Statistics and Its Interface

Volume 6 (2013)

Number 1

Parameter estimation for HIV ODE models incorporating longitudinal structure

Pages: 9 – 18



Hua Liang (University of Rochester Medical Center, Rochester, New York, U.S.A.)

Yao Yu (Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, New York, U.S.A.)


We apply nonlinear mixed-effects models (NLME) to estimate parameters in Perelson’s HIV dynamic model, a system of mechanism-based ordinary differential equations (ODE). The unknown parameters of the dynamic model and the baseline of infected CD4<sup+ T cells are estimated simultaneously. Meanwhile variance components for random-effects and parameters for individuals are also estimated. Because we solve the ODE directly without making any model approximations or fixing any parameters to obtain close-form solutions as in literature, the drawing conclusion maintains biological interpretability for dynamic parameters which is critically helpful. Simulation studies are conducted to examine the performance of this approach, especially the influence of measurement errors and model assumptions underlying the parameter estimation method. Moreover, we apply this approach to real data collected from an AIDS clinical trial of HIV-1 study.


HIV dynamic model, measurement errors, nonlinear mixed-effects model, variance components, random-effects

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