation of the program and to determine if the parents and their child wanted to participate in the program. Subjects were selected for the present study if they reported three or more asthma episodes over a 16.5-week period.
Apparatus The mini-Wright peak flow meter (Armstrong Industries, Inc., Northbrook, Ill.), model PF-239, was used by subjects to obtain PEFR measurements daily. In addition, the weekly asthma diary and the report of asthma episode/attack6 were completed by the subjects and/or their parents at home. The weekly asthma diary provides the following information: *The biofeedback program consisted of facial EMG training. Subjects received either no feedback, contingent analog feedback for EMG decreases, or contingent feedback for maintaining EMG levels within a particular range. The prediction method used is independent of any changes in PEFR that may have occurred as a result of EMG training.
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Harm et al
TABLE
II. Comparisons
variables
for both
of first
significant
and highest
posterior
probabilities
with
selected
groups
Prior probability LOW
Posterior probability
Ratio
% Mean PEFR
First significant Highest
0.267 0.363
9.9 8.2
x3 11 -
(1) a daily subjective evaluation of the severity of asthma, (2) daily morning and evening PEFR measurements, and (3) a daily medication schedule that indicates when medications were either missed or taken late. The report of an asthma episode/attack form elicits information about severity of a particular asthma episode/attack, medication compliance preceding the episode, time, place, and duration of the attack, possible precipitating factors, and patient activity before the episode.
Procedure During the first laboratory visit, each subject was taught how to use the mini-Wright peak flow meter correctly; use of the meter was also demonstrated. Each subject was then asked to blow into the instrument for the experimenter. Parents were present for the instructions and demonstration of the peak flow meter. They were asked to supervise the child’s collection of PEFR measurements at home. Care was taken to ensure that a child and his or her parents understood the techniques for obtaining flow rates and for accurately reading the meter. In addition, the participants were provided written instructions for the use of the peak flow meter. The children or their parents completed the asthma diary each week. Peak flow data entered in the diary consisted of the highest of three blows into the meter each morning and evening. After each asthma episode, either the children or their parents completed the asthma-attack form. Both verbal and written explanations of the criteria for an asthma episode/attack were provided. Participants returned to the laboratory once per week for a period of 4 months. During laboratory visits, the diaries and episode/attack forms were discussed in order to ensure they were complete and accurate and to make sure there was agreement between the child and his or her parents on all items. The meetings also provided an opportunity to answer any questions about the forms or the child’s performance and to encourage the participants to continue with data collection.
Data analysis Prior probubility. The initial step was the determination of the prior probability (base rate) for the occurrence of asthma experienced by each subject. This was calculated as follows: The number of 12-hour periods after a peak flow recording during which one or more asthma episodes/attacks occurred was divided by the total number of 12.hour periods of data collection, yielding p(A).
% Episodes predicted
47.5 3.0 -~
% improvement prior-posterior
-9 * .)i :’ ) 1
Conditional posterior probabilities. The posterior probability values were calculated for each subject starting at the second highest PEFR score at which an asthma episode occurred and then moving down step-wise to the next highest PEFR score at which an asthma episode occurred until a value was reached that yielded the greatest improvement to predict the occurrence over the prior probability. Two probabilities by use of PEFR were calculated for each subject at each step. The first was the probability of asthma occurring in a 12-hour period after a PEFR less than or equal to the flow rate at a particular step. The second was the probability of asthma occurring in a ! Z-hour period after a PEFR greater than the particular flow rate at the same step. These two probabilities arc represented by the notations p(A) 1PEFR S B and p(A) / PEFR 1, B, respectively, where A is the occurrence of asthma and B is the PEFR value at a particular step. The probabilities were computed by use of the ratio method. l.c.. the p(A) 1 PEFR G B was determined by the use of the number of 12-hour periods preceded by a PEFR G R In which an asthma episode/attack occurred as the numerator and the total number of 12-hour periods preceded by a PEFR cB as the denominator. Similarly, in computing the p(A) 1PEFR :> B, the numerator was the number of 12. hour periods preceded by a PEFR > B in which an asthma episode/attack occurred, and the denominator wab the total number of 12.hour periods preceded by a PEFR ‘:, IS. All probability equations are presented in Appendix A The power to predict the occurrence of asthma in a I ?hour period relies also on the ratio of the two conditional posterior probabilities. The two posterior probabilities dcscribed above constitute a prediction ratio of hits to missc> The numerator is the probability of the occurrence of asthma given a PEFR less than or equal to the value .it 2 particular step and represents the probability of true pozitivcs or Ms. The denominator is the probability of the i;ccurrencc oi’ asthma given a PEFR greater than the villuc ai the same step and represents the probability of false negatives OI misses. Because of the wide range of peak flow values icaused by age differences among the children), flow rates for each child were converted to the percent of his or her mean PEFR in order to summarize findings across subjects. Thus, predictability of asthma was based on each individual’s average flow rate rather than on population norms. In addition, the children varied considerably in the number of episode oc-currences, and hence, in the number of flow rates at which posterior probabilities could be calculated. Therefore, pas--
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terior probabilities and the ratio of hits to misses is reported for an upper and lower anchor point of the flow rates examined for each subject. The upper anchor point was the PEFR at which the posterior probability reached its highest value. The lower anchor point was the highest flow rate at which improvement in prediction from the prior to the posterior probability was statistically significant. The latter will be referred to as the first significant posterior probability. It was determined by calculating a Z-score* at each successively lower peak flow va1ue.j In addition, the percent of episodes predicted and the percent of improvement in prediction over the prior probability were calculated for both anchor points. Data selection. The first 180 12-hour periods of PEFR data were used to calculate the conditional probabilities. PEFR values were excluded from the analyses for the following reasons: (1) An asthma episode was recorded for a particular day but the time of the episode could not be determined. (2) An episode occurred within 2 hours before the PEFR score. (3) An episode from the previous 12-hour period was still in progress when the PEFR was recorded. The purpose underlying these criteria was to avoid the use of PEFR values that did not directly correspond to the onset of an asthma episode.
