Indices of Nonspecific Bronchial Responsiveness in a Pediatric Population

Indices of Nonspecific Bronchial Responsiveness in a Pediatric Population* Francesco Forastiere, M.D.;t Riccardo PisteUi, M.D.;* lbola Michelozzi, B.Sc.;t Giuseppe M. Corbo, M.D.;*

Nera Agabiti, M.D.;* Roberto BerloUini, M.D.;t Giuliano Ciappi, M.D.;t Carlo A. Perocci, M.D.t

A cross-sectional survey of the prevalence of asthma and bronchial hyperreactivity among schoolchildren (7 to 11 years old) was carried out in three areas of the Latium region (Central Italy). Out of 1,777 children tested with methacholine challenge (Mer), 15.1 percent had a 20 percent fall in FEV1 after a provocative concentration (PC.FEV1) of4 mglml of methacholine or less; 69.7 percent had a PC.FEV1<64.0 mglml, whereas 50.3 percent were oonresponders. Two continuous measures of bronchial responsiveness, the slope (percentage of change in FEV. per mglml of methacholine) and the area under the dose response curve, were calculated in order to avoid the loss of information in oonresponders. Applying a receiver operating characteristic (ROC) curve analysis, the three estimators did DOt show any statistically signi&caot difference in their overall performance in detecting asthma (ROC

areas: PC.FEV.=O.683, slope =0.681, area=0.702) or asthma-like symptoms. The log transformation of slope, having a unimodal and slighdy skewed shape, is an appealing continuous measure of bronchial responsiveness useful for epidemiologic studies. The final choice ofan appropriate estimator of the concentration-response curve to methacholine, however, depends upon both the statistical tests or the modelling procedures to be used and clari&cation of the prognostic value of different indices of bronchial (Chest 1991; 100:927-34) responsiveness.

Interest in the epidemiology ofbronchial asthma has grown in recent years as both morbidity and mortality from the disease, especially in younger age groups, seem to be increasing. l -3 There has been controversy regarding the definition of the disease," however, and epidemiologic investigations have to cope with the lack of consistent measurement methods. 5•6 Clinical observations show that most patients with asthma have bronchial hyperresponsiveness,7.8 though the extent of such a relation is debated,9.10 and bronchial provocation tests have now been well standardized. l1 •12 Therefore, current interest focuses on the epidemiologic features of bronchial responsiveness. 13-16 Bronchial responsiveness is usually measured by provocation tests employing pharmacologic agents such as histamine or methacholine. 11 The provocation concentration or dose of the drug causing a 20 percent decline in FEV1(PCmFEVI or PDmFEVI ) is traditionally utilized by clinicians to summarize the information content of the dose-response curve. In epidemiologic studies, however, many subjects do not have a 20 percent decrease of FEV1 using the range of drug

concentrations normally employed for safety reasons, so that a loss of information is likely to occur. The use of smaller changes in FEV1, eg, PC6FEV1,17 may only partially solve the problem because of intrasubject variability ofresults. Various mathematic methods have been proposed to provide continuous measures of responsiveness,18-21 in order both to increase the sensitivity to early disease and to avoid losing information in nonresponders. More specificall~ Townley et al l8 suggested calculation of the area under the doseresponse curve, whereas O'Connor et al21 proposed a simple measure as the slope of response calculated from the first and the last point of the curve (percentage of decline in FEV1/unit of dose). Although the censored distribution of PCmFEVI has been described in children from Australia,22 New Zealand,23 and more recentl~ in English schoolchildren,24 data from unselected pediatric samples showing the population distribution of the continuous indices of BR have never been reported. Thus, the relative ability of various measures of BR to discriminate asthmatics (or subjects with asthmalike symptoms) from normal subjects, especially in children, has not been fully assessed. ls.21 Moreover, the question still remains open whether precision improves significantly by using continuous measures instead of dividing responsiveness into discrete categories16.21 and whether such continuous indices have a practical utility for epidemiologic studies.

