Modeling the short-, middle- and long-term viral load responses for comparing estimated dynamic parameters

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate antiviral therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by drug exposures, drug resistance and other factors during the long-term treatment evaluation process. The study of HIV dynamics is one of the most important development in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Although many HIV dynamic models have been proposed by AIDS researchers in the last decade, they have only been used to quantify short-term viral dynamics and do not correctly describe long-term virologic responses to antiretroviral treatment. In other words, these simple viral dynamic models can only be used to fit short-term viral load data for estimating dynamic parameters. In this paper, a mechanism-based differential equation models is introduced for characterizing the long-term viral dynamics with antiretroviral therapy. We applied this model to fit different segments of the viral load trajectory data from a simulation experiment and an AIDS clinical trial study, and found that the estimates of dynamic parameters from our modeling approach are very consistent. We may conclude that our model can not only characterize long-term viral dynamics, but can also quantify short- and middle-term viral dynamics. It suggests that if there are enough data in the early stage of the treatment, the results from our modeling based on short-term information can be used to capture the performance of long-term care with HIV-1 infected patients.     

Design of long-term HIV dynamic studies using semiparametric mixed-effects models

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV-1 infection and also in assessing the effectiveness of antiviral therapies. There are many AIDS clinical trials on HIV dynamics currently in development worldwide, giving rise to many design issues yet to be addressed. For example, most studies are focused on short-term viral dynamics and the existing models may not be applicable to describe long-term virologic response. In this paper, we use a simulation-based approach to study the designs of long-term viral dynamics under semiparametric nonlinear mixed-effects models. These models not only can preserve the meaningful interpretation of the short-term HIV dynamics, but also characterize the long-term virologic responses to antiretroviral (ARV) treatment. We investigate a number of feasible clinical protocol designs similar to those currently used in AIDS clinical trials. In particular, we evaluate whether earlier samplings can result in more useful information about the viral response trajectory; we also evaluate the effectiveness of two strategies: more frequent samplings per subject with fewer subjects versus fewer samplings per subject with more subjects while keeping the total number of samplings constant. The results of our investigation provide quantitative guidance for designing and selecting ARV therapy.     

Assessing antiviral potency of anti-HIV therapies in vivo by comparing viral decay rates in viral dynamic models

A virologic marker, the number of HIV RNA copies or viral load, is currently used to evaluate anti-HIV therapies in AIDS clinical trials. This marker can be used to assess the antiviral potency of therapies, but is easily affected by noncompliance, drug resistance, toxicities, and other factors during the long-term treatment evaluation process. Recently it has been suggested to use viral dynamics to assess the potency of antiviral drugs and therapies, since viral decay rates in viral dynamic models have been shown to be related to the antiviral drug potency directly, and they need a shorter evaluation time. In this paper we first review the two statistical approaches for characterizing HIV dynamics and estimating viral decay rates: the individual nonlinear least squares regression (INLS) method and the population nonlinear mixed-effect model (PMEM) approach. To compare the viral decay rates between two treatment arms, parametric and nonparametric tests, based on the estimates of viral decay rates (the derived variables) from both the INLS and PMEM methods, are proposed and studied. We show, using the concept of exchangeability, that the test based on the empirical Bayes' estimates from the PMEM is valid, powerful and robust. This proposed method is very useful in most practical cases where the INLS-based tests and the general likelihood ratio test may not apply. We validate and compare various tests for finite samples using Monte Carlo simulations. Finally, we apply the proposed tests to an AIDS clinical trial to compare the antiviral potency between a 3-drug combination regimen and a 4-drug combination regimen. The proposed tests provide some significant evidence that the 4-drug regimen is more potent than the 3-drug regimen, while the naive methods fail to give a significant result.*To whom correspondence should be addressed.     

