Parameter Identifiability and Estimation of HIV/AIDS Dynamic Models |
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Authors: | Hulin Wu Haihong Zhu Hongyu Miao Alan S Perelson |
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Institution: | (1) Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, NY 14642, USA;(2) Theoretical Biology and Biophysics Group, MS-K710, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA |
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Abstract: | We use a technique from engineering (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with
Intervention, 2005) to investigate the algebraic identifiability of a popular three-dimensional HIV/AIDS dynamic model containing six unknown
parameters. We find that not all six parameters in the model can be identified if only the viral load is measured, instead
only four parameters and the product of two parameters (N and λ) are identifiable. We introduce the concepts of an identification function and an identification equation and propose the
multiple time point (MTP) method to form the identification function which is an alternative to the previously developed higher-order
derivative (HOD) method (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330–336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with
Intervention, 2005). We show that the newly proposed MTP method has advantages over the HOD method in the practical implementation. We also
discuss the effect of the initial values of state variables on the identifiability of unknown parameters. We conclude that
the initial values of output (observable) variables are part of the data that can be used to estimate the unknown parameters,
but the identifiability of unknown parameters is not affected by these initial values if the exact initial values are measured
with error. These noisy initial values only increase the estimation error of the unknown parameters. However, having the initial
values of the latent (unobservable) state variables exactly known may help to identify more parameters. In order to validate
the identifiability results, simulation studies are performed to estimate the unknown parameters and initial values from simulated
noisy data. We also apply the proposed methods to a clinical data set to estimate HIV dynamic parameters. Although we have
developed the identifiability methods based on an HIV dynamic model, the proposed methodologies are generally applicable to
any ordinary differential equation systems. |
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Keywords: | Identifiability Inverse problem Statistical estimation Viral dynamics |
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