Evaluation of methacholine dose-response curves by linear and exponential mathematical models: goodness-of-fit and validity of extrapolation

Eur Respir J. 1996 Mar;9(3):506-11. doi: 10.1183/09031936.96.09030506.

Abstract

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adult
  • Bronchial Hyperreactivity / diagnosis*
  • Bronchial Provocation Tests* / methods
  • Dose-Response Relationship, Drug
  • Female
  • Forced Expiratory Volume / drug effects
  • Humans
  • Linear Models
  • Male
  • Methacholine Chloride* / administration & dosage
  • Models, Biological
  • Models, Theoretical*
  • Predictive Value of Tests
  • Reproducibility of Results
  • Respiratory Function Tests
  • Sensitivity and Specificity

Substances

  • Methacholine Chloride