The relationship between virologic and immunologic responses in AIDS clinical research using mixed-effects varying-coefficient models with measurement error

In this article we study the relationship between virologic and immunologic responses in AIDS clinical trials. Since plasma HIV RNA copies (viral load) and CD4+ cell counts are crucial virologic and immunologic markers for HIV infection, it is important to study their relationship during HIV/AIDS treatment. We propose a mixed-effects varying-coefficient model based on an exploratory analysis of data from a clinical trial. Since both viral load and CD4+ cell counts are subject to measurement error, we also consider the measurement error problem in covariates in our model. The regression spline method is proposed for inference for parameters in the proposed model. The regression spline method transforms the unknown nonparametric components into parametric functions. It is relatively simple to implement using readily available software, and parameter inference can be developed from standard parametric models. We apply the proposed models and methods to an AIDS clinical study. From this study, we find an interesting relationship between viral load and CD4+ cell counts during antiviral treatments. Biological interpretations and clinical implications are discussed.     

A comparison study of models and fitting procedures for biphasic viral dynamics in HIV-1 infected patients treated with antiviral therapies

The study of HIV dynamics is one of the most important developments in recent AIDS research. It has led to a new understanding of the pathogenesis of HIV infection. But, although important findings in HIV dynamics have been published in prestigious scientific journals in the last 5 years, the model-fitting procedures used in these publications have not been studied in any detail. In this paper, we evaluate the performance of four model-fitting procedures proposed and used in biphasic HIV dynamic data analysis via extensive Monte Carlo simulations. We propose some guidelines for practitioners to select an appropriate method for their own data analysis. Real data examples from an AIDS clinical trial are provided as illustrations.     

Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system

HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.     

Hierarchical Bayesian inference for HIV dynamic differential equation models incorporating multiple treatment factors

Studies on HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV‐1 infection and also in assessing the effectiveness of antiretroviral (ARV) treatment. Viral dynamic models can be formulated through a system of nonlinear ordinary differential equations (ODE), but there has been only limited development of statistical methodologies for inference. This article, motivated by an AIDS clinical study, discusses a hierarchical Bayesian nonlinear mixed‐effects modeling approach to dynamic ODE models without a closed‐form solution. In this model, we fully integrate viral load, medication adherence, drug resistance, pharmacokinetics, baseline covariates and time‐dependent drug efficacy into the data analysis for characterizing long‐term virologic responses. Our method is implemented by a data set from an AIDS clinical study. The results suggest that modeling HIV dynamics and virologic responses with consideration of time‐varying clinical factors as well as baseline characteristics may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to ARV treatment and to help the evaluation of clinical trial design in response to existing therapies.     

RNA-based gene therapy for the treatment and prevention of HIV: from bench to bedside

Gene therapy is considered a feasible approach for the treatment and prevention of HIV/AIDS. Targeting both viral genes and host dependency factors can interfere with the viral lifecycle and prevent viral replication. A number of approaches have been taken to target these genes, including ribozymes, aptamers, and RNAi based therapies. A number of these therapies are now beginning to make their way into clinical trials and providing proof of principle that gene therapy is a safe and realistic option for treating HIV. Here, we focus on those therapies that have progressed along the pipeline to preclinical and clinical testing.     

Comparison of Linear,Nonlinear and Semiparametric Mixed‐effects Models for Estimating HIV Dynamic Parameters

The potency of antiretroviral agents in AIDS clinical trials can be assessed on the basis of an early viral response such as viral decay rate or change in viral load (number of copies of HIV RNA) of the plasma. Linear, parametric nonlinear, and semiparametric nonlinear mixed‐effects models have been proposed to estimate viral decay rates in viral dynamic models. However, before applying these models to clinical data, a critical question that remains to be addressed is whether these models produce coherent estimates of viral decay rates, and if not, which model is appropriate and should be used in practice. In this paper, we applied these models to data from an AIDS clinical trial of potent antiviral treatments and found significant incongruity in the estimated rates of reduction in viral load. Simulation studies indicated that reliable estimates of viral decay rate were obtained by using the parametric and semiparametric nonlinear mixed‐effects models. Our analysis also indicated that the decay rates estimated by using linear mixed‐effects models should be interpreted differently from those estimated by using nonlinear mixed‐effects models. The semiparametric nonlinear mixed‐effects model is preferred to other models because arbitrary data truncation is not needed. Based on real data analysis and simulation studies, we provide guidelines for estimating viral decay rates from clinical data. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling viral and CD4 cellular population dynamics in HIV: approaches to evaluate intervention strategies.

