Drug combination is a major treatment approach in cancer and antiviral therapies. A key issue is to find which combinations are additive, synergistic or antagonistic. In this paper, we develop statistical methods for experimental design and data analysis of combination studies of drugs that have log-linear dose-response curves. This class of dose response includes the Hill, sigmoid and simple exponential models. The experimental design (dose-finding and sample size determination) is derived by means of uniform measures that maximize the minimum power of the F-test to detect any departures from additive action and at the same time minimizes the maximum bias due to lack of fit among all potential departures of a given meaningful magnitude. Furthermore, we propose a model-free interaction index surface to capture the interaction of two drugs. The nonparametric function of the interaction index is estimated using the technique developed in thin plate splines. These methods are applicable to both in vivo and in vitro experiments. A study of two anticancer drugs, suberoylanilide hydroxamic acid (Vorinostat) and Etoposide applied sequentially against the cell line HL-60, is given to illustrate the proposed methods of experimental design and interaction analysis.