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.     

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)     

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.     

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.     

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.     

Rapid human immunodeficiency virus decay in highly active antiretroviral therapy (HAART)-experienced children after starting mega-HAART

Increasing numbers of patients are treated with mega-highly active antiretroviral therapy (HAART), or multiple-combination antiretroviral therapy, in an attempt to overcome the viral resistance that has contributed to treatment failure. Studies of human immunodeficiency virus (HIV) viral dynamics are used to quantify the potency of a given regimen. While mega-HAART is expected to provide potent therapy, its potency among heavily experienced HIV-infected children who have failed previous treatment is untested. HIV dynamics studies performed in children have provided minimal information on viral dynamics during mega-HAART. The present study estimates first- and second-phase viral dynamics in six children on mega-HAART, following failure of combination therapy. The first phase of viral decay was rapid, relative to rates reported in previous pediatric studies (median delta = 0.778d(-1), range = 0.583 to 1.088, half-life 1 [t1(1/2)] = 0.894d), while the second phase revealed results similar to those of previous studies (median mu = 0.026d(-1), range = -0.005 to 0.206, t2(1/2) = 9.316d). This indicates that mega-HAART can provide potent therapy among heavily experienced pediatric patients.     

Design of Viral Dynamic Studies for Efficiently Assessing Potency of Anti‐HIV Therapies in AIDS Clinical Trials

The study of HIV dynamics is one of the most important developments in recent AIDS research. It greatly improves our understanding of the pathogenesis of HIV infection. Recently it has been proposed to use HIV dynamics to evaluate the efficacy of antiviral treatments. Currently a large number of AIDS clinical trials on HIV dynamics are in development worldwide. However, many design issues that arise from HIV dynamic studies have not been addressed. In this paper, we study these problems using intensive Monte Carlo simulations and analytic methods. We evaluate a finite number of feasible candidate designs, which are currently used and proposed in AIDS clinical trials from different perspectives. We compare the viral dynamic marker and classical viral load change markers in terms of power for identifying treatment difference, asymptotic relative efficiency, and sensitivity. Finally we propose some useful suggestions for practitioners based on our results.     

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.     

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.     

Joint Modeling of the Clinical Progression and of the Biomarkers' Dynamics Using a Mechanistic Model

Summary Joint models are used to rigorously explore the relationship between the dynamics of biomarkers and clinical events. In the context of HIV infection, where the multivariate dynamics of HIV‐RNA and CD4 are complex, a mechanistic approach based on a system of nonlinear differential equations naturally takes into account the correlation between the biomarkers. Using data from a randomized clinical trial comparing dual antiretroviral therapy to a single drug regimen, a full maximum likelihood approach is proposed to explore the relationship between the evolution of the biomarkers and the time to a clinical event. The role of each marker as an independent predictor of disease progression is assessed. We show that the joint dynamics of HIV‐RNA and CD4 captures the effect of antiretroviral treatment; the CD4 dynamics alone is found to capture most but not all of the treatment effect.     

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.     

Optimal clinical trial designs for immune-based therapies in persistent viral infections

There is now effective therapy for infection by the Human Immunodeficiency Virus (HIV), but there is no cure. Consequently, antiviral drugs must be administered continuously to suppress viral replication. Recently, a large phase III international immune-based therapy trial was discontinued because it is difficult to measure clinical endpoints while antivirals are administered. Since the immune system has evolved under the selective force of microbial infections, the immune reaction is antiviral. This commentary explores the rationale of using "Diagnostic Treatment Interruptions" of antiviral therapies to determine efficacies of immune-based therapies.     

Joint Inference on HIV Viral Dynamics and Immune Suppression in Presence of Measurement Errors

Summary : In an attempt to provide a tool to assess antiretroviral therapy and to monitor disease progression, this article studies association of human immunodeficiency virus (HIV) viral suppression and immune restoration. The data from a recent acquired immune deficiency syndrome (AIDS) study are used for illustration. We jointly model HIV viral dynamics and time to decrease in CD4/CD8 ratio in the presence of CD4 process with measurement errors, and estimate the model parameters simultaneously via a method based on a Laplace approximation and the commonly used Monte Carlo EM algorithm. The approaches and many of the points presented apply generally.     

Targeting host cofactors to inhibit viral infection

The majority of FDA-approved drugs indicated for the treatment of viral infections are inhibitors of viral proteins, of which the emergence of resistant strains is a major concern. This issue is exacerbated as most developed antiviral therapies are indicated for the treatment of viruses with error-prone replication. These problems may be addressed by the development of drugs that modulate the function of host factors involved in various aspects of a viral life cycle. Targeting host factors uncouples the mutation of a druggable protein gene from the replication and survival selection pressure exerted on a virus. Currently, a host-targeting antiviral (HTA), maraviroc, is approved for the treatment of human immunodeficiency virus (HIV) infection. In addition, several HTAs indicated for the treatment of hepatitis C virus (HCV) or HIV infection are at various stages of clinical evaluation. Targeting host factors is an attractive complement to therapies directly targeting a viral protein because of the expected higher genetic barrier for resistance and an overall increase in the diversity of treatment options. We examine how the integrated roles of emerging host cofactor screening approaches and drug development strategies may advance current treatment options.     