*From the tEpidemiologic Unit, Latium Hegional Health Authority; :j:Department of Respiratory Physiology, Catholic University, Rome. Manuscript received August 16; revision accepted February 7. Reprint requests: Dr. Rwastiere~ Osservatorlo Epidemiologico Hegionale ~ Via S. Costanza 53~ Rome, Italy 00198

ATS=American Thoracic Society; ANOVA=aoaIysis of variance; BR = bronchial responsiveness; MCT = methacholine challenge test; PC.FEV1. or PD.FEV.: provocation concentration (PC) or dose (PD); 01 the drug causing a !O percent decline in FEV.; ROC curve = receiver operating characteristics curve

CHEST I 100 I 4 I OCTOBER, 1991

927

The data collected during a cross-sectional survey on asthma and bronchial reactivity are used here as follow: (1) to describe the distributions of diJrerent measures of airways reactivity in a pediatric population; (2) to assess the degree of their association with asthma related conditions; and (3) to better elucidate the advantages or disadvantages of using continuous rather than discrete measures of DR for epidemiologic studies. METHODS

Subjecb and DotG Colkcflon This cross-sectional survey was carried out in 1987 within three geographic areas of the Latium region of Central Italy (the city of lome, an industrialized town, CivitavecclUa, and three small communities in a rural area ofViterbo), and was designed to analyze the role of environmental £acton in asthma prevalence. Figure 1 summarizes the study design and the response rates of the ~ A total of 2,789 children t1 to 11 yean old) in the second to &fth grades of 17 primary schools randomly chosen within the three areas were enrolled. Data regarding symptoms or diseases were obtained from the parents of 2,648 children (94.9 percent) through

a self-administered questionnaire adapted from the American TboracIc Society- Division of Lung Diseases iDstrument,· together with written CODSeDt tor a mecIicaI eumioatton and a broocbJa1 cba1IeDp test. A mecIicaI esamiDation was performed for 2,306 (82.7 percent) of the 2,789 randomly chosen subjects. The children (exdudiDg eight individuals with oeuroIogic diIorden) underwent baseline pulmonary function testiDg using a computerized system CODDeCted to a ~8IIed spirometer. FOrced vital capdty maneuven were performed according to a standard techniqueII with at least three attempts to obtain the best FEV. and FVC. A total of 188 subjects did DOt uoderp the broochJaI chaIIeage: 12 children with heart disease, mwith a high diastolic blood pressure, 30 with a baseline FEV. less than 80 percent of the predicted value or FEVIF'VC below 0.7, and ~ 106 children with unreliable baelme lung 6mction data. The methacholine cbaIlenge test was performed wbile wearing a nose dip. using tidal volume breathing of &eIOI01s. The nebuhzer (DeVilbiss~ driven by compressed air, delivered an outpJt of 0.15 ± 0.000 mIImin (JDe8D ± SD) of each solution, which was inhaled fOr I min. Pbospbate-bufFered saline solution was inhaled &nt, followed by fOurEold increasing concentrations of methacholine (from 0.06 to 64 mWml)' corresponding to an estimated 6na1 dose orl11.9 fUDOI. A total of 48 children whose FEV. feU by more than 10 percent after the inhalation of the saline solution were excluded.

ITARCF:r

:ULmON I

I

(IM.HI 1'eIpllDIe)

1MB subjects with

questioDDaiJe data

I

(81.7")

I~~I

---_1_--

1 !l98lung6mction tests --+ 106 unrehable

tests

1191 reliable hmg function data

---+ 30 FEV. <80'6 pred 01'

FEVIF'VC <0.7

2130 atteDded a

medwrJWtoe chaIIeage test ---+ 48 FEV. <9O'IJ after

saline solution

---+ ~ uaable to

perfOrm the test

FICURE 1. Study design and response rates of the cross-sectional survey (Latium, I~ 1987).