RESULTS Posterior probability
values, ratio of hits to misses,
the percent of the mean peak flow, the percent of episodes predicted, and the percent of improvement in prediction over the prior probability were examined at both the first significant and the highest posterior probabilities. The mean values for each of these variables at the two anchor points are presented in Table II. The average first significant and highest posterior probabilities were 0.267 and 0.363, respectively. These values represent a 381% (range of 61% to 1859%) increase in the p(A) 1 PEFR < B above the p(A) at the first significant posterior probability and a 491% (range of 48% to 2841%) increase at the
*The Z-score provided a proportional test of significant differences between the prior and the posterior probabilities of the occurrence of attacks. Computation of the Z-score, however, was modified from standard procedures and, hence, cannot be considered a true test of significance. The purpose of this use of the modified Z-score was to provide a standardized way of determining a lower anchor point from which to compare subsequent posterior probabilities and ratios of hits to misses. The modified Z-score was as follows: Posterior probability ~(Fvior)
- Prior probability (1 - Prior)
” of Sample
where n of sample refers to the number of 12-hour periods PEFR was less than or equal to the selected value.
expiratory
flow
rates to predict
asthma
691
highest posterior probability. No significant difference was found between the prior and posterior probabilities for five subjects. The mean difference from the prior to the posterior probability for these five subjects was, however, a 78% increase (range of 48% to 149%) in predictability of their attacks. In addition, improvement in prediction from the prior to the posterior probability occurred at 83% of the mean PEFR. The highest posterior probability occurred at 77% of the mean PEFR. Greater predictability was coincident with greater levels of airway obstruction. In order to determine the ratio of hits to misses, the p(A) 1PEFR 6 B was divided by the p(A) 1PEFR > B. The mean ratio at the first significant and highest posterior probability was 9.9 and 8.2, respectively. Thus, more prediction errors occurred at the highest posterior probability than at the first significant posterior probability. The data from several subjects yielded extreme values for the ratio of hits to misses (values ranged from 1.79 to 70.17). In order to avoid inflating the average values presented in Table II, the following procedure was used: First, means and standard deviations were calculated. Second, values more than two standard deviations above the mean were removed, and new means were calculated. This procedure removed only two ratio of hits to misses values at the first significant posterior probability and two at the highest posterior probability. Since one of the primary goals of prediction is to maximize the number of events predicted, we examined the percent of the total number of episodes predicted at the two anchor points (see Table II). Approximately half (47.5%) the episodes were predicted at the first significant posterior probability, whereas only 23% of the episodes were predicted at the highest posterior probability. Slightly less than one fourth of the total number of episodes were predicted at the highest posterior probability. Thus, more episodes were predicted at the first significant posterior probability, i.e., more episodes were predicted at higher peak flow rates.
DISCUSSION The results of the present study demonstrate that the use of PEFRs in conditional probability equations can dramatically improve the ability to predict asthma attacks. Choosing a peak flow rate that will be most beneficial to an individual requires careful consideration of the posterior probability, the improvement in predictability from the prior to the posterior probability, the degree of airway obstruction, the ratio of hits to misses, and the percent of episodes predicted at a particular flow rate.
692
Harm et al.
Although the average size of improvement in predictability over the prior probability and the average ratio of hits to misses at both anchor points were impressive, there was a wide range of individual values for both of these factors. Such wide ranges in predictability and ratio of hits to misses suggest the necessity of individual patient evaluation. The primary objective in determining the PEFR for an individual is to provide the patient with an objective measure that will allow him or her to institute interventions early enough to prevent a high percentage of episodes from occurring or to reduce their severity. Costs and benefits associated with a particular PEFR for a patient should be evaluated with this objective in mind. For example, higher values for the percent of improvement in prediction over the prior probability and for the posterior probability (higher hit rates) were associated with lower flow rates. and hence, greater airway obstruction. The more obstructed an individual is before instituting interventions, the more difficult it will be for the patient to abort or reduce the severity of an asthma attack. Although the hit rate is higher, the reduced effectiveness of intervention at lower flow rates lessens the potential for aborting or reducing the severity of an attack and increases cost to the patient. Since the cost of experiencing an asthma episode is high compared to the cost of instituting intervention, it is also more important to have a low error rate than to have a high hit rate. The power of flow rates to predict the occurrence of asthma is dependent not only on the probability that asthma will occur given a PEFR less than or equal to some value (hit rate) but also on the probability that asthma will occur given a flow rate greater than the same value (misses or error rate). In the present study more prediction errors (misses) occurred at the highest posterior probability than at the first significant posterior probability, i.e.. asthma occurred more often when the PEFR was above the flow value associated with the highest posterior probability than at the first significant posterior probability. The clinical value of a high probability that asthma will occur at a particular flow rate (high hit rate) is compromised if there is also a high probability that asthma will occur at even higher flow rates (higher error rate-false negatives). In addition: considerably fewer episodes were predicted at higher values for improvement in prediction and posterior probabilities. The use of a PEFR associated with the largest improvement in prediction or the highest posterior probability may encourage the patient to delay intervention, seriously hindering his or her ability to prevent an attack. It would also reduce
the number of episodes the patient might potentlall\ avoid by early intervention. * Examining conditional probabilities at successrvel~ lower PEFRs allows one to select a PEFR value for an individual that will provide a combinatron ot thi: largest improvement in prediction and the largest nun;-ber of episodes predicted with the fewest errors. Thi* method was used successfully in this study to improve the prediction of asthma within a I Z-hour pcriotl, 1.;~ of this method in behavioral self-management pro. grams would improve the program’s effectiveness considerably. The patient would know in advance that there is an increased probability that he c+r:,he wiii have an episode in the next 12 hours. Such ndvanccx warning would alert the patient to begin intzr\.entilm:3 that may prevent the episode I‘rom occunmg Thi:, will also reduce problems encountered with patients who have difficulty detecting subjective symptom<. The result would he greater reductions iI1 medical. physical, and psychologic costs tci patients. -In) method that could help patients prevent even borne 01 their asthma episodes warrants further investigation
*Appendix B provides a complete example tar compu~ng the p!oPabilities and the ratio of hits to misses. ah nell .IS a set o1 judgments or considerations for sclectmg the best PEFR m ihe example data set
REFERENCES I.