Spontaneous clearance of viral infections by mesoscopic fluctuations

Spontaneous disease extinction can occur due to a rare stochastic fluctuation. We explore this process, both numerically and theoretically, in two minimal models of stochastic viral infection dynamics. We propose a method that reduces the complexity in models of viral infections so that the remaining dynamics can be studied by previously developed techniques for analyzing epidemiological models. Using this technique, we obtain an expression for the infection clearance time as a function of kinetic parameters. We apply our theoretical results to study stochastic infection clearance for specific stages of HIV and HCV dynamics. Our results show that the typical time for stochastic clearance of a viral infection increases exponentially with the size of the population, but infection still can be cleared spontaneously within a reasonable time interval in a certain population of cells. We also show that the clearance time is exponentially sensitive to the viral decay rate and viral infectivity but only linearly dependent on the lifetime of an infected cell. This suggests that if standard drug therapy fails to clear an infection then intensifying therapy by adding a drug that reduces the rate of cell infection rather than immune modulators that hasten infected cell death may be more useful in ultimately clearing remaining pockets of infection.     

Cell and viral regulatory elements enhance the expression and function of a human immunodeficiency virus inhibitory gene.

Regulated expression of recombinant genes in CD4+ cells is an important objective for gene therapy of AIDS, as these cells represent the principal target for viral replication of human immunodeficiency virus (HIV). We report here that specific combinations of CD4 cell-specific and viral regulatory elements can enhance expression of an antiviral gene product. Different viral regulatory elements were incorporated into a previously reported CD4 locus control region to increase the expression of reporter genes in T and monocytic cell lines. The CD4-specific regulatory elements were included to enhance expression in CD4 cells, and viral regulatory regions, including the cytomegalovirus immediate-early (CMV IE) upstream enhancer, which contains the kappa B and Ap1 regulatory elements and a Tat-responsive element of the HIV type 1 long terminal repeat, were used to increase gene expression and modulate its activity in response to viral infection. In transient transfection assays, this vector was 100- to 1,000-fold more active than the original CD4 regulatory elements alone. Expression of an inhibitory form of the Rev protein, Rev M10, was more effective than previously described vectors and protected against productive viral replication in CD4+ peripheral blood mononuclear cells. The combination of CD4 lineage-specific and viral regulatory elements will facilitate the development of more effective antiviral genetic strategies for AIDS.     

Linear and nonlinear mixed-effects models for censored HIV viral loads using normal/independent distributions

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Linear (and nonlinear) mixed-effects models (with modifications to accommodate censoring) are routinely used to analyze this type of data and are based on normality assumptions for the random terms. However, those analyses might not provide robust inference when the normality assumptions are questionable. In this article, we develop a Bayesian framework for censored linear (and nonlinear) models replacing the Gaussian assumptions for the random terms with normal/independent (NI) distributions. The NI is an attractive class of symmetric heavy-tailed densities that includes the normal, Student's-t, slash, and the contaminated normal distributions as special cases. The marginal likelihood is tractable (using approximations for nonlinear models) and can be used to develop Bayesian case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with two HIV AIDS studies on viral loads that were initially analyzed using normal (censored) mixed-effects models, as well as simulations.     

The chemical bases of the various AIDS epidemics: Recreational drugs,anti-viral chemotherapy and malnutrition

In 1981 a new epidemic of about two-dozen heterogeneous diseases began to strike non-randomly growing numbers of male homosexuals and mostly male intravenous drug users in the US and Europe. Assuming immunodeficiency as the common denominator the US Centers for Disease Control (CDC) termed the epidemic, AIDS, for acquired immunodeficiency syndrome. From 1981-1984 leading researchers including those from the CDC proposed that recreational drug use was the cause of AIDS, because of exact correlations and of drug-specific diseases. However, in 1984 US government researchers proposed that a virus, now termed human immunodeficiency virus (HIV), is the cause of the non-random epidemics of the US and Europe but also of a new, sexually random epidemic in Africa. The virus-AIDS hypothesis was instantly accepted, but it is burdened with numerous paradoxes, none of which could be resolved by 2003: Why is there no HIV in most AIDS patients, only antibodies against it? Why would HIV take 10 years from infection to AIDS? Why is AIDS not self-limiting via antiviral immunity? Why is there no vaccine against AIDS? Why is AIDS in the US and Europe not random like other viral epidemics? Why did AIDS not rise and then decline exponentially owing to antiviral immunity like all other viral epidemics? Why is AIDS not contagious? Why would only HIV carriers get AIDS who use either recreational or anti-HIV drugs or are subject to malnutrition? Why is the mortality of HIV-antibody-positives treated with anti-HIV drugs 7–9%, but that of all (mostly untreated) HIV-positives globally is only 1–4%? Here we propose that AIDS is a collection of chemical epidemics, caused by recreational drugs, anti-HIV drugs, and malnutrition. According to this hypothesis AIDS is not contagious, not immunogenic, not treatable by vaccines or antiviral drugs, and HIV is just a passenger virus. The hypothesis explains why AIDS epidemics strike non-randomly if caused by drugs and randomly if caused by malnutrition, why they manifest in drug- and malnutrition-specific diseases, and why they are not self-limiting via anti-viral immunity. The hypothesis predicts AIDS prevention by adequate nutrition and abstaining from drugs, and even cures by treating AIDS diseases with proven medications.