The goal of this proposal is to develop statistical methods to optimally design and efficiently analyze preclinical drug combination studies in cancer. Drug combination is central to cancer chemotherapy. A statistical approach is necessary since even the administration of precisely the same dose to virtually genetically identical animals may result in different measures of effect. Such data variation needs to be controlled in the experimental design and accounted for in the analysis. Classically, the isobologram and the median effect model have been used to indicate synergism/antagonism. Both methods, for the most part, ignore the uncertainty associated with the estimated combination index and do not adequately describe where the treatment effect is statistically different from the optimum effect, where the joint effect is superior to single-drug treatments, whether the efficacy is affected by the time sequential interval in the administration of the drug and how to efficiently use data from xenograft models to compare different treatment regimens. More importantly, few methods are available to choose combinations and samples sizes (e.g., number of animals) needed to achieve the goal of the study. Our recent preliminary studies have shown that tumor xenograft experiments on combinations can be optimally designed so that dose-effect of the combination can be estimated with moderate sample sizes and more efficiently analyzed, allowing optimal allocation of research resources and produces most interpretable data. The approach represents an integration of concepts in modem statistical methods, number-theoretic methods and pharmacology. In this application, we propose (1) To develop experimental design to optimally choose combinations and determine sample sizes in combination studies of two drugs for common classes of single drug dose-effect models that include non-constant relative potency based on a powerful statistical test; (2) To extend the methods to account for the effect of the time interval between administrations of the two drugs and to include multiple-drug combinations with applications to a three-drug combination for lung cancer cell lines; (3) To generalize the combination index based on a validated statistical model and to develop methods to characterize synergy so that the regions of dose-effect can be explored and the intrinsic nature of tumor growth can be accounted for in comparing dose schedules; (4) To apply the developed statistical methods to combination studies in a currently NCI funded program project on childhood solid tumors and an NCI cooperative agreement and to enrich computer programs in developed in Aims 1-3 in the freely available R language. It is expected that the method will benefit studies involving combinations in developmental therapeutics broadly and analyses in Specific Aim 4 will of immediate benefit to the therapeutic development goals of two NCI funded projects.