Extrapolation of methacholine log-dose response curves with a Cumulative Gaussian Distribution function

Abstract

Methacholine provocation tests are aimed at determining bronchial responsiveness. Recent investigations stress the importance of considering the entire log-dose response curve, yielding not only the provocative dose producing a 20% change in forced expiratory volume in one second (FEV1) (PC20), but also the plateau value and the steepest slope of the curve (reactivity). In three control subjects and seven patients with mild to moderate asthma, we have obtained methacholine log-dose response curves in which a plateau was reached. A new model, the Cumulative Gaussian Distribution (CGD) function was fitted to the whole curve. The upper part of the curve was also analysed with the Hofstee equation, which has been used in a number of other investigations and aimed at plateau estimation. The plateau values obtained by the fits were compared with the values actually measured (average response of last 3 points with a variation coefficient < 5% of the mean value) by using the coefficient of determination (R2) (Applied Statistics. Sachs). If all data points were considered, both fits yielded a plateau which slightly overestimated the measured plateau values. R2 for the CGD fit ranged from 0.93-0.99, indicating a highly significant correlation between actual and fitted data points. If the curves were truncated, such that the last four provocative doses were omitted from the analysis, the CGD fit still yielded plateau values; the mean difference from the measured plateaux, in % of the measured plateau values, was -2.6% (SD 18.2). In only three out of the 10 cases did the Hofstee equation yield plateau values with a deviation from 'measured' < 47% of the measured value.(ABSTRACT TRUNCATED AT 250 WORDS)