7I.
3.
4.
5.
6.
Chai H, Purcell K, Brady K. Falliers CJ: Therapeutic and mvestigational evaluation of asthmatic children. .I .Al.LkROY 41.2.;. 1968 McFadden EB, Kiser R. D&root WJ: Acute bronsbial asthma-relations between clinical and physiologic manifestarionh. ‘I’ Engl J Med 288:221, 1973 Fishcl MA, Pitchenik A, Gardner LB: An index predicting relapse and need for hospitalization in patients with acute bronchial asthma. N Engl J Med 305:783. 1981 Banner AS, Ranchhodlal SS, Addington WW: Rapid prediction of need for hospitalization in acute asthma. JAMA 235:1337, 1976 Taplin PS, Creer TL: A procedure for using peak cxpiratorc Row rate data to increase the predictability of asthma episodes J Asthma Res 16:15, 1978 Creer TL: Psychosocial interventions. J Respir Med 24: 19Xi)
Appendix Probability
A equations
Prior probability
(base rate)
The probability of the occurrenceof asthmaduring some time period: No. J2-hour periods where one or more e&odes occurred p(A) = Total No. 12-hour periods -
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Conditional probabilities
Example
which (A) occurred
1 2 3 4 5 6 I 8 9
10 11 12 13 14 1.5 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
asthma
Ratio of hits to misses:
Total No. 12-hourperiods precededby PEFR 5 B
-=Hits Misses
p(A) 1PEFR 5 B p(A) ( PEFR > B
B data set PEFR
Day
rates to predict
No. of. 12-hourperiods preceded by PEFR > B in which (A) occurred p(A) 1PEFR > B = Total No. 12-hourperiods precededby PEFR > B
No. 12-hour periods preceded by PEFR I B in
Appendix
flow
A.M.
P.M.
225 250 225 225 350 375 400 375 400 225 225
400 325 300 225 400 350 350 425 400 400 300
350 250 300 275 250 300 325 225 300 300 275 325 250 300 325 375 225 250 300
300 225 250 300 275 250 300 350 350 325 300 325 320 330 350 300 300 325 225
*Time of episode.
PEFR TE* 11 A.M.
7 2 5 2 2 2 2 2 2 2
P.M.
2
P.M.
P.M. P.M. P.M. P.M. P.M. P.M. P.M. P.M. P.M.
1 P.M.
4 2 2 3 6
P.M. P.M. P.M. P.M. P.M.
1 P.M.
693
(2) The probability of asthma (A) occurring in a 12.hour period after PEFR greater than the selected value (B):
( 1) The probability of asthma (A) occurring in a 12-hour period after a PEFR less than or equal to some selected value (B):
p(A) 1 PEFR I B =
expiratory
Day
A.M.
P.M.
31 32 33 34 35 36 37 38 39 40 41
250 225 300 300 300 350 350 350 350 350 350
42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
300 350 375 400 375 425 350 400 350 250 325 350 325 350 350 325 375 375 400
PEFR TE*
Day
A.M.
P.M.
375 350 250 375 450 300 400 375 375 400 375
61 62 63 64 65 66 67 68 69 70 71
250 350 425 400 325 375 375 350 250 400 375
400 400 375 425 375 400 400 375 375 425 400
350 300 425 425 400 350 350 400 375 350 400 375 350 375 325 350 425 325 400
72 73 74 75 76 77 78 79 80
380 350 385 335 375 360 400 250 350 380 400 425 380 400 350 400 380 390 375
410 400 425 400 425 400 425 400 400 420 415 400 390 400 400 400 450 425 250
8
P.M.
~P.M.
81 82 83 84 85 86 87 88 89 90
TE”
12 Noon
2 2 3 3 2
P.M. P.M. P.M. P.M. P.M.
694
Harm et al.
Computation
of probabilities
Selected
and ratio of hits to misses
PEFR
390,
24
No. of periods of (A) and PEFR 5 B No. of periods PEFR 5 B p(A) / PEFR 5 B
118 0.203
No. of periods of (A) and
3
360 23 IIb 0.198
350
300
275
260
18
13
j(
!S
9.5 0.189
39 0.265
-37 0.407
.i i. 11.4;7
14
I6
4“-
4
9
PEFR > B No. of periods PEFR > B p(A) 1PEFR > B
62 0.048
Ratio (H : M)
4.23
0.062
85 0.106
131 0. 107
15.3 0. 10s
1% (1.IO’)
3.19
1.78
7.4X
3.91
LX3
64
% Mean PEFR
112
109
101
Xb
70
‘? J^.
