Modeling long-term HIV dynamics and antiretroviral response: effects of drug potency, pharmacokinetics, adherence, and drug resistance

The risk of drug resistance during long-acting antimicrobial therapy

The emergence of drug resistance during antimicrobial therapy is a major global health problem, especially for chronic infections like human immunodeficiency virus, hepatitis B and C, and tuberculosis. Sub-optimal adherence to long-term treatment is an important contributor to resistance risk. New long-acting drugs are being developed for weekly, monthly or less frequent dosing to improve adherence, but may lead to long-term exposure to intermediate drug levels. In this study, we analyse the effect of dosing frequency on the risk of resistance evolving during time-varying drug levels. We find that long-acting therapies can increase, decrease or have little effect on resistance, depending on the source (pre-existing or de novo) and degree of resistance, and rates of drug absorption and clearance. Long-acting therapies with rapid drug absorption, slow clearance and strong wild-type inhibition tend to reduce resistance caused by partially resistant strains in the early stages of treatment even if they do not improve adherence. However, if subpopulations of microbes persist and can reactivate during sub-optimal treatment, longer-acting therapies may substantially increase the resistance risk. Our results show that drug kinetics affect selection for resistance in a complicated manner, and that pathogen-specific models are needed to evaluate the benefits of new long-acting therapies.

Mechanistic Modeling of SARS-CoV-2 and Other Infectious Diseases and the Effects of Therapeutics

Modern viral kinetic modeling and its application to therapeutics is a field that attracted the attention of the medical, pharmaceutical, and modeling communities during the early days of the AIDS epidemic. Its successes led to applications of modeling methods not only to HIV but a plethora of other viruses, such as hepatitis C virus (HCV), hepatitis B virus and cytomegalovirus, which along with HIV cause chronic diseases, and viruses such as influenza, respiratory syncytial virus, West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which generally cause acute infections. Here we first review the historical development of mathematical models to understand HIV and HCV infections and the effects of treatment by fitting the models to clinical data. We then focus on recent efforts and contributions of applying these models towards understanding SARS-CoV-2 infection and highlight outstanding questions where modeling can provide crucial insights and help to optimize nonpharmaceutical and pharmaceutical interventions of the coronavirus disease 2019 (COVID-19) pandemic. The review is written from our personal perspective emphasizing the power of simple target cell limited models that provided important insights and then their evolution into more complex models that captured more of the virology and immunology. To quote Albert Einstein, "Everything should be made as simple as possible, but not simpler," and this idea underlies the modeling we describe below.

Concentration-response model of rilpivirine in a cohort of HIV-1-infected naive and pre-treated patients

BACKGROUND

Rilpivirine is widely prescribed in people living with HIV. Although trough plasma concentrations have been associated with virological response, the drug pharmacodynamics remain incompletely characterized.

OBJECTIVES

To develop the first pharmacodynamic model of rilpivirine in order to establish the rilpivirine concentration-response relationship for future treatment optimization.

METHODS

A retrospective observational study was conducted in patients receiving the once-daily rilpivirine/tenofovir disoproxil fumarate/emtricitabine regimen. Individual rilpivirine trough plasma concentrations over time were predicted using a previous pharmacokinetic model. An established susceptible, infected, recovered model was used to describe HIV dynamics without assuming disease steady-state. Population analysis was performed with MONOLIX 2018 software. Simulations of the viral load evolution as a function of time and rilpivirine trough plasma concentration were performed.

RESULTS

Overall, 60 naive and 39 pre-treated patients were included with a follow-up ranging from 2 to 37 months. The final model adequately described the data and the pharmacodynamic parameters were estimated with a good precision. The population typical value of rilpivirine EC50 was estimated at 65 ng/mL. A higher infection rate constant of CD4 cells for HIV-1 was obtained in pre-treated patients. Consequently, the time to obtain virological suppression was longer in pre-treated than in naive patients.

CONCLUSIONS

The concentration-response relationship of rilpivirine was satisfactorily described for the first time using an original population pharmacodynamic model. Simulations performed using the final model showed that the currently used 50 ng/mL rilpivirine trough plasma concentration efficacy target might need revision upwards, particularly in pre-treated patients.

Dynamic regression with recurrent events

Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same event. Most regression models with recurrent events tacitly assume constant effects of covariates over time, which may not be realistic in practice. To address time-varying effects, we develop a dynamic regression model to target the mean frequency of recurrent events. We propose an estimation procedure which fully exploits observed data. Consistency and weak convergence of the proposed estimator are established. Simulation studies demonstrate that the proposed method works well, and two real data analyses are presented for illustration.