The BR was measured by the change in FEV. &om the postsaline value at 30 and 90 s after each inhalation fOllowing the technique suggested by Cockcroft et a1. -Inhalations were continued until the FEV. bad fallen by 20 percent or more or the last concentration of methacholine bad been administered. After excluding ~ cbildren unable to perform sequential spirometric ID8IletMm or metbacboline inhalations, 1,777 Mers remained for the present analysis. Atopic status was evaluated by prick testiDg." Eight commercially available allergen extracts were tested as CoIIows: D pteronUItftUl, grass, mugwort, parietaria, cat, olea, mixed trees and Alternaria. Histamine dihydrochloride (10 mtVml) and diluent were used as positive and negative control substances. After 15 min, the wbeaIs greater than 4 mml were outlined and the markings transferred to square millimeter paper by means of a tape. The wheal me was calculated by the product of the long aDs by its perpendicular. Data AntJIv... The questionnaire data here used were all considered as discrete variables: wheeze with colds, wheeze apart from colds, wheeze after exercise, dyspnea associated with wheeze, cough and phlegm apart from colds. nocturnal cough, or allergic rhinitis. "Any wheeze" was de8ned as a positive answer to at least one of the wheezing symptoms; "penistent wheeze" indicates wheeze with colds aod occasiooally apart from colds or wheeze on most days or nights. cCPhysician-diagnosed asthma" is defined as an a8lrmative answer to the question, "Has a doctor ever said that this cbdcI had asthmar. F~ "asthma" was operationally de8ned as either a "physician diagnosed asthma" or at least three oftbe tour wheezing symptoms.· Other variables collected were as fOllows: an upper respintory infection in the prior two weeb; asthma among the parents aodIor siblings (familial asthma); a severe respiratory disease in the 6nt two years of life (early childhood respiratory disease: ECRD); current parental smoking. The Mers were graded using three ddFerent estimates: (1) The PCJEV. was calculated by interpolation from the log coocentra-

lion-response curve according to a widely used clinical method.· (2) The slope of a line extending from the origin to the last point of the nonlog curve rslopej was determined, as has been suggested as a simpli8ed approach to 8t a mathematical model to the raw data. II It could be considered as a percentage change in FEVl per mwml of methacholine. (3) The area under the concentrationresponse curve CCareaj was calculated by geometric partitioning of the total area and summing the individual partitions.·8 An arbitrary atopy score was calculated by dividing the size of the largest wheal of each subject after subtracting the negative control (WZ) by the size of the histamine control (HI). The resulting ntio (W7IHI) was categorized as increasing atopic status as follows: 0, noomeasurable wheal sizes; 1, W7.IH1<0.5; 2, W7.1HI=0.51.0; 3, W7.1HI>1.0. The overall performance of the three estimators of MCT with respect to asthma or other respiratory symptoms (used in turn as cCgold standardj was analyzed using the receiver operating characteristics curve techniqu~ (Appendix~ The Kolmogorov-Smirnov test (IC-S test) was applied to verify the goodness of 6t to a normal distribution; the chi-square test was used to evaluate ordinary 2 x 2 tables. and one-way analysis of variance (ANOVA) was employed for comparison ofcontinuous data between groups. RESULTS

Table 1 reports the characteristics of the children attending the medical examination in comparison to those subjects whose parents refused the medical tests. Participants tended to be older than nonparticipants. Statistically significant differences were found for fathers education and parental smoking, probably because ofa higher social class among nonparticipants. The two groups did not differ for respiratory symptoms with the only exception ofccwheeze apart from colds."

Medical Examination Participants

Numben

Sex, males Age, meaolSD Father's education, less than 9 yean

Parental smoking, yes Wheeze with colds Wheeze apart from colds Wheeze after exercise Breathlessness with wheeze Cough apart from colds Phlegm apart from colds Physician-diagnosed asthma Asthmat A~O

Height, meaolSD

FVC liter, meanlSD

FEV.liter, meanlSD

,-test

Nonparticipants

MCTYes

MCTNot

p*

1,777 51.1 8.9 (1.2) 62.3 67.6 8.9 2.5 2.4 7.8 4.9 2.3 5.7 6.5 74.2 139.4 (21.4) 2.29 (0.44) 2.12 (0.39)

529 50.9 8.6 (1.3) 64.3 68.8 13.4 4.3 4.3 10.6 6.6 2.8 8.5 9.5 67.3 136.3 (18.4) 2.12t(0.47) 1.91*(0.43)

0.92 <0.001 0.41 0.60 <0.01 0.03 0.02 0.04 0.13 0.52 0.02 0.019 <0.01 <0.001 <0.001 <0.001

