Evaluation of methacholine dose-response curves by linear and exponential mathematical models: goodness-of-fit and validity of extrapolation.
Several models have been proposed to analyse dose-response curves recorded in bronchoprovocation challenge tests. The aims of the present work were: 1) to investigate which model (linear vs exponential) and which minimization method (trials and errors vs Levenberg-Marquardt) gives better results in terms of data interpolation (goodness-of-fit); and 2) to verify the validity of extrapolation by comparing forced expiratory volume in one second (FEV1) observed after 4 mg methacholine with values extrapolated after truncation of the curves at 2 mg. For these purposes, methacholine dose-response curves were obtained in 832 subjects from a random population sample, as part of the European Community Respiratory Health Survey (ECRHS) in Italy. Methacholine was inhaled up to a maximum dose of 6 mg by dosimeter technique. The coefficient of determination (r2) was significantly higher with the exponential model (0.81 +/- 0.22; mean +/- SD) than with the linear model (0.69 +/- 0.27). With both models, extrapolated values were usually lower than observed values. As a consequence, a 20% fall in FEV1 with respect to postsaline FEV1 was observed in only 24% and 21% of the tests, where a 20% fall had been predicted, respectively, according to the linear and exponential model. In conclusion, exponential models are better than linear models with respect to data interpolation of methacholine dose-response curves. However, they are worse with respect to extrapolation to higher doses. With any model, extrapolation of dose-response curves by one doubling-dose should be avoided.
Verlato
G
G
Cattedra di Statistica Medica e Biometria, Università di Verona, Italy.
Cerveri
I
I
Villani
A
A
Pasquetto
M
M
Ferrari
M
M
Fanfulla
F
F
Zanolin
E
E
Rijcken
B
B
de Marco
R
R
D000328:Adult; D016535:Bronchial Hyperreactivity / Q000175:diagnosis*; D001985:Bronchial Provocation Tests / Q000379:methods; D004305:Dose-Response Relationship, Drug; D005260:Female; D005541:Forced Expiratory Volume / Q000187:drug effects; D006801:Humans; D016014:Linear Models; D008297:Male; D016210:Methacholine Chloride / Q000008:administration & dosage; D008954:Models, Biological; D008962:Models, Theoretical; D011237:Predictive Value of Tests; D015203:Reproducibility of Results; D012129:Respiratory Function Tests; D012680:Sensitivity and Specificity
D016210:Methacholine Chloride