% Episodes predicted c/cImprovement over prior
89 135
85 132
67 126
48 177
31 271
.a7 278
Mean PEFR = 347.64; total number of periods with asthma = 27; total number of 12-hour periods = 180 p(A) =
27 periods with asthma? = 0.150 180 12-hour periods
*Second highest PEFR at which episode was reported (on day 89) tTwenty-seven periods in which one or more episodes occurred.
Selecting the best PEFR 1. Selecting a PEFR that is higher than the patient’s average PEFR is generally not the best choice despite the fact that a very large percent of the individual’s episodes would be predicted, and the ratio of hits to misses is higher than for any other PEFR. For this particular patient, choosing the PEFR of 390 would mean he would be instituting behavioral interventions during 94 of the 118 12-hour periods (where PEFR was s390) when no asthma occurred. Under these conditions, compliance with behavioral interventions would seriously deteriorate. 2. Selecting a lower PEFR (300 or 275 in this example) yields a higher probability that an episode will occur and greater improvement in prediction over the prior probability.
The error rate is also higher; however, it does not increase by as much as the hit rate. In addition, at these PEFRs. respiration is not so compromised that effectiveness of behavioral interventions would be seriously reduced. Finally, at these lower PEFR values, 41% to 48% of the episode:, can still be predicted. 3. Selecting an even lower PEFR (2.50 in this example) yields only a minimal increase in the probability that an episode will occur, which is essentially nullified by the increased error rate (observed as a drop in the ratio of hits to misses). In addition, there is a reduction in the percent of episodes predicted. Finally, since the patient is more obstructed at this level, the effectiveness of behavioral interventions may be reduced.
et al.
3. Burge PS: Occupational asthma in electronics workers caused by colophony fumes: follow-up of affected workers. Thorax 37:348, 1982 4. Paggiaro PL, Loi AM, Rosai 0, Ferrante B. Pardi F, Roaseli MG. Baschieri L: Follow-up study of patients with respiratory disease due to toluene diisocyanate (TDI). Clin Allergy 14:463. IO84 5. Moller DR, McKay RT, Bernstein IL, Brooks SM: Long-term follow-up of workers with TDI asthma. Am Rev Respir Dis 129:A159, 1984 (abst) 6. Cartier A, Malo J-L. Forest F, Lafrance M, Pincau L, St-Aubin J-J, Dubois J-Y: Occupational asthma in snow crab-processing workers. J ALLERGYCLIN IMMUNOL 74:26 I . 1984 7. Dehaut P, Rachiele A, Martin RR, Malo JL: Histamine doseresponse curves in asthma: reproducibility and sensitivity of different indices to assess response. Thorax 38:516. 1983 8. ATS statement. Snowbird workshop on standardizatron of spirometry Am Rev Respir Dis 119:83 I. I979 9. Knudson RJ. Siatin RC, Lebowitz MD, Burrows B: The maximal expiratory flow-volume curves Am Rev Respir Dis 113587, 1976 10. Cockcroft DW, Killian DN, Mellon JJA, Hargreave FE: Bronchial reactivity to inhaled histamine: a method and clinical survey. Clin Allergy 7:235, 1977
1 I. Malo JL. Pineau L. Cattier A, Martm RR: Krierence valuch of the provocative concentrattons of methachoimc mar ciju~-~ 6% and 20% changes in forced expiratory voiumt. :I-,one ‘VC~V& in a normal population. Am Rev Respir Dis I?,: ,i !‘I? \ 12. Lam S, Wong R. Yeung M: Nonspecific broncht:ti rc:~~%vrt) in occupational asthma. J ALI~RGY CLIN Ibtiw:~.:a~ ki.18 ! Y7Q 13. Butcher BT, O’Neil CE. Reed MA. Calvagg~i, i) i’~:ictl) !i Development and loss of toluene diisocyanatc ~r‘acttv I?> I:>‘ munologic. pharmdcoh~ic. and provocative chdlh’ngr ~tudl? J AL.LERW CI.IN hlMLlNOl ?o,‘.; I, I’?82 14. Cartier A, Thomson NC. Froth PA. Roberta Ii. Iiargrea\c Iii:. Allergen-induced increase in bronchial respon~!vencss to ht; tamine: relationship to the late asthmatic response and changin auway caliber. J A1.i tKo~ Cl IN I~~Mu?IO!?) 170. 1982 15. Malo JL, Ouimet G, Cartier A. Levitz D. &is\ <‘K Comhincd alveolitis and asthma due tcr hexamethylcnc c!!tso,:y,mare (HDI). with dcmonstrdtion ot crossed respirator! and lmmu nologic reactivitics to diphenylmethane diisoc! .tnarc t MDI) .i AILERW CI.IN IMWNOI 72:31X 19X3 16. Yeung M. Grzybowski S. Prcgncisik in ~wup.tt~~mi;asthma Thorax JO:24 1. 1985
Improving the abiiity of peak rates to predict asthma Deborah L. Harm, Ph.D., Harry Kotses, Ph.D., and Thomas L. Creer, Ph.D. Athens, Ohio A major problem in the behavioral management of childhood usthma concerns recognition of the early signs of an impending episode. An objective measure commonly used to aid recognition rrf early warning signs is the peak expiratov flow rate (PEFR). This study examined the abilit\ of PEFRs to predict asthma within a I’-hour period; the prediction method used was based on prior and conditional posterior probabilities. Twenty$ve children with asthma recorded their PEFR twice daily, and also recorded the date and time of their asthma episodes. Conditional posterior probabilities and the ratio of hits to misses were computed for each subject at successively 1owerJlow rates. The average improvement in predictabilifi from the prior probability to the highest posterior probability was 491%. The ratio of hits to misses and the number of episodes predicted, however, decreased as the posterior probability increased. Selection of thr PEFR ut lower posterior probabilities resulted in fewer prediction errors and led to prediction of a higher number of episodes than selection of the PEFR at the highest posterior probability.