Total 2,306 51.0 8.9 (1.2) 62.8 67.9 10.0 2.9 2.8 8.5 5.3 2.4 6.3 7.2

p* 342 50.7 8.1 (1.3) 46.5 62.3 9.6 0.6 2.9 11.7 7.0 3.5 8.5 8.2

0.92 <0.001 <0.001 0.04

0.&1 0.013 0.92 0.052

o.m 0.23 0.13 0.51

*p-values (chi-square or Student's fOr means) refer to the comparison between MCT YES and MCT Nar and between those who attended and did not attend the medical examination. tPhysician-diagnosed asthma or three of the fOllowiDp: wheeze with colds, wheeze apart from colds, wheeze after exercise, breathlessness with wheeze. available fOr 415 subjects.

*Data

CHEST I 100 I 4 I OCTOBER, 1881

121

PC20 FEV1

a) 1000

800 500

800 N

N

0

0

800

0

f

••• •

c

•

400

•••

200

0

0.06

to

0.25

4.0

18.0

0.1

1

10

100

.. decline FEV per mglml methacholine

AREA

1000

LOGAREA

d) 500

400

400

N

N

0

0

300

0

f

C

200

• 84.0

84.0

Methacholine mg/ml

500

•• ••

300

100

e)

0

400

0

f

c

LOGSLOPE

b)

f

•• • C

200

•

100

0

0

2

4

8

8

10

Units of methacholine Area

12

14

300 200 100 0 0.01

0.1

1

10

Units of methacholine Area

100

FIGURE 2 a,b,c,d. Frequency distributions of PC.,FEV, (a) Logslope; (b) area; (c) and logarithmic transfonnatlon of the area; (d) Prior to logarithmic transfonnation, a &xed value of 0.01 was added to each value of slope to avoid zero numbers.

Participants were further subdivided into those tested with a methacholine challenge and those excluded from the test. Children included in the present analysis were older than those excluded, and both asthmarelated respiratory symptoms and atopy were less common. Furthermore, mean height and lung volumes (means ofFVC and FEVI) were higher in the methacholine test group. The observed differences, besides the effect ofage, could be partly explained by the fact that individuals with FEV. less than 80 percent of predicted and those responsive even to a saline solution were not permitted to perform a challenge test. The frequency distribution of PC2IO FEV. showed that 269 children (15.1 percent) had a PC2IOFEVI less or equal to 4 mglml, while a total of884 subjects (49.7 percent) had a 20 percent fall in FEVI after 64 mglml of methacholine (Fig 2a). An average percentage of decline in FEV. per mglml of methacholine (slope) of 0.54 (SD =5.96) was observed among the study subjects. The distribution of the logarithmic transfonna930

tion of slope data (Logslope) (Fig 2b) had a unimodal and slightly skewed shape (skewness =0.76, Kurtosis =0.85, K-S test: p
Table 2- Preoolence of Bapiratory Symptoma in a Population of 1, 111 SchoolchUdnm and Compariaon of ROC Areaa ROC Areas* SymptomslDiagnosis

Prevalence, %

PCJEV.

Slope

Area

Wheeze with colds Wheeze apart from colds Wheeze after exercise Breathlessness with wheeze Cough apart from colds Phlegm apart from colds Nocturnal cough Allergic rhinitis Any wheeze Persistent wheeze Physician-diagnosed asthma Asthmat

8.9 2.5 2.4 7.8 4.9 2.3 4.2 5.6 9.3 2.1 5.7 6.5

0.618 0.731 0.681 0.657 0.540 0.612 0.576 0.633 0.614 0.769 0.674 0.683

0.618 0.726 0.694 0.658 0.524 0.591 0.574 0.623 0.613 0.769 0.670 0.681

0.617 0.729 0.679 0.656 0.546 0.592 0.571 0.623 0.612 0.775 0.691 0.702

*No statistical differences among the three estimators was detected using a z-test for differences between ROC area. 3. tPhysician-diagnosed asthma or three of the followings: wheeze with colds, wheeze apart from colds, wheeze after exercise, breathlessness with wheeze.