Insight into treatment of HIV infection from viral dynamics models

The odds of living a long and healthy life with HIV infection have dramatically improved with the advent of combination antiretroviral therapy. Along with the early development and clinical trials of these drugs, and new field of research emerged called viral dynamics, which uses mathematical models to interpret and predict the time-course of viral levels during infection and how they are altered by treatment. In this review, we summarize the contributions that virus dynamics models have made to understanding the pathophysiology of infection and to designing effective therapies. This includes studies of the multiphasic decay of viral load when antiretroviral therapy is given, the evolution of drug resistance, the long-term persistence latently infected cells, and the rebound of viremia when drugs are stopped. We additionally discuss new work applying viral dynamics models to new classes of investigational treatment for HIV, including latency-reversing agents and immunotherapy.

Tackling HIV and AIDS: contributions by non-human primate models

During the past three decades, non-human primate (NHP) models have gained an increasing importance in HIV basic and translational research. In contrast to natural host models, infection of macaques with virulent simian or simian-human immunodeficiency viruses (SIV, SHIV) results in a disease that closely resembles HIV infection and AIDS. Although there is no perfect animal model, and each of the available models has its benefits and limitations, carefully designed NHP studies with selection of experimental variables have unraveled important questions of basic pathogenesis and have provided the tools to explore and screen intervention strategies. For example, NHP studies have advanced our understanding of the crucial events during early infection, and have provided proof-of-concept of antiretroviral drug treatment and prevention strategies such as pre-exposure prophylaxis (PrEP) regimes that are increasingly used worldwide, and upon overcoming further barriers of implementation, have the potential to make the next generation AIDS-free. Remaining goals include the pursuit of an effective HIV vaccine, and HIV cure strategies that would allow HIV-infected people to ultimately stop taking antiretroviral drugs. Through a reiterative process with feed-back from results of human studies, NHP models can be further validated and strengthened to advance our scientific knowledge and guide clinical trials.

Impact of disease, drug and patient adherence on the effectiveness of antiviral therapy in pediatric HIV

INTRODUCTION

Maintaining effective antiretroviral treatment for life is a major problem in both resource-limited and resource-rich countries. Despite the progress observed in paediatric antiretroviral therapy, approximately 12% of children still experience treatment failure due to drug resistance, inadequate dosing and poor adherence. We explore the current status of antiretroviral therapy in children with focus on the interaction between disease, drug pharmacokinetics and patient behavior, all of which are strongly interconnected and determine treatment outcome. Areas covered: An overview is provided of the viral characteristics and available drug combinations aimed at the prevention of resistance. In this context, the role of patient adherence is scrutinized. A detailed assessment of factors affecting adherence is presented together with the main strategies to enhance treatment response in children. Expert opinion: Using modeling and simulation, a framework for characterizing the forgiveness of non-adherence for specific antiretroviral drugs in children is proposed in which information on pharmacokinetics, pharmacokinetic-pharmacodynamic relationships and viral dynamics is integrated. This approach represents an opportunity for the simplification of dosing regimens taking into account the interaction between these factors. Based on clinical trial simulation scenarios, we envisage the possibility of assessing the impact of variable adherence to antiretroviral drug combinations in HIV-infected children.

Personalized life expectancy and treatment benefit index of antiretroviral therapy

BACKGROUND

The progression of Human Immunodeficiency Virus (HIV) within host includes typical stages and the Antiretroviral Therapy (ART) is shown to be effective in slowing down this progression. There are great challenges in describing the entire HIV disease progression and evaluating comprehensive effects of ART on life expectancy for HIV infected individuals on ART.

METHODS

We develop a novel summative treatment benefit index (TBI), based on an HIV viral dynamics model and linking the infection and viral production rates to the Weibull function. This index summarizes the integrated effect of ART on the life expectancy (LE) of a patient, and more importantly, can be reconstructed from the individual clinic data.

RESULTS

The proposed model, faithfully mimicking the entire HIV disease progression, enables us to predict life expectancy and trace back the timing of infection. We fit the model to the longitudinal data in a cohort study in China to reconstruct the treatment benefit index, and we describe the dependence of individual life expectancy on key ART treatment specifics including the timing of ART initiation, timing of emergence of drug resistant virus variants and ART adherence.

CONCLUSIONS

We show that combining model predictions with monitored CD4 counts and viral loads can provide critical information about the disease progression, to assist the design of ART regimen for maximizing the treatment benefits.

Models of Viral Population Dynamics

Models of viral population dynamics have contributed enormously to our understanding of the pathogenesis and transmission of several infectious diseases, the coevolutionary dynamics of viruses and their hosts, the mechanisms of action of drugs, and the effectiveness of interventions. In this chapter, we review major advances in the modeling of the population dynamics of the human immunodeficiency virus (HIV) and briefly discuss adaptations to other viruses.

