A model-based approach for assessingin vivocombination therapy interactions

Abstract

We present an approach for evaluating the efficacy of combination antitumor agent schedules that accounts for order and timing of drug administration. Our model-based approach compares in vivo tumor volume data over a time course and offers a quantitative definition for additivity of drug effects, relative to which synergism and antagonism are interpreted. We begin by fitting data from individual mice receiving at most one drug to a differential equation tumor growth/drug effect model and combine individual parameter estimates to obtain population statistics. Using two null hypotheses: (i) combination therapy is consistent with additivity or (ii) combination therapy is equivalent to treating with the more effective single agent alone, we compute predicted tumor growth trajectories and their distribution for combination treated animals. We illustrate this approach by comparing entire observed and expected tumor volume trajectories for a data set in which HER-2/neu-overexpressing MCF-7 human breast cancer xenografts are treated with a humanized, anti-HER-2 monoclonal antibody (rhuMAb HER-2), doxorubicin, or one of five proposed combination therapy schedules.A ssessing the efficacy of a combination of antitumor agents by analyzing in vivo tumor growth is an increasingly popular experimental design. However, analyses of tumor growth curves and of drug interactions are both complex statistical problems. Many methods for assessing growth address only a univariate summary, such as doubling time or tumor volume at an arbitrary endpoint, and either lack power or inflate the type I error rate (1). Multivariate methods that use the entire nonlinear growth curve are preferred (1, 2), but most published methods have been limited to linear growth models that may not be appropriate for long time courses or multiple-drug administration. No method of which we are aware has incorporated differences in drug administration time and/or order of drug administration in a statistical analysis comparing treatment schedules.Another stumbling block in evaluating combination therapy is clearly defining additivity or summation of effect (also referred to as ''independence'') (3). Antagonism or synergism is generally interpreted as an outcome that falls short of or exceeds, respectively, the effect expected from a purely additive interaction of individual drugs. There is, however, much debate as to how these quantities are to be calculated (4), and their definitions are often context and model dependent, particularly for nonlinear doseeffect relationships. Some definitions focus on addition of effects, whereas others consider the combinations of doses necessary to reach a preset effect. These definitions are not equivalent except, perhaps, when the system is linear. Consequently, there is no consensus on a quantitative definition of synergism and antagonism. Finally, most classical methods for assessing drug additivity (4-7) are designed only for a univariate measure of drug effectiveness and require experimental data at multiple doses to de...

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