Estimating derivatives of pharmacokinetic response curves with varying bandwidths

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.