Mixed-Effects Models with Skewed Distributions for Time-Varying Decay Rate in HIV Dynamics

After initiation of treatment, HIV viral load has multiphasic changes, which indicates that the viral decay rate is a time-varying process. Mixed-effects models with different time-varying decay rate functions have been proposed in literature. However, there are two unresolved critical issues: (i) it is not clear which model is more appropriate for practical use, and (ii) the model random errors are commonly assumed to follow a normal distribution, which may be unrealistic and can obscure important features of within- and among-subject variations. Because asymmetry of HIV viral load data is still noticeable even after transformation, it is important to use a more general distribution family that enables the unrealistic normal assumption to be relaxed. We developed skew-elliptical (SE) Bayesian mixed-effects models by considering the model random errors to have an SE distribution. We compared the performance among five SE models that have different time-varying decay rate functions. For each model, we also contrasted the performance under different model random error assumption such as normal, Student-t, skew-normal or skew-t distribution. Two AIDS clinical trial data sets were used to illustrate the proposed models and methods. The results indicate that the model with a time-varying viral decay rate that has two exponential components is preferred. Among the four distribution assumptions, the skew-t and skew-normal models provided better fitting to the data than normal or Student-t model, suggesting that it is important to assume a model with a skewed distribution in order to achieve reasonable results when the data exhibit skewness.

Integrated population pharmacokinetic/viral dynamic modelling of lopinavir/ritonavir in HIV-1 treatment-naïve patients

BACKGROUND

Lopinavir (LPV)/ritonavir (RTV) co-formulation (LPV/RTV) is a widely used protease inhibitor (PI)-based regimen to treat HIV-infection. As with all PIs, the trough concentration (C trough) is a primary determinant of response, but the optimum exposure remains poorly defined. The primary objective was to develop an integrated LPV population pharmacokinetic model to investigate the influence of α-1-acid glycoprotein and link total and free LPV exposure to pharmacodynamic changes in HIV-1 RNA and assess viral dynamic and drug efficacy parameters.

METHODS

Data from 35 treatment-naïve HIV-infected patients initiating therapy with LPV/RTV 400/100 mg orally twice daily across two studies were used for model development and simulations using ADAPT. Total LPV (LPVt) and RTV concentrations were measured by high-performance liquid chromatography with ultraviolet (UV) detection. Free LPV (LPVf) concentrations were measured using equilibrium dialysis and mass spectrometry.

RESULTS

The LPVt typical value of clearance (CLLPVt/F) was 4.73 L/h and the distribution volume (VLPVt/F) was 55.7 L. The clearance (CLLPVf/F) and distribution volume (Vf/F) for LPVf were 596 L/h and 6,370 L, respectively. The virion clearance rate was 0.0350 h(-1). The simulated LPVLPVt C trough values at 90% (EC90) and 95% (EC95) of the maximum response were 316 and 726 ng/mL, respectively.

CONCLUSIONS

The pharmacokinetic-pharmacodynamic model provides a useful tool to quantitatively describe the relationship between LPV/RTV exposure and viral response. This comprehensive modelling and simulation approach could be used as a surrogate assessment of antiretroviral (ARV) activity where adequate early-phase dose-ranging studies are lacking in order to define target trough concentrations and possibly refine dosing recommendations.

Modeling antiretroviral drug responses for HIV-1 infected patients using differential equation models

We review mathematical modeling and related statistical issues of HIV dynamics primarily in response to antiretroviral drug therapy in this article. We start from a basic model of virus infection and then review a number of more advanced models with consideration of pharmacokinetic factors, adherence and drug resistance. Specifically, we illustrate how mathematical models can be developed and parameterized to understand the effects of long-term treatment and different treatment strategies on disease progression. In addition, we discuss a variety of parameter estimation methods for differential equation models that are applicable to either within- or between-host viral dynamics.

A novel pharmacokinetic approach to predict virologic failure in HIV-1-infected paediatric patients

OBJECTIVE

The objective of this study was to develop in children an HIV dynamic model able to predict simultaneously the viral load and CD4 lymphocyte evolutions, and to take into account, through a composite inhibition score, the relative contribution of each drug of the combination efavirenz-didanosine-lamivudine and use this score as a predictor of treatment failure in a multidrug therapy.

DESIGN

Open phase II trial (BURKINAME - ANRS 12103) registered in the ClinicalTrials.gov database (http://clinicaltrials.gov) with the no. NCT00122538.

