Efficient estimation of log-normal means with application to pharmacokinetic data

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In this paper, the problem of interest is efficient estimation of log-normal means. Several existing estimators are reviewed first, including the sample mean, the maximum likelihood estimator, the uniformly minimum variance unbiased estimator and a conditional minimal mean squared error estimator. A new estimator is then proposed, and we show that it improves over the existing estimators in terms of squared error risk. The improvement is more significant with small sample sizes and large coefficient of variations, which is common in clinical pharmacokinetic (PK) studies. In addition, the new estimator is very easy to implement, and provides us with a simple alternative to summarize PK data, which are usually modelled by log-normal distributions. We also propose a parametric bootstrap confidence interval for log-normal means around the new estimator and illustrate its nice coverage property with a simulation study. Our estimator is compared with the existing ones via theoretical calculations and applications to real PK studies.