Computational models, such as in epidemiology, provide a powerful tool that can be used to systematically examine an array of dynamic interactions among populations as well as to evaluate altemate disease intervention strategies. The specific objectives in this study were to: a/ examine the interaction of cellular (CD4) and HIV population dynamics and evaluate the impact of the use of combination chemotherapies on viral and CD4 populations (Experiment #1), b/ demonstrate how modelling can be used to evaluate the impact of an intervention (condom use) on reducing the rate of HIV/AIDS (Experiment #2). In this study, we used state transition models and conducted simulation experiments to evaluate various alternatives for the control and/or prevention of HIV/AIDS. The result indicated that combination therapy (double or triple drug therapies) was very effective. The HIV viral population decreased rapidly and remained suppressed for years. On the other hand, the CD4 cell population increased above 400 cells per ml and was maintained above that level for many years. Mono-therapy was not as effective; although the viral load decreased rapidly, it increased to its original levels within a few months. Since condom use is one of the key interventions of HIV/AIDS, we evaluated its use in 25%, 50% and 75% of an adult, sexually active population. Increasing condom use by 50% and 75% above an estimated baseline of 25% reduced the incidence of AIDS by 53% in Blacks, 49% in Hispanics and 43% in Whites. The study shows how a cellular/molecular level model can be incorporated within a macro-epidemiologic systems dynamics model to evaluate a variety of scientific questions such as to see if cellular/molecular level interventions reduce morbidity and mortality rates in HIV.     

Virus-like particles: designing an effective AIDS vaccine

Viruses that infect eukaryotic organisms have the unique characteristic of self-assembling into particles. The mammalian immune system is highly attuned to recognizing and attacking these viral particles following infection. The use of particle-based immunogens, often delivered as live-attenuated viruses, has been an effective vaccination strategy for a variety of viruses. The development of an effective vaccine against the human immunodeficiency virus (HIV) has proven to be a challenge, since HIV infects cells of the immune system causing severe immunodeficiency resulting in the syndrome known as AIDS. In addition, the ability of the virus to adapt to immune pressure and reside in an integrated form in host cells presents hurdles for vaccinologists to overcome. A particle-based vaccine strategy has promise for eliciting high titer, long-lived, immune responses to a diverse number of viral epitopes against different HIV antigens. Live-attenuated viruses are effective at generating both cellular and humoral immune responses. However, while these vaccines stimulate immunity, challenged animals rarely clear the viral infection and the degree of attenuation directly correlates with protection from disease. Further, a live-attenuated vaccine has the potential to revert to a pathogenic form. Alternatively, virus-like particles (VLPs) mimic the viral particle without causing an immunodeficiency disease. VLPs are self-assembling, non-replicating, non-pathogenic particles that are similar in size and conformation to intact virions. A variety of VLPs for lentiviruses are currently in preclinical and clinical trials. This review focuses on our current status of VLP-based AIDS vaccines, regarding issues of purification and immune design for animal and clinical trials.     

Semiparametric functional mapping of quantitative trait loci governing long-term HIV dynamics

MOTIVATION: Functional mapping has proven to be powerful for characterizing quantitative trait loci (QTL) that control complex dynamic traits. More recently, functional mapping has been extended to identify the host QTL responsible for HIV dynamics by incorporating a parametric bi-exponential function for earlier stages of viral load trajectories. However, existing functional mapping cannot be used to map long-term HIV dynamics because no mathematical functions are available for later stages of HIV dynamic changes. RESULTS: We derived a statistical model for functional mapping of dynamic QTL through characterizing HIV load trajectories during a long-term period semiparametrically. The new model was constructed within the maximum likelihood framework and implemented with the EM-simplex algorithm. It allows for the test of differences in the genetic control of short- and long-term HIV dynamics and the characterization of the effects of viral-host genome interaction. Extensive simulation studies have been performed to test the statistical behavior of this model. The new model will provide an important tool for genetic and genomic studies of human complex diseases like HIV/AIDS and their pathological progression. AVAILABILITY: Available on request from the corresponding author.     