METHODS

Forty-nine children aged from 2.5 to 15 years were administered once-daily dose of lamivudine, didanosine and efavirenz. The three drugs effect was then characterized by a composite inhibition score combining the effect of each drug, according to their site and mechanism of action and their relative contribution.

RESULTS

Efavirenz was the most potent antiretroviral and was responsible for 65% of the total effect, and then didanosine for 23% and lamivudine was the less potent with 12% of the total observed effect. An EC90 for efavirenz was determined (3.3 mg/l). AUC90 was estimated for lamivudine and didanosine: 8.4 and 1.5 mg h/l, respectively. The composite inhibition score was the best predictor of virologic failure compared with the concentrations of each drug taken independently [hazard ratio (HR) 0.6 per 10% increase, 95% confidence interval (CI) 0.41-0.88].

CONCLUSION

The relative contributions of three combined drugs were assessed on plasma viral load and CD4 lymphocyte count kinetics in HIV-1-infected children. Pharmacokinetics targets have been suggested for lamivudine and didanosine. A composite inhibition score has been determined to be a high predictor of treatment failure in a multidrug therapy.

A model of HIV drug resistance driven by heterogeneities in host immunity and adherence patterns

Background

Population transmission models of antiretroviral therapy (ART) and pre-exposure prophylaxis (PrEP) use simplistic assumptions – typically constant, homogeneous rates – to represent the short-term risk and long-term effects of drug resistance. In contrast, within-host models of drug resistance allow for more detailed dynamics of host immunity, latent reservoirs of virus, and drug PK/PD. Bridging these two levels of modeling detail requires an understanding of the “levers” – model parameters or combinations thereof – that change only one independent observable at a time. Using the example of accidental tenofovir-based pre-exposure prophyaxis (PrEP) use during HIV infection, we will explore methods of implementing host heterogeneities and their long-term effects on drug resistance.

Results

We combined and extended existing models of virus dynamics by incorporating pharmacokinetics, pharmacodynamics, and adherence behavior. We identified two “levers” associated with the host immune pressure against the virus, which can be used to independently modify the setpoint viral load and the shape of the acute phase viral load peak. We propose parameter relationships that can explain differences in acute and setpoint viral load among hosts, and demonstrate their influence on the rates of emergence and reversion of drug resistance. The importance of these dynamics is illustrated by modeling long-lived latent reservoirs of virus, through which past intervals of drug resistance can lead to failure of suppressive drug regimens. Finally, we analyze assumptions about temporal patterns of drug adherence and their impact on resistance dynamics, finding that with the same overall level of adherence, the dwell times in drug-adherent versus not-adherent states can alter the levels of drug-resistant virus incorporated into latent reservoirs.

Conclusions

We have shown how a diverse range of observable viral load trajectories can be produced from a basic model of virus dynamics using immunity-related “levers”. Immune pressure, in turn, influences the dynamics of drug resistance, with increased immune activity delaying drug resistance and driving more rapid return to dominance of drug-susceptible virus after drug cessation. Both immune pressure and patterns of drug adherence influence the long-term risk of drug resistance. In the case of accidental PrEP use during infection, rapid transitions between adherence states and/or weak immunity fortifies the “memory” of previous PrEP exposure, increasing the risk of future drug resistance. This model framework provides a means for analyzing individual-level risks of drug resistance and implementing heterogeneities among hosts, thereby achieving a crucial prerequisite for improving population-level models of drug resistance.

Impact of pre-therapy viral load on virological response to modern first-line HAART

BACKGROUND

We tested whether pre-HAART viraemia affects the achievement and maintenance of virological success in HIV-1-infected patients starting modern first-line therapies.

METHODS

A total of 1,430 patients starting their first HAART (genotype-tailored) in 2008 (median; IQR: 2006-2009) were grouped according to levels of pre-HAART viraemia (≤ 30,000, 30,001-100,000, 100,001-300,000, 300,001-500,000 and > 500,000 copies/ml). The impact of pre-therapy viraemia on the time to virological success (viraemia ≤ 50 copies/ml) and on the time to virological rebound (first of two consecutive viraemia values > 50 copies/ml after virological success) were evaluated by Kaplan-Meier curves and Cox regression analyses.

