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A kernel-smoothing method with locally varying bandwidths for the nonparametric estimation of derivatives of a function is proposed for highly nonequidistant data as they occur in pharmacokinetic response curves. We construct estimates having the particular property that the derivative estimates correspond exactly to the corresponding derivatives of the curve estimate even under locally varying bandwidth choice. The effects on the estimation of peak location (characteristic points) are investigated. In an example, characteristic points are estimated for a recently developed in vivo isotope dilution assay for vitamin A (retinol) nutritional status. The in vivo kinetics of appearance and disappearance of isotopically labeled retinol can be described with the proposed method.

Substantial adsorption of Pu, Cd and Pb onto mouth surfaces of mice occurs during consumption of drinking water that contains these elements. If this adsorption is not taken into account, the amounts deposited in the eviscerated carcass (muscle plus skeleton) after gastrointestinal absorption are overestimated by 2-9 times for the experiments described. An evaluation of data indicate that significant adsorption can also occur during gavage administration. Methods are described for estimation of amounts deposited in the carcass after exposure of mice to these metals via drinking water or gavage.