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Purpose. The effect of an anticancer treatment on tumor cell proliferation in vitro can be described as a three-dimensional surface where the inhibitory effect is related to drug concentration and treatment time. The analysis of this kind of response surface could provide critical information: for example, it could indicate whether a prolonged exposure to a low concentration of an anticancer agent will produce a different effect from exposure to higher concentrations for a shorter period of time. The parametric approach available in the literature was not flexible enough to accommodate the behavior of the response surface in some of the data sets collected as part of our research programs. Therefore, a new, general, nonparametric approach was developed. Methods. The response surface of the inhibition of cell-based tumor growth was described using a radial basis function neural network (RBF-NN). The RBF-NN was trained using regularization theory, which provided the initialization of a constrained quadratic optimization algorithm that imposes monotonicity of the surface with respect to both concentration and exposure time. Results. In the two analyzed cases (doxorubicin and flavopiridol), the proposed method was accurate and reliable in describing the inhibition surface of tumor cell growth as a function of drug concentration and exposure time. Residuals were small and unbiased. The new method improved on the parametric approach when the relative importance of drug concentration and exposure time in determining the overall effect was not constant across the experimental data. Conclusions. The proposed RBF-NN can be reliably applied for the analysis in cell-based tumor growth inhibition studies. This approach can be used for optimizing the administration regimens to be adopted in vivo. The use of this methodology can be easily extended to any cell-based experiment, in which the outcome can be seen as a function of two experimental variables. [ABSTRACT FROM AUTHOR]