Parameter estimation for semiparametric ordinary differential equation models

Abstract

We propose a new class of two-stage parameter estimation methods for semiparametric ordinary differential equation (ODE) models. In the first stage, state variables are estimated using a penalized spline approach; In the second stage, form of numerical discretization algorithms for an ODE solver is used to formulate estimating equations. Estimated state variables from the first stage are used to obtain more data points for the second stage. Asymptotic properties for the proposed estimators are established. Simulation studies show that the method performs well, especially for small sample. Real life use of the method is illustrated using Influenza specific cell-trafficking study.

Keywords:

• Ordinary differential equation
• penalized spline
• semiparametric coefficient models
• data augmentation estimation
• two-stage estimation

Acknowledgments

The authors thank Dr. Hua Liang and Dr. Yun Fang for helpful discussions.

Additional information

Funding

This research was partially supported by the NIH grants HHSN272201000055C, AI087135, and two University of Rochester CTSI pilot awards (UL1RR024160) from the National Center For Research Resources. This work was done when authors were affiliated with University of Rochester.