Hybrid Bayesian inference on HIV viral dynamic models

Abstract

Modelling of HIV dynamics in AIDS research has greatly improved our understanding of the pathogenesis of HIV-1 infection and guided for the treatment of AIDS patients and evaluation of antiretroviral therapies. Some of the model parameters may have practical meanings with prior knowledge available, but others might not have prior knowledge. Incorporating priors can improve the statistical inference. Although there have been extensive Bayesian and frequentist estimation methods for the viral dynamic models, little work has been done on making simultaneous inference about the Bayesian and frequentist parameters. In this article, we propose a hybrid Bayesian inference approach for viral dynamic nonlinear mixed-effects models using the Bayesian frequentist hybrid theory developed in Yuan [Bayesian frequentist hybrid inference, Ann. Statist. 37 (2009), pp. 2458–2501]. Compared with frequentist inference in a real example and two simulation examples, the hybrid Bayesian approach is able to improve the inference accuracy without compromising the computational load.

Keywords:

• hybrid Bayesian density
• 0–1 loss
• Monte Carlo EM algorithm
• HIV dynamics
• nonlinear mixed-effects models

Acknowledgments

The authors thank Ao Yuan for valuable suggestions on the variance estimation of the hybrid Bayesian inference. We thank the editor, associate editor, and two reviewers for their valuable comments. This research was sponsored, in part, by the National Institute of Health grant 1R01CA149429 (GH), by NIAID/NIH grant AI080338 (YH), and by the National Science Foundation of China grant 10901155 and 61134013 (QL).