A comparison of methods for estimating individual pharmacokinetic parameters

Characteristics of the methods for estimating individual pharmacokinetic parameters are compared both theoretically and numerically. The methods examined represent the range of most of modern methods and include the ordinary least squares, iteratively reweighted least squares, extended least squares, generalized least squares, maximum quasi-likelihood and its extended scheme, and minimum relative entropy methods. When the function representing the mean itself is used as a variance function, which may be then related to a Poisson distribution, the iteratively reweighted least squares estimator and maximum quasi-likelihood estimator are both identical to that of the minimum relative entropy method. These methods work by minimizing a kind of relative entropy between observed data and corresponding theoretical values. Furthermore, these methods guarantee agreement between the sum of the observed values and the estimate of the sum. This relation does not hold in general for the other estimators. The sum can, in a sense, be viewed as an approximation of the area under the curve. In addition, it is shown by numerical study that these methods are robust against the misspecification of the variance model and work as effectively as such sophisticated methods as the extended least squares, generalized least squares, and maximum extended quasi-likelihood methods. These sophisticated methods require complicated numerical optimization techniques and should be used only in cases where the estimation of the variance function is demanded. In the other cases, the method of minimum relative entropy or its equivalent is sufficient or even preferable for estimating individual pharmacokinetic parameters.