Abstract 103: The additive damage model for dose-response of cancer drug combinations
Authors: El-Kareh Ardith W. , Jones Leslie B. , Secomb Timothy W. 
Published: February 2011

Abstract
New drug combinations are initially tested by generating dose-response data for their cytotoxic effect on cancer cell lines. Such data are then used to assess whether further development in animal models or clinical trials is merited. Several mathematical models have been proposed to describe and evaluate such data, including the Chou-Talalay median effect model, the Syracuse-Greco model, the isobologram model, and the White et al surface response model. Some of these models contain a parameter representing synergy or antagonism of the combination, while for others, deviations from the model fits are used as synergy tests. Here, the additive damage model, a new model proposed to describe drug combination cytotoxicity, is tested. Unlike previous models which are either empirical or derive drug effect in terms of fractional inhibition of enzyme-facilitated reaction rates, the current model is based on the concept of cellular damage, as measured by the maximum achieved concentration of some intracellular species of drug bound to target. Individual cells succumb at their threshold level of damage, assumed to be heterogeneous across a cell population. Survival relative to controls is therefore expressed in terms of the statistical distribution of the damage threshold over the population. In the case of two drugs acting simultaneously, total damage is a linear superposition of damage terms for each drug. The damage terms allow for saturation of cellular uptake or target binding. Here, two possible damage threshold distribution functions are considered, the cumulative lognormal function, and a power-law function (Hill equation). Two key features of the model that mathematically distinguish it from the median effect model are saturation effects in the drug concentration, and the difference in heterogeneity of the lethal damage threshold between the two drugs. The model was tested for 12 data sets for the cisplatin-paclitaxel combination, an additional 12 for other platinum-taxane combinations, and 15 data sets for a variety of drug combinations including the newer agents gefinitib and trastuzumab. The Hill form of the model was found in some cases to fit the data slightly better than the lognormal form. While a lognormal distribution would be expected as the result of linear superposition of a large number of cellular processes, each of which followed some statistical distribution across the cell cycle, nonlinearity and coupling can explain why power law forms may fit data better, a phenomenon already observed in other biological applications such as human memory. Overall, the model provided significantly superior fits to the data compared to previous models, by the Akaike Information Criterion. This suggests that deviations from the Chou-Talalay model previously interpreted as synergy or antagonism can equally well be explained in terms of saturation effects and differing heterogeneities in the threshold concentrations of two drugs.
Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 101st Annual Meeting of the American Association for Cancer Research; 2010 Apr 17-21; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2010;70(8 Suppl):Abstract nr 103.