RESULTS

Median pre-HAART viraemia was 5.1 log10 copies/ml (IQR 4.5-5.5), and 53% of patients had viraemia > 100,000 copies/ml. By week 48, the prevalence of patients reaching virological success was > 90% in all pre-HAART viraemia ranges, with the only exception of range > 500,000 copies/ml (virological success = 83%; P < 0.001). Higher pre-HAART viraemia was tightly correlated with longer median time to achieve virological success. Cox multivariable estimates confirmed this result: patients with pre-HAART viraemia > 500,000 copies/ml showed the lowest hazard of virological undetectability after adjusting for age, gender, pre-HAART CD4+ T-cell count, transmitted drug resistance, calendar year and third drug administered (adjusted hazard ratio [95% CI]: 0.27 [0.21, 0.35]; P < 0.001). Pre-HAART viraemia > 500,000 copies/ml was also associated with higher probability of virological rebound compared with patients belonging to lower viraemia strata at weeks 4, 12 and 24 (P = 0.050).

CONCLUSIONS

At the time of modern HAART, and even though an average > 90% of virological success, high pre-HAART viraemia remains an independent factor associated with delayed and decreased virological success. Patients starting HAART with > 500,000 copies/ml represent a significant population that may deserve special attention.

Antiretroviral dynamics determines HIV evolution and predicts therapy outcome

Despite the high inhibition of viral replication achieved by current anti-HIV drugs, many patients fail treatment, often with emergence of drug-resistant virus. Clinical observations show that the relationship between adherence and likelihood of resistance differs dramatically among drug classes. We developed a mathematical model that explains these observations and predicts treatment outcomes. Our model incorporates drug properties, fitness differences between susceptible and resistant strains, mutations and adherence. We show that antiviral activity falls quickly for drugs with sharp dose-response curves and short half-lives, such as boosted protease inhibitors, limiting the time during which resistance can be selected for. We find that poor adherence to such drugs causes treatment failure via growth of susceptible virus, explaining puzzling clinical observations. Furthermore, our model predicts that certain single-pill combination therapies can prevent resistance regardless of patient adherence. Our approach represents a first step for simulating clinical trials of untested anti-HIV regimens and may help in the selection of new drug regimens for investigation.

HIV model parameter estimates from interruption trial data including drug efficacy and reservoir dynamics

Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3-5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients.

The use of nonhuman primate models of HIV infection for the evaluation of antiviral strategies

Several nonhuman primate models are used in HIV/AIDS research. In contrast to natural host models, infection of macaques with virulent simian immunodeficiency virus (SIV) isolates results in a disease (simian AIDS) that closely resembles HIV infection and AIDS. Although there is no perfect animal model, and each of the available models has its limitations, a carefully designed study allows experimental approaches that are not feasible in humans, but that can provide better insights in disease pathogenesis and proof-of-concept of novel intervention strategies. In the early years of the HIV pandemic, nonhuman primate models played a minor role in the development of antiviral strategies. Since then, a better understanding of the disease and the development of better compounds and assays to monitor antiviral effects have increased the usefulness and relevance of these animal models in the preclinical development of HIV vaccines, microbicides, and antiretroviral drugs. Several strategies that were first discovered to have efficacy in nonhuman primate models are now increasingly used in humans. Recent trends include the use of nonhuman primate models to explore strategies that could reduce viral reservoirs and, ultimately, attempt to cure infection. Ongoing comparison of results obtained in nonhuman primate models with those observed in human studies will lead to further validation and improvement of these animal models so they can continue to advance our scientific knowledge and guide clinical trials.

Non-linear mixed effects modeling of antiretroviral drug response after administration of lopinavir, atazanavir and efavirenz containing regimens to treatment-naïve HIV-1 infected patients

The objective of this analysis was to compare three methods of handling HIV-RNA data below the limit of quantification (LOQ) when describing the time-course of antiretroviral drug response using a drug-disease model. Treatment naïve Scandinavian HIV-positive patients (n = 242) were randomized to one of three study arms. Two nucleoside reverse transcriptase inhibitors were administrated in combination with 400/100 mg lopinavir/ritonavir twice daily, 300/100 mg atazanavir/ritonavir once a day or 600 mg efavirenz once a day. The viral response was monitored at screening, baseline and at 1, 2, 3, 4, 12, 24, 48, 96, 120, and 144 weeks after study initiation. Data up to 400 days was fitted using a viral dynamics non-linear mixed effects drug-disease model in NONMEM. HIV-RNA data below LOQ of 50 copies/ml plasma (39%) was omitted, replaced by LOQ/2 or included in the analysis using a likelihood-based method (M3 method). Including data below LOQ using the M3 method substantially improved the model fit. The drug response parameter expressing the fractional inhibition of viral replication was on average (95% CI) estimated to 0.787 (0.721-0.864) for lopinavir and atazanavir treatment arms and 0.868 (0.796-0.923) for the efavirenz containing regimen. At 400 days after treatment initiation 90% (76-100) of the lopinavir and atazanavir treated patients were predicted to have undetectable viral levels and 96% (89-100%) for the efavirenz containing treatment. Including viral data below the LOQ rather than omitting or replacing data provides advantages such as better model predictions and less biased parameter estimates which are of importance when quantifying antiretroviral drug response.

