Nonlinear response surface in the study of interaction analysis of three combination drugs |
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| Authors: | Wen Wan Xin‐Yan Pei Steven Grant Jeffrey B. Birch Jessica Felthousen Yun Dai Hong‐Bin Fang Ming Tan Shumei Sun |
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| Affiliation: | 1. Department of Biostatistics, Virginia Commonwealth University, Richmond, USA;2. Department of Internal Medicine, Virginia Commonwealth University, Richmond, USA;3. Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, USA;4. Department of Statistics, Georgetown University, Washington, USA |
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| 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 ( ) 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  ). First, use the model robust regression method (MRR), a semiparametric method, to fit the entire response surface of the  , 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  . 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. |
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| Keywords: | Genetic algorithm (GA) Interaction index () Model robust regression (MRR) Synergism Three‐drug combination Viability |
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) 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 
). First, use the model robust regression method (MRR), a semiparametric method, to fit the entire response surface of the 
, 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 
. 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.