Table 3-Ability ofVarioul Levels ofPC,JEVu Slope and Area in Identifying Aathmatica (n=116) tmdN~(n=1,661)* Area

Slope

PC..FEV. mglml

Sens

Spec

1.0 2.0 4.0 (t) 8.0 16.0 32.0 64.0

0.224 0.362 0.431 0.509 0.569 0.655 0.716

0.957 0.913 0.870 0.777 0.705 0.602 0.522

Perc 98th

95th 90th (t) 80th

70th 60th 50th

Sens

Spec

0.207 0.336 0.457 0.543 0.629 0.733 0.871

0.961 0.917 0.818 0.718 0.617 0.519 0.259

Perc 2nd 5th 10th

20th (t) 30th 40th 50th

Sens

Spec

0.172 0.345 0.483 0.586 0.664 0.733 0.914

0.959 0.918 0.820 0.719 0.617 0.516 0.261

*Sensitivity (Sens) and specificity (Spec) reported according to different cutoff points of pc.. FEV. or percentiles (Perc) of the distribution of slope and area. u tThe ccoptimum cut-offpoint (the best trade off between high sensitivity and low false positive rate) is indicated for each estimator.

values of sensitivity and specificity for different cutoff points of the three estimators, PC.FEV1, slope and area, as reported in Table 3. The potential gain in a hypothesis testing situation of using a continuous measure of BR was also evaluated. We examined the crude relationship between a number of dichotomized variables already reported to be associated with BR (age, atop~ URI, familial asthma, early childhood respiratory disease, parental smoking) and two ofthe measures ofairways reactivity: a continuous one, the logarithmic transformation of slope (Logslope), and a discrete one, PC.FEV1. Given the aim ofthe present comparison, the role ofpotential confounders or effect modifiers, such as sex, age, and air pollution exposure, was not taken into account. Table 4 shows the results of the comparisons for mean values of Logslope by ANOVA and for distributions ofPC.FEV1 by chi-square statistic. For the latter purpose, both the group of those highly responsive to methacholine (S4 mwml) and the group of those with an intermediate response (>4 - 64 mg/ml) were separately compared with nonresponders (>64 mwml) to

obtain chi-square statistics. The results obtained with the three tests were similar for most variables tested. Specifically, a highly significant association was found for age (younger subjects have a higher level of BR) and for all three levels ofthe atopy score, while neither familial asthma nor early childhood respiratory diseases was related to an increase in BR regardless of the method of comparison. Recent respiratory infection, however, was highly correlated to BR using the parametric test, and when highly reactive subjects were compared with nonresponders; whereas, the difference in prevalence was not statistically significant when the group with an intermediate response to methacholine was compared with the nonresponders. Parental smoking, 6nall~ was clearly associated with BR (p = 0.0057) when measured on a continuous scale, while this association does not reach statistical significance using PC.FEV1 (p=0.073). DISCUSSION

The range of concentrations of methacholine employed in the protocol of this study was designed to CHEST I 100 I 4 I OClOBER. 1991

131

Table 4-AuocitJtion of Persmaal and Environmental CharacterUtica with B r o n c h i a l _ E%praaed 1M lAJplope and PC,.FEV.* PCmFEV1 Methacholine Concentration (mglml) Logslope

DF Aget Atopy 1 Atopy 2 Atopy 3 URI; Familial asthma ECRD§ Parental smoking

1/1,725 1/1,503 1/1,441 1/1,408 1/1,725 1/1,724 1/1,586 1/1,706

S4.0 vs >64.0

4.0-64.0 vs >64.0

F Ratio

pValue

ChiSquare

pValue

ChiSquare

pValue

17.49 20.37 50.70

<0.0001 <0.0001 <0.0001 <0.0001 0.0005 0.3678 0.5469 0.0057

15.22 21.38 42.89 52.61 11.18 0.05 2.55 3.21

<0.0001 <0.0001 <0.0001 <0.0001 0.0008 0.8258 0.1096 0.0734

10.61 17.64 11.24 16.30 0.56 0.08 0.83 0.04

0.0012 <0.0001 0.0008 <0.()001 0.4532 0.7794 0.3628 0.8414

43.99

12.11 0.81 0.36 7.67

*An ANOVA comparison has been performed for Logslope, while chi-square statistics have been computed for PCmFEV p For all the

comparisons, the reference category is children without the characteristic. tYounger «9 years) vs older (9-11 years) subjects. ;URI: upper respiratory infection in the prior two weeks. §ECRD: early childhood respiratory disease.

