Estimation of direct formulation effect under log‐normal distribution in bioavailability/bioequivalence studies

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Abstract
This paper considers estimation of a measure of relative bioavailability of a test formulation to a reference formulation, on the original scale, under the assumption of a log-normal distribution for the data from a 2 × 2 crossover bioavailability/bioequivalence study. We propose the minimum variance unbiased estimator which is equal to the maximum likelihood estimator adjusted for bias by a correction factor. We also derive the variance of the minimum variance unbiased estimator and its unbiased estimator. We derive the biases and mean square errors of the maximum likelihood estimator, the ratio of the least squares means, and the least squares mean of individual subject ratios, with respect to this measure, and compare them in a simulation study. Both theoretical and empirical results strongly suggest that one always consider the minimum variance unbiased estimator. A numerical example illustrates the proposed estimation procedure.

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