Experimental design and statistical analysis for three-drug combination studies

Drug combination is a critically important therapeutic approach for complex diseases such as cancer and HIV due to its potential for efficacy at lower, less toxic doses and the need to move new therapies rapidly into clinical trials. One of the key issues is to identify which combinations are additive, synergistic, or antagonistic. While the value of multidrug combinations has been well recognized in the cancer research community, to our best knowledge, all existing experimental studies rely on fixing the dose of one drug to reduce the dimensionality, e.g. looking at pairwise two-drug combinations, a suboptimal design. Hence, there is an urgent need to develop experimental design and analysis methods for studying multidrug combinations directly. Because the complexity of the problem increases exponentially with the number of constituent drugs, there has been little progress in the development of methods for the design and analysis of high-dimensional drug combinations. In fact, contrary to common mathematical reasoning, the case of three-drug combinations is fundamentally more difficult than two-drug combinations. Apparently, finding doses of the combination, number of combinations, and replicates needed to detect departures from additivity depends on dose–response shapes of individual constituent drugs. Thus, different classes of drugs of different dose–response shapes need to be treated as a separate case. Our application and case studies develop dose finding and sample size method for detecting departures from additivity with several common (linear and log-linear) classes of single dose–response curves. Furthermore, utilizing the geometric features of the interaction index, we propose a nonparametric model to estimate the interaction index surface by B-spine approximation and derive its asymptotic properties. Utilizing the method, we designed and analyzed a combination study of three anticancer drugs, PD184, HA14-1, and CEP3891 inhibiting myeloma H929 cell line. To our best knowledge, this is the first ever three drug combinations study performed based on the original 4D dose–response surface formed by dose ranges of three drugs.