curve fitting

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A General Measure of In Vitro Phototoxicity Derived from Pairs of Dose–Response Curves and its Use for Predicting the In Vivo Phototoxicity of Chemicals

Hermann-Georg Holzhütter

In pharmacology, it is common to evaluate the influence of external effectors (for example, temperature, pH, and presence of a second drug) on dose–response relations by the potency factor (PF50): PF50 = ED50 (– effector) ED50 (+ effector) where ED50 (± effector) denotes the 50% effective dose in the presence and in the absence of the effector, respectively. In this paper, the external effector is ultraviolet (UV) light, and PF50 is referred to as the photoirritancy factor (PIF). There are two parameters which limit the applicability and toxicological reliability of the PIF. Firstly, the physical properties (for example, water solubility) of the chemical tested and the constraints of the biological test system may make it difficult, or even impossible, to achieve sufficiently high doses to observe 50% of the maximal response. In such cases, no numeric value of the potency factor can be computed. Secondly, the potency factor does not take into account the absolute change in response induced by UV light, i.e. depending on the shape of the ±UV dose–response curves, the absolute change in response may be small although the PIF is large, and vice versa. This paper proposes a more general measure of phototoxicity, the mean photo effect (MPE), which can be assessed from pairs of dose–response curves, even if the 50% response level is not reached in one curve or in both. The MPE is a weighted average of PIFd values across different dose levels (d being common to both dose–response curves). The absolute response changes, ΔRd, i.e. the differences between the –UV curve and the +UV curve are used as weighting factors. The numerical computation of the MPE is based on theoretical curves obtained by fitting a mathematical model to the experimental dose–response data. Plotting PIFd and ΔRd versus the corresponding doses permits differences in the shapes of the two curves to be assessed, and possible alterations in the toxic mechanisms induced by UV light to be revealed. The variance of MPE is estimated by a bootstrap procedure. The use of the MPE is illustrated by its application to dose–response data obtained with a human keratinocyte assay of fibroblasts in the EU/COLIPA international validation project on photoirritancy.
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