# Implications for Clinical Pharmacodynamic Studies of the Statistical Characterization of an *In Vitro* Antiproliferation Assay

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## Abstract

*Modeling of nonlinear pharmacodynamic (PD) relationships necessitates the utilization of a weighting function in order to compensate for the heteroscedasticity. The structure of the variance was studied for concentration–effect data generated in an* in vitro *96-well plate cell growth inhibition assay, where data are numerous (480 data points per experiment) and replication is easy. From the five candidate models that were considered, the power function*\({\text{S}}_{\text{Y}}^{\text{2}} = \phi _2 \overline {\text{Y}} ^{\phi 3}\), *where*\(\overline {\text{Y}}\)*is the sample mean and*\({\text{S}}_{\text{Y}}^{\text{2}}\)*is the sample variance, was shown to be the most appropriate to describe the nonuniformity of the variance along the range of measured effect for 253 sets of*\(\left( {\overline {\text{Y}} ;{\text{s}}_{\text{Y}}^{\text{2}} } \right)\)*data. The Hill model was fit to the concentration–effect data with weighted nonlinear regression, where the weights were equal to the reciprocal of the predicted variance. The examination of the distribution of the 253 sets of parameters of the PD model showed that* IC_{50}*was lognormally distributed whereas the distribution of γ was normal. The characterization of the appropriate variance function and concentration–effect function in a simple* in vitro *experimental setting with a large number of experiments, with each experiment including a large number of data points, will be useful for guiding similar* in vitro *concentration–effect studies where data are plentiful and for guiding PD modeling in complex clinical settings in which extensive data for model characterization is impossible to obtain.*

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