(JALLERGYCLINIMMUNOL76:6%94, 1985.)
From the Department of Psychology, Ohio University, Athens, Ohio. Supported in part by Grants HL27402 and HL2972 from the Division of Lung Diseases, National Heart, Lung, and Blood Institute. Received for publication July 25, 1984. Accepted for publication March 12, 1985. Reprint requests: Thomas L. Creer, Ph.D., Ohio University, Dept. of Psychology, Porter Hall, Athens, Ohio 45701.
688
A major problem in the management of childhood asthma concerns recognition of the early signs of an impending asthma episode. The difficulty is that patients with asthma vary considerably in the degree of correspondence between subjective sensations and objective measures of airway obstruction. individual correlations bettieen children’s subjective ratings of the severity of asthma and their PEFR have been re-
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TABLE
Abbreviations used PEFR: Peak expiratory flow rate EMG: Electromyograph
expiratory
1. Descriptive
diction errors when regression equations are used. The results of the Taplin and Creels study found entering PEFR scores in a probability equation can be
rates to predict
statistics
asthma
689
on selected
variables
Age (yr) ported to range from 0.25 to 0.70.’ Similarly, large discrepancies between a patient’s subjective ratings of the severity of impaired pulmonary function and objective spirometric measures were reported in several clinical studies involving emergency room treatment of asthma.2-4These studies provide evidence of the problems in detectability and predictability of asthma episodes that could interfere with adequate management of the disorder. The importance of the use of objective pulmonary measures to improve the prediction and detection of asthma is unquestionable. PEFR has been used with some success in predicting relapse and the need for hospitalization for asthma.‘. 4 Furthermore, the use of PEFR scores in conditional probability equations predicts asthma episodes within a 12-hour period. Taplin and CreerSused PEFR in a probability equation to predict the occurrence of asthma in two children. The base rate, or prior probability, for the occurrence of asthma and a critical PEFR value that most increased the predictability of asthma were determined for each child. Two conditional probabilities were calculated for each subject. The first was the probability of asthma in a 12hour period after a PEFR less than or equal to the critical value. The second was the probability of asthma in a 1Zhour period after a PEFR greater than the critical value. The results yielded approximately a threefold increase over the base rate in the predictability of asthma for both subjects. This method is useful for two reasons. First, it provides a valuable objective component to self-management procedures. If an individual had an objective indicator that an asthma episode was likely to occur within the next 12-hour period, he would be alerted to attend to subjective signs of asthma and could institute early interventions that could either prevent the attack or reduce its severity. The use of these interventions should lead to better control of the child’s asthma and reduce medical costs. Second, use of conditional probabilities improves accuracy in predicting the occurrence of asthma for an individual. The two probabilities taken together provide a ratio of hits and misses in the prediction of asthma episodes. This method takes into account the prior probability of asthma in a single subject and removes the problem of between-subject variance that contributes to pre-
flow
PEFR No. episodes
Mean
Range
11.36 321.19 15.40
6.0 to 16.0 99.17 to 543.67 3.0 to 51 .o
applied to self-management programs for children with asthma. However, drawing general conclusions from these results was limited by the small sample of subjects. The purpose of the current study was to evaluate the use of a relatively simple method for predicting the occurrence of asthma in individual children. The study examined the ability of peak flow rates to predict asthma. The approach used was based on prior and conditional probabilities. The general hypothesis was that PEFRs can be used in a probability equation to improve the prediction of the occurrence of asthma over the prior probability. METHOD Subjects The participants were 25 children with asthma ranging in age from 6 to 16 years. There were 16 male and nine female children with mean ages of 11.9 and 10.3, respectively. A summary of descriptive statistics for age, PEFR, and number of episodes is presented in Table I. Twelve of the subjects and their parents were participants in an outpatient biofeedback treatment program* being conducted at Children’s Hospital in Columbus, Ohio. The other 13 subjects and their parents were participants in a self-manage-
ment training program conducted at the National Asthma Center in Denver, Colo. Subjects were referred to both programs by their physicians. An interview was conducted with each family to provide an explanation of the program and to determine if the parents and their child wanted to participate in the program. Subjects were selected for the present study if they reported three or more asthma episodes over a 16.5-week period.
Apparatus The mini-Wright peak flow meter (Armstrong Industries, Inc., Northbrook, Ill.), model PF-239, was used by subjects to obtain PEFR measurements daily. In addition, the weekly asthma diary and the report of asthma episode/attack6 were completed by the subjects and/or their parents at home. The weekly asthma diary provides the following information: *The biofeedback program consisted of facial EMG training. Subjects received either no feedback, contingent analog feedback for EMG decreases, or contingent feedback for maintaining EMG levels within a particular range. The prediction method used is independent of any changes in PEFR that may have occurred as a result of EMG training.
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TABLE
II. Comparisons
variables
for both
of first
significant
and highest
posterior
probabilities
with
selected
groups
Prior probability LOW
Posterior probability
Ratio
% Mean PEFR
First significant Highest
0.267 0.363
9.9 8.2
x3 11 -
(1) a daily subjective evaluation of the severity of asthma, (2) daily morning and evening PEFR measurements, and (3) a daily medication schedule that indicates when medications were either missed or taken late. The report of an asthma episode/attack form elicits information about severity of a particular asthma episode/attack, medication compliance preceding the episode, time, place, and duration of the attack, possible precipitating factors, and patient activity before the episode.
