Bayesian Hierarchical Modeling of the HIV Evolutionary Response to Therapy

Abstract

A major challenge for the treatment of human immunodeficiency virus (HIV) infection is the development of therapy-resistant strains. We present a statistical model that quantifies the evolution of HIV populations when exposed to particular therapies. A hierarchical Bayesian approach is used to estimate differences in rates of nucleotide changes between treatment- and control-group sequences. Each group's rates are allowed to vary spatially along the HIV genome. We employ a coalescent structure to address the sequence diversity within the treatment and control HIV populations. We evaluate the model in simulations and estimate HIV evolution in two different applications: a conventional drug therapy and an antisense gene therapy. In both studies, we detect evidence of evolutionary escape response in the HIV population. Supplementary materials for this article are available online.

KEY WORDS:

• Coalescent
• MCMC
• PAC likelihood
• Viral evolution

Acknowledgments

This work was supported by a grant from the Center for AIDS Research of the University of Pennsylvania. The authors thank G. Binder, B. Doms, and N. Ray for their data and advice.

Notes

The Wilson and McVean (2006) calculations have mutation at the codon level, but can be adapted to our model with mutation on the nucleotide level.

We use the PAC-A version of the approach given by Li and Stephens (2003).

We use 10 orderings in our applications in Section 4, though our simulation experiments suggested that even five orderings are sufficient for a stable estimate of the PAC likelihood.

Our inference in simulation studies in Section 3.1 was also not sensitive to the values of δ_μ and δ_ρ.

NOTE: The “high” setting is a rate of μ₀ = 0.05 or ρ₀ = 0.05 and the “low” setting is a rate of μ₀ = 0.005 or ρ₀ = 0.005. For “high” rates, variances were set to σ² = 0.25 and τ² = 0.05. For “low” rates, variances were set to σ² = 0.05 and τ² = 0.001. In all conditions, κ was set to 0.5.

NOTE: Note that the coverage rates in the final two columns are also averaged across all blocks.

NOTE: “Large” data size consists of simulation setting F in Table 2 whereas “small” data size consists of simulation settings A–E in Table 2. We used the upper third and lower third of our true treatment effects to define “large” versus “small” treatment effects.