Maximum likelihood estimation of long-term HIV dynamic models and antiviral response

HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation-maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2-ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between-patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.

Cumulative viral load and virologic decay patterns after antiretroviral therapy in HIV-infected subjects influence CD4 recovery and AIDS

BACKGROUND

The impact of viral load (VL) decay and cumulative VL on CD4 recovery and AIDS after highly-active antiretroviral therapy (HAART) is unknown.

METHODS AND FINDINGS

Three virologic kinetic parameters (first year and overall exponential VL decay constants, and first year VL slope) and cumulative VL during HAART were estimated for 2,278 patients who initiated HAART in the U.S. Military HIV Natural History Study. CD4 and VL trajectories were computed using linear and nonlinear Generalized Estimating Equations models. Multivariate Poisson and linear regression models were used to determine associations of VL parameters with CD4 recovery, adjusted for factors known to correlate with immune recovery. Cumulative VL higher than the sample median was independently associated with an increased risk of AIDS (relative risk 2.38, 95% confidence interval 1.56-3.62, p<0.001). Among patients with VL suppression, first year VL decay and slope were independent predictors of early CD4 recovery (p = 0.001) and overall gain (p<0.05). Despite VL suppression, those with slow decay during the first year of HAART as well as during the entire therapy period (overall), in general, gained less CD4 cells compared to the other subjects (133 vs. 195.4 cells/µL; p = 0.001) even after adjusting for potential confounders.

CONCLUSIONS

In a cohort with free access to healthcare, independent of established predictors of AIDS and CD4 recovery during HAART, cumulative VL and virologic decay patterns were associated with AIDS and distinct aspects of CD4 reconstitution.

A DYNAMIC BAYESIAN NONLINEAR MIXED-EFFECTS MODEL OF HIV RESPONSE INCORPORATING MEDICATION ADHERENCE, DRUG RESISTANCE AND COVARIATES()

HIV dynamic studies have contributed significantly to the understanding of HIV pathogenesis and antiviral treatment strategies for AIDS patients. Establishing the relationship of virologic responses with clinical factors and covariates during long-term antiretroviral (ARV) therapy is important to the development of effective treatments. Medication adherence is an important predictor of the effectiveness of ARV treatment, but an appropriate determinant of adherence rate based on medication event monitoring system (MEMS) data is critical to predict virologic outcomes. The primary objective of this paper is to investigate the effects of a number of summary determinants of MEMS adherence rates on virologic response measured repeatedly over time in HIV-infected patients. We developed a mechanism-based differential equation model with consideration of drug adherence, interacted by virus susceptibility to drug and baseline characteristics, to characterize the long-term virologic responses after initiation of therapy. This model fully integrates viral load, MEMS adherence, drug resistance and baseline covariates into the data analysis. In this study we employed the proposed model and associated Bayesian nonlinear mixed-effects modeling approach to assess how to efficiently use the MEMS adherence data for prediction of virologic response, and to evaluate the predicting power of each summary metric of the MEMS adherence rates. In particular, we intend to address the questions: (i) how to summarize the MEMS adherence data for efficient prediction of virologic response after accounting for potential confounding factors such as drug resistance and covariates, and (ii) how to evaluate treatment effect of baseline characteristics interacted with adherence and other clinical factors. The approach is applied to an AIDS clinical trial involving 31 patients who had available data as required for the proposed model. Results demonstrate that the appropriate determinants of MEMS adherence rates are important in order to more efficiently predict virologic response, and investigations of adherence to ARV treatment would benefit from measuring not only adherence rate but also its summary metric assessment. Our study also shows that the mechanism-based dynamic model is powerful and effective to establish a relationship of virologic responses with medication adherence, virus resistance to drug and baseline covariates.

Skew-normal Bayesian nonlinear mixed-effects models with application to AIDS studies

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. Nonlinear mixed-effects (NLME) models have been used for modeling between-subject and within-subject variations in viral load measurements. Mostly, normality of both within-subject random error and random-effects is a routine assumption for NLME models, but it may be unrealistic, obscuring important features of between-subject and within-subject variations, particularly, if the data exhibit skewness. In this paper, we develop a Bayesian approach to NLME models and relax the normality assumption by considering both model random errors and random-effects to have a multivariate skew-normal distribution. The proposed model provides flexibility in capturing a broad range of non-normal behavior and includes normality as a special case. We use a real data set from an AIDS study to illustrate the proposed approach by comparing various candidate models. We find that the model with skew-normality provides better fit to the observed data and the corresponding estimates of parameters are significantly different from those based on the model with normality when skewness is present in the data. These findings suggest that it is very important to assume a model with skew-normal distribution in order to achieve robust and reliable results, in particular, when the data exhibit skewness.

Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error

This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least squares (NLS) estimator is investigated in this study. A numerical algorithm such as the Runge-Kutta method is used to approximate the ODE solution. The asymptotic properties are established for the proposed estimators considering both numerical error and measurement error. The B-spline is used to approximate the time-varying coefficients, and the corresponding asymptotic theories in this case are investigated under the framework of the sieve approach. Our results show that if the maximum step size of the p-order numerical algorithm goes to zero at a rate faster than n(-1/(p∧4)), the numerical error is negligible compared to the measurement error. This result provides a theoretical guidance in selection of the step size for numerical evaluations of ODEs. Moreover, we have shown that the numerical solution-based NLS estimator and the sieve NLS estimator are strongly consistent. The sieve estimator of constant parameters is asymptotically normal with the same asymptotic co-variance as that of the case where the true ODE solution is exactly known, while the estimator of the time-varying parameter has the optimal convergence rate under some regularity conditions. The theoretical results are also developed for the case when the step size of the ODE numerical solver does not go to zero fast enough or the numerical error is comparable to the measurement error. We illustrate our approach with both simulation studies and clinical data on HIV viral dynamics.

Accelerated Recurrence Time Models

For the analysis with recurrent events, we propose a generalization of the accelerated failure time model to allow for evolving covariate effects. These so-called accelerated recurrence time models postulate that time to expected recurrence frequency, upon transformation, is a linear function of covariates with frequency-dependent coefficients. This modeling strategy shares the same spirit as quantile regression. An estimation and inference procedure is developed by generalizing the celebrated Powell's (1984, 1986) estimator for censored quantile regression. Consistency and asymptotic normality of the proposed estimator are established. An algorithm is devised to attain good computational efficiency. Simulations demonstrate that this proposal performs well under practical settings. This methodology is illustrated in an application to the well-known bladder cancer study.

Quantifying the treatment efficacy of reverse transcriptase inhibitors: new analyses of clinical data based on within-host modeling

Background

Current measures of the clinical efficacy of antiretroviral therapy (ART) in the treatment of HIV include the change in HIV RNA in the plasma and the gain in CD4 cells.

Methods

We propose new measures for evaluating the efficacy of treatment that is based upon combinations of non-nucleoside and nucleoside reverse transcriptase inhibitors. Our efficacy measures are: the CD4 gain per virion eliminated, the potential of CD4 count restoration and the viral reproduction number (R₀). These efficacy measures are based upon a theoretical understanding of the impact of treatment on both viral dynamics and the immune reconstitution. Patient data were obtained from longitudinal HIV clinical cohorts.

Results

We found that the CD4 cell gain per virion eliminated ranged from 10^-2 to 600 CD4 cells/virion, the potential of CD4 count restoration ranged from 60 to 1520 CD4 cells/μl, and the basic reproduction number was reduced from an average of 5.1 before therapy to an average of 1.2 after one year of therapy. There was substantial heterogeneity in these efficacy measures among patients with detectable viral replication. We found that many patients who achieved viral suppression did not have high CD4 cell recovery profiles. Our efficacy measures also enabled us to identify a subgroup of patients who were not virally suppressed but had the potential to reach a high CD4 count and/or achieve viral suppression if they had been switched to a more potent regimen.

Conclusion

We show that our new efficacy measures are useful for analyzing the long-term treatment efficacy of combination reverse transcriptase inhibitors and argue that achieving a low R₀ does not imply achieving viral suppression.

Evaluation of antiretrovirals in animal models of HIV infection

Animal models of HIV infection have played an important role in the development of antiretroviral drugs. Although each animal model has its limitations and never completely mimics HIV infection of humans, a carefully designed study allows experimental approaches that are not feasible in humans, but that can help to better understand disease pathogenesis and to provide proof-of-concept of novel intervention strategies. While rodent and feline models are useful for initial screening, further testing is best done in non-human primate models, such as simian immunodeficiency virus (SIV) infection of macaques, because they share more similarities with HIV infection of humans. In the early years of the HIV pandemic, non-human primate models played a relatively minor role in the antiretroviral drug development process. Since then, a better understanding of the disease and the development of better drugs and assays to monitor antiviral efficacy have increased the usefulness of the animal models. In particular, non-human primate models have provided proof-of-concept for (i) the benefits of chemoprophylaxis and early treatment, (ii) the preclinical efficacy of novel drugs such as tenofovir, (iii) the virulence and clinical significance of drug-resistant viral mutants, and (iv) the role of antiviral immune responses during drug therapy. Ongoing comparison of results obtained in animal models with those observed in human studies will further validate and improve these animal models so they can continue to help advance our scientific knowledge and to guide clinical trials. This article forms part of a special issue of Antiviral Research marking the 25th anniversary of antiretroviral drug discovery and development, Vol 85, issue 1, 2010.