Procedure During the first laboratory visit, each subject was taught how to use the mini-Wright peak flow meter correctly; use of the meter was also demonstrated. Each subject was then asked to blow into the instrument for the experimenter. Parents were present for the instructions and demonstration of the peak flow meter. They were asked to supervise the child’s collection of PEFR measurements at home. Care was taken to ensure that a child and his or her parents understood the techniques for obtaining flow rates and for accurately reading the meter. In addition, the participants were provided written instructions for the use of the peak flow meter. The children or their parents completed the asthma diary each week. Peak flow data entered in the diary consisted of the highest of three blows into the meter each morning and evening. After each asthma episode, either the children or their parents completed the asthma-attack form. Both verbal and written explanations of the criteria for an asthma episode/attack were provided. Participants returned to the laboratory once per week for a period of 4 months. During laboratory visits, the diaries and episode/attack forms were discussed in order to ensure they were complete and accurate and to make sure there was agreement between the child and his or her parents on all items. The meetings also provided an opportunity to answer any questions about the forms or the child’s performance and to encourage the participants to continue with data collection.
Data analysis Prior probubility. The initial step was the determination of the prior probability (base rate) for the occurrence of asthma experienced by each subject. This was calculated as follows: The number of 12-hour periods after a peak flow recording during which one or more asthma episodes/attacks occurred was divided by the total number of 12.hour periods of data collection, yielding p(A).
% Episodes predicted
47.5 3.0 -~
% improvement prior-posterior
-9 * .)i :’ ) 1
Conditional posterior probabilities. The posterior probability values were calculated for each subject starting at the second highest PEFR score at which an asthma episode occurred and then moving down step-wise to the next highest PEFR score at which an asthma episode occurred until a value was reached that yielded the greatest improvement to predict the occurrence over the prior probability. Two probabilities by use of PEFR were calculated for each subject at each step. The first was the probability of asthma occurring in a 12-hour period after a PEFR less than or equal to the flow rate at a particular step. The second was the probability of asthma occurring in a ! Z-hour period after a PEFR greater than the particular flow rate at the same step. These two probabilities arc represented by the notations p(A) 1PEFR S B and p(A) / PEFR 1, B, respectively, where A is the occurrence of asthma and B is the PEFR value at a particular step. The probabilities were computed by use of the ratio method. l.c.. the p(A) 1 PEFR G B was determined by the use of the number of 12-hour periods preceded by a PEFR G R In which an asthma episode/attack occurred as the numerator and the total number of 12-hour periods preceded by a PEFR cB as the denominator. Similarly, in computing the p(A) 1PEFR :> B, the numerator was the number of 12. hour periods preceded by a PEFR > B in which an asthma episode/attack occurred, and the denominator wab the total number of 12.hour periods preceded by a PEFR ‘:, IS. All probability equations are presented in Appendix A The power to predict the occurrence of asthma in a I ?hour period relies also on the ratio of the two conditional posterior probabilities. The two posterior probabilities dcscribed above constitute a prediction ratio of hits to missc> The numerator is the probability of the occurrence of asthma given a PEFR less than or equal to the value .it 2 particular step and represents the probability of true pozitivcs or Ms. The denominator is the probability of the i;ccurrencc oi’ asthma given a PEFR greater than the villuc ai the same step and represents the probability of false negatives OI misses. Because of the wide range of peak flow values icaused by age differences among the children), flow rates for each child were converted to the percent of his or her mean PEFR in order to summarize findings across subjects. Thus, predictability of asthma was based on each individual’s average flow rate rather than on population norms. In addition, the children varied considerably in the number of episode oc-currences, and hence, in the number of flow rates at which posterior probabilities could be calculated. Therefore, pas--
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terior probabilities and the ratio of hits to misses is reported for an upper and lower anchor point of the flow rates examined for each subject. The upper anchor point was the PEFR at which the posterior probability reached its highest value. The lower anchor point was the highest flow rate at which improvement in prediction from the prior to the posterior probability was statistically significant. The latter will be referred to as the first significant posterior probability. It was determined by calculating a Z-score* at each successively lower peak flow va1ue.j In addition, the percent of episodes predicted and the percent of improvement in prediction over the prior probability were calculated for both anchor points. Data selection. The first 180 12-hour periods of PEFR data were used to calculate the conditional probabilities. PEFR values were excluded from the analyses for the following reasons: (1) An asthma episode was recorded for a particular day but the time of the episode could not be determined. (2) An episode occurred within 2 hours before the PEFR score. (3) An episode from the previous 12-hour period was still in progress when the PEFR was recorded. The purpose underlying these criteria was to avoid the use of PEFR values that did not directly correspond to the onset of an asthma episode.
RESULTS Posterior probability
values, ratio of hits to misses,
the percent of the mean peak flow, the percent of episodes predicted, and the percent of improvement in prediction over the prior probability were examined at both the first significant and the highest posterior probabilities. The mean values for each of these variables at the two anchor points are presented in Table II. The average first significant and highest posterior probabilities were 0.267 and 0.363, respectively. These values represent a 381% (range of 61% to 1859%) increase in the p(A) 1 PEFR < B above the p(A) at the first significant posterior probability and a 491% (range of 48% to 2841%) increase at the
*The Z-score provided a proportional test of significant differences between the prior and the posterior probabilities of the occurrence of attacks. Computation of the Z-score, however, was modified from standard procedures and, hence, cannot be considered a true test of significance. The purpose of this use of the modified Z-score was to provide a standardized way of determining a lower anchor point from which to compare subsequent posterior probabilities and ratios of hits to misses. The modified Z-score was as follows: Posterior probability ~(Fvior)
- Prior probability (1 - Prior)
” of Sample
where n of sample refers to the number of 12-hour periods PEFR was less than or equal to the selected value.
