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J Am Stat Assoc. 2014 Apr 2;109(506):700-716.

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

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Department of Biostatistics and Computational Biology, University of Rochester, School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, NY 14642.
Department of Epidemiology and Biostatistics, State University of New York, Albany, NY 12144.
Department of Statistics, George Washington University, 801 22nd St. NW, Washington, D.C. 20052.


The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.


Adaptive group LASSO; Differential equations; High-dimensional data; Sparse additive models; Time course microarray data; Variable selection

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