A novel method for assessing in vitro oncology drug combinations using growth rates

We propose a new method that allows screening oncology drug combinations using data from in vitro studies to select agents that have the promise of showing a synergistic effect in vivo. In contrast to known approaches that define combination effects either on the concentration scale or on the percent inhibition scale, we use the growth rate of treated cells as a primary indicator of treatment activity. The developed method is based on a novel statistical model that describes the growth of cancer cells that are subject to treatment with a combination of compounds. The model assumes a multicompartment cell population with transition rates between compartments modeled according to biochemical reaction properties, and cells in each compartment growing according to exponential law. This translates to a linear system of ordinary differential equations, whose solution is accurately approximated by a closed-form expression using rapid equilibrium assumptions. Special cases of the aforementioned model represent situations when the combination effect is absent or when the considered drugs act as the same compound. Assuming the normal distribution for the growth rate measurement error, we describe a formal statistical testing procedure to distinguish between different mechanisms of action for the considered compounds, and to test if a significant combination effect is being observed.