expiratory
flow
rates to predict
asthma
691
highest posterior probability. No significant difference was found between the prior and posterior probabilities for five subjects. The mean difference from the prior to the posterior probability for these five subjects was, however, a 78% increase (range of 48% to 149%) in predictability of their attacks. In addition, improvement in prediction from the prior to the posterior probability occurred at 83% of the mean PEFR. The highest posterior probability occurred at 77% of the mean PEFR. Greater predictability was coincident with greater levels of airway obstruction. In order to determine the ratio of hits to misses, the p(A) 1PEFR 6 B was divided by the p(A) 1PEFR > B. The mean ratio at the first significant and highest posterior probability was 9.9 and 8.2, respectively. Thus, more prediction errors occurred at the highest posterior probability than at the first significant posterior probability. The data from several subjects yielded extreme values for the ratio of hits to misses (values ranged from 1.79 to 70.17). In order to avoid inflating the average values presented in Table II, the following procedure was used: First, means and standard deviations were calculated. Second, values more than two standard deviations above the mean were removed, and new means were calculated. This procedure removed only two ratio of hits to misses values at the first significant posterior probability and two at the highest posterior probability. Since one of the primary goals of prediction is to maximize the number of events predicted, we examined the percent of the total number of episodes predicted at the two anchor points (see Table II). Approximately half (47.5%) the episodes were predicted at the first significant posterior probability, whereas only 23% of the episodes were predicted at the highest posterior probability. Slightly less than one fourth of the total number of episodes were predicted at the highest posterior probability. Thus, more episodes were predicted at the first significant posterior probability, i.e., more episodes were predicted at higher peak flow rates.
DISCUSSION The results of the present study demonstrate that the use of PEFRs in conditional probability equations can dramatically improve the ability to predict asthma attacks. Choosing a peak flow rate that will be most beneficial to an individual requires careful consideration of the posterior probability, the improvement in predictability from the prior to the posterior probability, the degree of airway obstruction, the ratio of hits to misses, and the percent of episodes predicted at a particular flow rate.
692
Harm et al.
Although the average size of improvement in predictability over the prior probability and the average ratio of hits to misses at both anchor points were impressive, there was a wide range of individual values for both of these factors. Such wide ranges in predictability and ratio of hits to misses suggest the necessity of individual patient evaluation. The primary objective in determining the PEFR for an individual is to provide the patient with an objective measure that will allow him or her to institute interventions early enough to prevent a high percentage of episodes from occurring or to reduce their severity. Costs and benefits associated with a particular PEFR for a patient should be evaluated with this objective in mind. For example, higher values for the percent of improvement in prediction over the prior probability and for the posterior probability (higher hit rates) were associated with lower flow rates. and hence, greater airway obstruction. The more obstructed an individual is before instituting interventions, the more difficult it will be for the patient to abort or reduce the severity of an asthma attack. Although the hit rate is higher, the reduced effectiveness of intervention at lower flow rates lessens the potential for aborting or reducing the severity of an attack and increases cost to the patient. Since the cost of experiencing an asthma episode is high compared to the cost of instituting intervention, it is also more important to have a low error rate than to have a high hit rate. The power of flow rates to predict the occurrence of asthma is dependent not only on the probability that asthma will occur given a PEFR less than or equal to some value (hit rate) but also on the probability that asthma will occur given a flow rate greater than the same value (misses or error rate). In the present study more prediction errors (misses) occurred at the highest posterior probability than at the first significant posterior probability, i.e.. asthma occurred more often when the PEFR was above the flow value associated with the highest posterior probability than at the first significant posterior probability. The clinical value of a high probability that asthma will occur at a particular flow rate (high hit rate) is compromised if there is also a high probability that asthma will occur at even higher flow rates (higher error rate-false negatives). In addition: considerably fewer episodes were predicted at higher values for improvement in prediction and posterior probabilities. The use of a PEFR associated with the largest improvement in prediction or the highest posterior probability may encourage the patient to delay intervention, seriously hindering his or her ability to prevent an attack. It would also reduce
the number of episodes the patient might potentlall\ avoid by early intervention. * Examining conditional probabilities at successrvel~ lower PEFRs allows one to select a PEFR value for an individual that will provide a combinatron ot thi: largest improvement in prediction and the largest nun;-ber of episodes predicted with the fewest errors. Thi* method was used successfully in this study to improve the prediction of asthma within a I Z-hour pcriotl, 1.;~ of this method in behavioral self-management pro. grams would improve the program’s effectiveness considerably. The patient would know in advance that there is an increased probability that he c+r:,he wiii have an episode in the next 12 hours. Such ndvanccx warning would alert the patient to begin intzr\.entilm:3 that may prevent the episode I‘rom occunmg Thi:, will also reduce problems encountered with patients who have difficulty detecting subjective symptom<. The result would he greater reductions iI1 medical. physical, and psychologic costs tci patients. -In) method that could help patients prevent even borne 01 their asthma episodes warrants further investigation
*Appendix B provides a complete example tar compu~ng the p!oPabilities and the ratio of hits to misses. ah nell .IS a set o1 judgments or considerations for sclectmg the best PEFR m ihe example data set
REFERENCES I.
7I.
3.
4.
5.
6.