avoid side effects, so that in 50.3 percent of subjects, the level ofBR could not be estimated using PC20 FEV1. Two alternative methods for calculating BR, slope,21 and area,19 so as to include "nonresponders;' have therefore, been investigated. These particular estimators have been selected because of their relative simplicity and since their distributions in population samples have been described.. The distribution of PC20 FEV1 in our sample tends to be skewed toward hyperresponsiveness, and these results are consistent with a previously reported unimodal distribution of bronchial responsiveness in a random population. 32 The logarithm of slope has a distribution very close to that originally described among adults. 21 For area, an interesting comparison group happens to be available. The area under the dose-response parabolic curve, integrated to a 35 percent fall in the FEV1, has been measured in a selected American population aged 5 to 21 years with and without a family history of asthma}S Normal individuals from asthma families had a bimodal distribution of bronchial response expressed as area, while normal subjects from normal families had a unimodal distribution. Our findings of a unimodal distribution of the log transformation of the area thus resembles the distribution reported for normal families 1s (Fig

2d).

It is now widely accepted that, although increased BR is often associated with the clinical features of asthma, the two should be considered as separate entities,9.10 partially because of an incomplete overlap between bronchial hyperresponsiveness and respiratory symptoms in population studies. 22,23 Our data show that a measurable PC20FEV1 has a sensitivity of 71.6 percent but a specificity of only 52.2 percent in 932

detecting subjects with diagnosed asthma or a combination of wheezing symptoms (Table 3). Various explanations of this incomplete overlap could be postulated including the young age we studied (age is inversely related to BR), a transitory increase in BR, different etiologic factors,22 and loss of information resulting from dichotomization ofcontinuously distributed test results. 10 Despite the differences in the distribution of the MCf estimators, there is no evidence from our data that one method of analysis of the concentrationresponse curve is superior to the others in detecting symptomatic subjects using the ROC analysis. Even if limitations of statistical power should be considered as a possible cause ofthe findings, the overall performance ofMCf seems to be independent ofthe estimator chosen, no matter what the prevalence of the variable examined. Generally speaking, the distribution ofa given MCf estimator determines the choice of parametric or nonparametric statistics to analyze the data. The epidemiologist's preference, or the need to use a particular measure (ie, calculating a relative risk), can at times, however, indicate the choice of a particular estimator of MCT. For our data, the log-transformed slope has a distribution slightly skewed. Its lack of normality, however, would not in practice prevent the use of parametric tests for comparison of means given the relative robustness of such statistics for the level of skewness we observed. 33 A further advantage of using Logslope is that modelling through linear regression methods could be easily performed with Logslope as an independent variable. On the other hand, since the distribution of PC,JEV1 is censored and that of area has a long tail, Non8pecific Bronchial ResponsNeness in PediatrIc Population (For8BtJere et aJ)

