title: Nonlinear response surface in the study of interaction analysis of three combination drugs.
abstract: Few articles have been written on analyzing three-way interactions between drugs. It may seem to be quite straightforward to extend a statistical method from two-drugs to three-drugs. However, there may exist more complex nonlinear response surface of the interaction index (II) with more complex local synergy and/or local antagonism interspersed in different regions of drug combinations in a three-drug study, compared in a two-drug study. In addition, it is not possible to obtain a four-dimensional (4D) response surface plot for a three-drug study. We propose an analysis procedure to construct the dose combination regions of interest (say, the synergistic areas with II≤0.9). First, use the model robust regression method (MRR), a semiparametric method, to fit the entire response surface of the II, which allows to fit a complex response surface with local synergy/antagonism. Second, we run a modified genetic algorithm (MGA), a stochastic optimization method, many times with different random seeds, to allow to collect as many feasible points as possible that satisfy the estimated values of II≤0.9. Last, all these feasible points are used to construct the approximate dose regions of interest in a 3D. A case study with three anti-cancer drugs in an in vitro experiment is employed to illustrate how to find the dose regions of interest.
authors.affiliation: Department of Biostatistics, Virginia Commonwealth University, Richmond, VA 23298, USA.
authors.forename: Wen
authors.initials: W
authors.lastname: Wan
authors.affiliation: Department of Internal Medicine, Virginia Commonwealth University, Richmond, VA 23298, USA.
authors.forename: Xin-Yan
authors.initials: XY
authors.lastname: Pei
authors.affiliation: Department of Internal Medicine, Virginia Commonwealth University, Richmond, VA 23298, USA.
authors.forename: Steven
authors.initials: S
authors.lastname: Grant
authors.affiliation: Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
authors.forename: Jeffrey B
authors.initials: JB
authors.lastname: Birch
authors.affiliation: Department of Internal Medicine, Virginia Commonwealth University, Richmond, VA 23298, USA.
authors.forename: Jessica
authors.initials: J
authors.lastname: Felthousen
authors.affiliation: Department of Internal Medicine, Virginia Commonwealth University, Richmond, VA 23298, USA.
authors.forename: Yun
authors.initials: Y
authors.lastname: Dai
authors.affiliation: Department of Statistics, Georgetown University, Washington, DC 20057, USA.
authors.forename: Hong-Bin
authors.initials: HB
authors.lastname: Fang
authors.affiliation: Department of Statistics, Georgetown University, Washington, DC 20057, USA.
authors.forename: Ming
authors.initials: M
authors.lastname: Tan
authors.affiliation: Department of Biostatistics, Virginia Commonwealth University, Richmond, VA 23298, USA.
authors.forename: Shumei
authors.initials: S
authors.lastname: Sun
mesh_terms: D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D004347:Drug Interactions; D004357:Drug Synergism; D006801:Humans; D010600:Pharmacology / Q000379:methods*
keywords: Genetic algorithm (GA); Interaction index (II); Model robust regression (MRR); Synergism; Three-drug combination; Viability