Calculating confidence intervals for summary measures of individual curves via nonlinear regression models

In biomedical research data are often collected serially over time. Hence, the main outcome is represented by response curves. A suitable approach to analyse such data is given by summary measures describing the main features of the response curves. An important issue is the precision of the estimated summary measures, which can be represented by confidence intervals. However, since summary measures frequently cannot be obtained via linear relationships, the calculation of confidence intervals involves some special considerations. In this paper attention is focused on unimodal response curves. Important summary measures for this type of response curves are the curve maximum (C-max), the time to curve maximum (t(max)) and the area under the curve (AUC). These summary measures can be calculated from the parameters of nonlinear regression models fitted to the data. Since the summary measures are nonlinear functions of the regression coefficients the multivariate delta method is used to derive formulas for the standard errors and confidence intervals of the summary measures. The method is illustrated by application to pharmacodynamic data.