Nonlinear Response Surface and Mixture Experiment Methodologies Applied to the Study of Synergism

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Abstract
A new paradigm for the study of the joint action (synergism, additivity and antagonism) of different agents that combines nonlinear response surface modeling with mixture experiment methodologies is described. We achieve a global nonlinear response surface model using raw data modeling and hierarchical parameter modeling along with numerical and graphical evaluations. The method is applied to a very large previously‐published (Faesselet al., 1998)in vitrostudy of the combined effect of Trimetrexate (TMQ) and AG2034 on inhibition of cancer cell growth. The modulator Folic acid (Folate) concentration is also included as a continuous process variable. The mixture portion of the analysis is best identified as an “NLMAZ‐PV” experiment, incorporating a nonlinear mixture‐amount model with zero amounts (control observations) and the process variable. The underlying nonlinear structural model, describing the relationship between the mixture amount and the observed effect, is the four parameter Hill (1910) equation. This model for studying synergism was developed as an improvement over the flagship synergy/antagonism model of Greco et al. (1995) and other response surface synergy models. This new modeling approach allows for irregularly‐shaped isobols, complex patterns of local synergism and antagonism, a modulating agent with no effect of its own, and extensions to three or more drugs (White et al., 2003).