Chai H, Purcell K, Brady K. Falliers CJ: Therapeutic and mvestigational evaluation of asthmatic children. .I .Al.LkROY 41.2.;. 1968 McFadden EB, Kiser R. D&root WJ: Acute bronsbial asthma-relations between clinical and physiologic manifestarionh. ‘I’ Engl J Med 288:221, 1973 Fishcl MA, Pitchenik A, Gardner LB: An index predicting relapse and need for hospitalization in patients with acute bronchial asthma. N Engl J Med 305:783. 1981 Banner AS, Ranchhodlal SS, Addington WW: Rapid prediction of need for hospitalization in acute asthma. JAMA 235:1337, 1976 Taplin PS, Creer TL: A procedure for using peak cxpiratorc Row rate data to increase the predictability of asthma episodes J Asthma Res 16:15, 1978 Creer TL: Psychosocial interventions. J Respir Med 24: 19Xi)
Appendix Probability
A equations
Prior probability
(base rate)
The probability of the occurrenceof asthmaduring some time period: No. J2-hour periods where one or more e&odes occurred p(A) = Total No. 12-hour periods -
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Conditional probabilities
Example
which (A) occurred
1 2 3 4 5 6 I 8 9
10 11 12 13 14 1.5 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
asthma
Ratio of hits to misses:
Total No. 12-hourperiods precededby PEFR 5 B
-=Hits Misses
p(A) 1PEFR 5 B p(A) ( PEFR > B
B data set PEFR
Day
rates to predict
No. of. 12-hourperiods preceded by PEFR > B in which (A) occurred p(A) 1PEFR > B = Total No. 12-hourperiods precededby PEFR > B
No. 12-hour periods preceded by PEFR I B in
Appendix
flow
A.M.
P.M.
225 250 225 225 350 375 400 375 400 225 225
400 325 300 225 400 350 350 425 400 400 300
350 250 300 275 250 300 325 225 300 300 275 325 250 300 325 375 225 250 300
300 225 250 300 275 250 300 350 350 325 300 325 320 330 350 300 300 325 225
*Time of episode.
PEFR TE* 11 A.M.
7 2 5 2 2 2 2 2 2 2
P.M.
2
P.M.
P.M. P.M. P.M. P.M. P.M. P.M. P.M. P.M. P.M.
1 P.M.
4 2 2 3 6
P.M. P.M. P.M. P.M. P.M.
1 P.M.
693
(2) The probability of asthma (A) occurring in a 12.hour period after PEFR greater than the selected value (B):
( 1) The probability of asthma (A) occurring in a 12-hour period after a PEFR less than or equal to some selected value (B):
p(A) 1 PEFR I B =
expiratory
Day
A.M.
P.M.
31 32 33 34 35 36 37 38 39 40 41
250 225 300 300 300 350 350 350 350 350 350
42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
300 350 375 400 375 425 350 400 350 250 325 350 325 350 350 325 375 375 400
PEFR TE*
Day
A.M.
P.M.
375 350 250 375 450 300 400 375 375 400 375
61 62 63 64 65 66 67 68 69 70 71
250 350 425 400 325 375 375 350 250 400 375
400 400 375 425 375 400 400 375 375 425 400
350 300 425 425 400 350 350 400 375 350 400 375 350 375 325 350 425 325 400
72 73 74 75 76 77 78 79 80
380 350 385 335 375 360 400 250 350 380 400 425 380 400 350 400 380 390 375
410 400 425 400 425 400 425 400 400 420 415 400 390 400 400 400 450 425 250
8
P.M.
~P.M.
81 82 83 84 85 86 87 88 89 90
TE”
12 Noon
2 2 3 3 2
P.M. P.M. P.M. P.M. P.M.
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Harm et al.
Computation
of probabilities
Selected
and ratio of hits to misses
PEFR
390,
24
No. of periods of (A) and PEFR 5 B No. of periods PEFR 5 B p(A) / PEFR 5 B
118 0.203
No. of periods of (A) and
3
360 23 IIb 0.198
350
300
275
260
18
13
j(
!S
9.5 0.189
39 0.265
-37 0.407
.i i. 11.4;7
14
I6
4“-
4
9
PEFR > B No. of periods PEFR > B p(A) 1PEFR > B
62 0.048
Ratio (H : M)
4.23
0.062
85 0.106
131 0. 107
15.3 0. 10s
1% (1.IO’)
3.19
1.78
7.4X
3.91
LX3
64
% Mean PEFR
112
109
101
Xb
70
‘? J^.
% Episodes predicted c/cImprovement over prior
89 135
85 132
67 126
48 177
31 271
.a7 278
Mean PEFR = 347.64; total number of periods with asthma = 27; total number of 12-hour periods = 180 p(A) =
27 periods with asthma? = 0.150 180 12-hour periods
*Second highest PEFR at which episode was reported (on day 89) tTwenty-seven periods in which one or more episodes occurred.
Selecting the best PEFR 1. Selecting a PEFR that is higher than the patient’s average PEFR is generally not the best choice despite the fact that a very large percent of the individual’s episodes would be predicted, and the ratio of hits to misses is higher than for any other PEFR. For this particular patient, choosing the PEFR of 390 would mean he would be instituting behavioral interventions during 94 of the 118 12-hour periods (where PEFR was s390) when no asthma occurred. Under these conditions, compliance with behavioral interventions would seriously deteriorate. 2. Selecting a lower PEFR (300 or 275 in this example) yields a higher probability that an episode will occur and greater improvement in prediction over the prior probability.
The error rate is also higher; however, it does not increase by as much as the hit rate. In addition, at these PEFRs. respiration is not so compromised that effectiveness of behavioral interventions would be seriously reduced. Finally, at these lower PEFR values, 41% to 48% of the episode:, can still be predicted. 3. Selecting an even lower PEFR (2.50 in this example) yields only a minimal increase in the probability that an episode will occur, which is essentially nullified by the increased error rate (observed as a drop in the ratio of hits to misses). In addition, there is a reduction in the percent of episodes predicted. Finally, since the patient is more obstructed at this level, the effectiveness of behavioral interventions may be reduced.