Efficient local estimation for time-varying coefficients in deterministic dynamic models with applications to HIV-1 dynamics

Recently deterministic dynamic models have become very popular in biomedical research and other scientific areas; examples include modeling human immunodeficiency virus (HIV) dynamics, pharmacokinetic/pharmacodynamic analysis, tumor cell kinetics, and genetic network modeling. In this article we propose estimation methods for the time-varying coefficients in deterministic dynamic systems that are usually described by a set of differential equations. Three two-stage local polynomial estimators are proposed, and their asymptotic normality is established. An alternative approach, a discretization method that is widely used in stochastic diffusion models, is also investigated. We show that the discretization method that uses the simple Enter discretization approach for the deterministic dynamic model does not achieve the optimal convergence rate compared with the proposed two-stage estimators. We use Monte Carlo simulations to study the finite-sample performance, and use a real data application to HIV dynamics to illustrate the proposed methods.