Population HIV-1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials

In this paper, we introduce a novel application of hierarchical nonlinear mixed-effect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV-1 dynamics (HIV-1 RNA copies) after initiation of potent antiviral treatments and can also be justified by a biological compartment model for the interaction between HIV and its host cells. This kind of model enjoys both biological interpretability and mathematical simplicity after reparameterization and simplification. A model simplification procedure is proposed and illustrated through examples. We interpret and justify various simplified models based on clinical data taken during different phases of viral dynamics during antiviral treatments. We suggest the hierarchical nonlinear mixed-effect model approach for parameter estimation and other statistical inferences. In the context of an AIDS clinical trial involving patients treated with a combination of potent antiviral agents, we show how the models may be used to draw biologically relevant interpretations from repeated HIV-1 RNA measurements and demonstrate the potential use of the models in clinical decision-making.     

An HIV Epidemic Model Based on Viral Load Dynamics: Value in Assessing Empirical Trends in HIV Virulence and Community Viral Load

Trends in HIV virulence have been monitored since the start of the AIDS pandemic, as studying HIV virulence informs our understanding of HIV epidemiology and pathogenesis. Here, we model changes in HIV virulence as a strictly evolutionary process, using set point viral load (SPVL) as a proxy, to make inferences about empirical SPVL trends from longitudinal HIV cohorts. We develop an agent-based epidemic model based on HIV viral load dynamics. The model contains functions for viral load and transmission, SPVL and disease progression, viral load trajectories in multiple stages of infection, and the heritability of SPVL across transmissions. We find that HIV virulence evolves to an intermediate level that balances infectiousness with longer infected lifespans, resulting in an optimal SPVL∼4.75 log₁₀ viral RNA copies/mL. Adaptive viral evolution may explain observed HIV virulence trends: our model produces SPVL trends with magnitudes that are broadly similar to empirical trends. With regard to variation among studies in empirical SPVL trends, results from our model suggest that variation may be explained by the specific epidemic context, e.g. the mean SPVL of the founding lineage or the age of the epidemic; or improvements in HIV screening and diagnosis that results in sampling biases. We also use our model to examine trends in community viral load, a population-level measure of HIV viral load that is thought to reflect a population''s overall transmission potential. We find that community viral load evolves in association with SPVL, in the absence of prevention programs such as antiretroviral therapy, and that the mean community viral load is not necessarily a strong predictor of HIV incidence.     

A stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients

Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models.     

Replicating viral vectors as HIV vaccines: Summary report from the IAVI-sponsored satellite symposium at the AIDS vaccine 2009 conference

In October 2009, The International AIDS Vaccine Initiative (IAVI) convened a satellite symposium entitled ‘Replicating Viral Vectors for use in AIDS Vaccines’ at the AIDS Vaccine 2009 Conference in Paris. The purpose of the symposium was to gather together researchers, representatives from regulatory agencies, and vaccine developers to discuss issues related to advancement of replication-competent viral vector- based HIV vaccines into clinical trials. The meeting introduced the rationale for accelerating the development of replicating viral vectors for use as AIDS vaccines. It noted that the EMEA recently published draft guidelines that are an important first step in providing guidance for advancing live viral vectors into clinical development. Presentations included case studies and development challenges for viral vector-based vaccine candidates. These product development challenges included cell substrates used for vaccine manufacturing, the testing needed to assess vaccine safety, conducting clinical trials with live vectors, and assessment of vaccination risk versus benefit. More in depth discussion of risk and benefit highlighted the fact that AIDS vaccine efficacy trials must be conducted in the developing world where HIV incidence is greatest and how inequities in global health dramatically influence the political and social environment in developing countries.     

Analysis of relation between virologic responses and immunologic responses, patient's factors in AIDS clinical trials using a semiparametric mixed-effects model

In this article we propose to use a semiparametric mixed-effects model based on an exploratory analysis of clinical trial data for a study of the relation between virologic responses and immunologic markers such as CD4+ and CD8 counts, and host-specific factors in AIDS clinical trials. The regression spline technique, used for inference for parameters in the model, reduces the unknown nonparametric components to parametric functions. It is simple and straightforward to implement the procedures using readily available software, and parameter inference can be developed from standard parametric models. We apply the model and the proposed method to an AIDS clinical study. Our findings indicate that viral load level is positively related to baseline viral load level, negatively related to CD4+ cell counts, but unrelated to CD8 cell counts and patient's age neither.