Randomization tests for assessing the equality of area under curves for studies using destructive sampling

Testing the equality of the area under a curve (AUC) for different dose groups is frequently done in pharmacokinetic research. Equality of AUCs is one indicator of bioequivalence. When the experimental unit must be sacrificed to obtain a response, AUC can be simply estimated using a linear combination of response means at various time points. The distribution of this estimator is simply obtained using standard statistical theory, and statistical hypothesis tests are easily constructed. These tests assume a normal distribution of responses at each time point (or at least large enough samples to assure that the mean response is normally distributed). The applicability of this test to cases of non-normal response distributions when small numbers of observations are sampled at each time point is questionable. Randomization tests are suggested for this problem. These tests provide a valuable alternative to this normal-theory test. Discussion of the assessment of dose proportionality is also presented.