categorization and use of nonparametric tests seem more appropriate for these indices. One alternative proposed by Wolynets34 for the analysis of a censored variable such as PCmFEV1, which use both censored and uncensored information to obtain maximum likelihood estimates ofthe regression coefficient, has been used recently for the analysis of an epidemiologic study on bronchial reactivi~35 However, rather than use such an elaborate technique, which seems unlikely to greatly improve results because so much data remain censored, it might be more reasonable to tum to a continuous index such as slope. Finall}; Chinn et al36 have proposed the estimation of PCmFEV1 by using all the data from the dose response curve rather than a simple interpolation between the last two measurements. Its use is justified to increase the number of subjects with available information, when the maximum dose of drug given is low; when a larger range of BR is explored, as in our case by administering up to 64 mg/ml methacholine, the information gain through Chinn's method tends to be negligible. From the point of view of the results of hypothesis testing, only minor differences seemed to arise when a parametric test in comparison with a chi-square method were used to analyze our data, since the pvalues presented in Table 4 were very close. For only one independent variable, parental smoking, does the continuous measure yield a statistically significant association which is only borderline using a categorized estimator such as PCmFEVI. On the other hand, by using a large dataset and a few relationships to test for association with hyperresponsiveness, we had a priori, a high probability of finding no differences between the two measures. Keeping in mind, therefore, that the effiCiency ofa parametric test is generally greater than a distribution-free method,33 and considering the results found for parental smoking, it seems likely that the analysis of slope data will be a more sensitive tool for better understanding the epidemiology of BR even under less statistically favorable circumstances. In conclusion, many estimators of Mer have been proposed on the basis ofbetter sensitivity or diagnostic accu~ In a pediatric population, we have not found evidence to support any particular measure. The log transformation of slope, however, is an appealing continuous measure ofbronchial responsiveness useful for epidemiologic studies. The statistical tests or the modelling procedures to be used, the possible need to show the strength of an association, and future clarification of the prognostic significance of different measures of bronchial responsiveness should guide the final choice of the appropriate estimator of the dose-response curve. ACKNOWLEDGMENTS: We thank Giorgio Schiano, Bibbiana De Stefanis, Adal~sa Elefante and Gianna Cento of the Local Health

Authorities VfI2, RM21 and RM1 for their cooperation in collecting the data; Professor Michael D. Lebowitz for his suggestions and comments; Dr. Peter Burney for his critical observations; and Dr. Susan Levenstein for her help in editing of the manuscript. We also thank Fisons-ltalchimici, S.p.A., for its contribution to Dr. N. Agabiti, and Biomedin (Padova) for spirometers and technical support. ApPENDIX: RECEIVER OPERATING CHARACfERISTICS CURVE ANALYSIS

A ROC curve29 is obtained by plotting sensitivity against the false positive rate (1- specificity) for all possible cutoff points of the diagnostic test. It is, thus, a representation ofthe ability ofthe test to discriminate between "cases" and "noncases" across the total spectrum of the diagnostic thresholds. The area under the ROC curve represents the probability that a randomly chosen diseased subject is rated or ranked with greater suspicion than a randomly chosen nondiseased subject. Recently, it has been demonstrated that this probability is well estimated, without the assumption of a normal distribution, by the Wilcoxon statistic,30 0.5 being the value attributable to a useless diagnostic test and 1 the value of a perfect one. Therefore, in our study, the area under the ROC curve and standard error has been calculated according to the Wilcoxon method. The ROC curves for PCmFEVI were constructed by plotting the values corresponding to the following concentrations of methacholine: 1, 2, 4, 8, 16, 32, 64, >64 mglml. The ROC curves for slope and area were constructed by plotting the values corresponding to the percentiles of their respective distribution in the sample: 98th, 95th, 90th, BOth, 70th, 60th, 50th, 25th, for slope, and 2nd, 5th, 10th, 20th, 30th, 40th, 50th, 75th for area. The comparison of ROC areas derived from the same subjects was performed according to the method suggested by Hanley . and McNeil. 31 A ROC curve analysis can be used to detect the "optimum" cutoff point (the statistically best trade off between sensitivity and specificity) to separate normal and nonnormal subjects for each estimator of the Mer. It is, graphically, the point on the ROC curve which has the greatest distance at right angles from the diagonal, in other words when the sum of sensitivity and specificity minus 1 is maximized {Youden's index).37 The ROC "best" cutoff point for the diagnosis of asthma in our study, for example, was at 4 mglml for PCmFEVI and at the 90th and the 20th percentile of the distributions for slope and area, respectively (Table 3). REFERENCES

1 Gergen PJ, Mullally DI, Evans R. National survey ofprevalence of asthma among children in United States. 1976-80. Pediatrics 1988; 81:1-7 2 Jackson RT, 8eaglehole R, Rea UU, Sutherland D. Mortality from asthma: a new epidemic in New Zealand. Br Moo J 1982; 285:771-73 3 Burney E Asthma deaths in England and Wales 1931-85: CHEST I 100 I 4 I OCTOBER, 1991

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