A Method for Estimating and Testing Area Under the Curve in Serial Sacrifice, Batch, and Complete Data Designs

The extent of drug availability is often measured by the area under the concentration-time curve. In animal studies, experimental constraints can limit the number of observations available on each animal. Estimation of area under the curve and its standard error are straightforward when each animal is measured at each time point. Bailer [1] Bailer, A J. 1988. Testing for the equality of area under the curves when usingdestructive measurement techniques. J Pharmacokinet Biopharm, 16(3): 303–309. [Google Scholar] and Nedelman et al. [2] Nedelman, J R, Gibiansky, E and Lau, D TW. 1995. Applying Bailer's method for AUC confidence intervals tosparse sampling. Pharm Res, 12(1): 124–128. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar], have described techniques for estimating the area under the curve and its standard error when each animal is measured once. Yeh [3] Yeh, C. 1990. “Estimation and significant tests of area under the curve derived from incomplete blood sampling”. In American Statistical Association Proceedings of the BiopharmaceuticalSection 74–81. [Google Scholar] has described a technique for the hybrid case where animals are measured more than once, but not at all time points. We describe a method for estimating area under the curve and its standard error which is applicable to all three types of designs. We give formulas for testing treatment differences, including dose trends and dose proportionality, in area under the curve for designs containing an arbitrary number of treatments. A jackknife estimator is also described.