On the statistical moments transformation in pharmacokinetic models: A study of the rate parameter and the mean residence time estimates

This paper simulates the sampling distributions of the rate parameter and the mean residence time (MRT) estimators for a specific two-compartment model. Two forms of measurement error, one additive and the other multiplicative, and two forms of weighting structures, one unweighted and the other weighted by the error variances, are investigated. The chief findings are: 1) unweighted estimates generally are highly biased but weighting reduces the bias many fold, 2) the asymptotic standard error approximations are acceptable only with weighted least squares, and 3) the mean squared errors of the MRT estimates compare favorably with those of the rate parameter estimates. Based on the favorable sampling distributions, it is recommended that weighted MRT estimates be calculated routinely as important descriptors of kinetic systems.