Estimation of confidence intervals for area under the curve from destructively obtained pharmacokinetic data

The area under the curve (AUC) of the concentration-time curve for a drug or metabolite, and the variation associated with the AUC, are primary results of most pharmacokinetic (PK) studies. In nonclinical PK studies, it is often the case that experimental units contribute data for only a single time point. In such cases, it is straightforward to apply noncompartmental methods to determine an estimate of the AUC. In this report, we investigate noncompartmental estimation of the AUC using the long-trapezoidal rule during the elimination phase of the concentration-time profile, and we account for the underlying distribution of data at each sampling time. For data that follow a normal distribution, the log-trapezoidal rule is applied to arithmetic means at each time point of the elimination phase of the concentration-time profile. For data that follow a lognormal distribution, as is common with PK data, the log-trapezoidal rule is applied to geometric means at each time point during elimination. Since the log-trapezoidal rule incorporates nonlinear combinations of mean concentrations at each sampling time, obtaining an estimate of the corresponding variation about the AUC is not straightforward. Estimation of this variance is further complicated by the occurrence of lognormal data. First-order approximations to the variance of AUC estimates are derived under the assumptions of normality, and lognormality, of concentrations at each sampling time. AUC estimates and variance approximations are utilized to form confidence intervals. Accuracies of confidence intervals are tested using simulation studies.