Modeling HIV persistence, the latent reservoir, and viral blips

HIV-1 eradication from infected individuals has not been achieved with the prolonged use of highly active antiretroviral therapy (HAART). The cellular reservoir for HIV-1 in resting memory CD4(+) T cells remains a major obstacle to viral elimination. The reservoir does not decay significantly over long periods of time but is able to release replication-competent HIV-1 upon cell activation. Residual ongoing viral replication may likely occur in many patients because low levels of virus can be detected in plasma by sensitive assays and transient episodes of viremia, or HIV-1 blips, are often observed in patients even with successful viral suppression for many years. Here we review our current knowledge of the factors contributing to viral persistence, the latent reservoir, and blips, and mathematical models developed to explore them and their relationships. We show how mathematical modeling has helped improve our understanding of HIV-1 dynamics in patients on HAART and of the quantitative events underlying HIV-1 latency, reservoir stability, low-level viremic persistence, and emergence of intermittent viral blips. We also discuss treatment implications related to these studies.

Identifying significant covariates for anti-HIV treatment response: mechanism-based differential equation models and empirical semiparametric regression models

In this paper, the mechanism-based ordinary differential equation (ODE) model and the flexible semiparametric regression model are employed to identify the significant covariates for antiretroviral response in AIDS clinical trials. We consider the treatment effect as a function of three factors (or covariates) including pharmacokinetics, drug adherence and susceptibility. Both clinical and simulated data examples are given to illustrate these two different kinds of modeling approaches. We found that the ODE model is more powerful to model the mechanism-based nonlinear relationship between treatment effects and virological response biomarkers. The ODE model is also better in identifying the significant factors for virological response, although it is slightly liberal and there is a trend to include more factors (or covariates) in the model. The semiparametric mixed-effects regression model is very flexible to fit the virological response data, but it is too liberal to identify correct factors for the virological response; sometimes it may miss the correct factors. The ODE model is also biologically justifiable and good for predictions and simulations for various biological scenarios. The limitations of the ODE models include the high cost of computation and the requirement of biological assumptions that sometimes may not be easy to validate. The methodologies reviewed in this paper are also generally applicable to studies of other viruses such as hepatitis B virus or hepatitis C virus.

Estimating drug efficacy and viral dynamic parameters: HIV and HCV

Mathematical models have proven valuable in understanding the in vivo dynamics of human immunodeficiency virus type 1 (HIV-1), the virus that causes AIDS, and hepatitis C virus (HCV), the virus that causes hepatitis C infection. By comparing mathematical models with the data obtained from patients being treated with antiviral drugs, it has been possible to determine many quantitative features of these infections. The most dramatic finding has been that even though AIDS and hepatitis C are diseases that occur on a timescale of one or more decades, there are very rapid dynamical processes that occur on timescales of hours to days, as well as slower processes that occur on timescales of weeks to months. We show how dynamical modeling and parameter estimation techniques have uncovered these important features of HIV and HCV infection and subsequently impacted the way in which patients are treated with potent antiviral drugs. Published in 2007 by John Wiley & Sons, Ltd.

Optimal timing and duration of induction therapy for HIV-1 infection

The tradeoff between the need to suppress drug-resistant viruses and the problem of treatment toxicity has led to the development of various drug-sparing HIV-1 treatment strategies. Here we use a stochastic simulation model for viral dynamics to investigate how the timing and duration of the induction phase of induction–maintenance therapies might be optimized. Our model suggests that under a variety of biologically plausible conditions, 6–10 mo of induction therapy are needed to achieve durable suppression and maximize the probability of eradicating viruses resistant to the maintenance regimen. For induction regimens of more limited duration, a delayed-induction or -intensification period initiated sometime after the start of maintenance therapy appears to be optimal. The optimal delay length depends on the fitness of resistant viruses and the rate at which target-cell populations recover after therapy is initiated. These observations have implications for both the timing and the kinds of drugs selected for induction–maintenance and therapy-intensification strategies.

Clinicians treating HIV infection must balance the need to suppress viral replication against the harmful side effects and significant cost of antiretroviral therapy. Inadequate therapy often results in the emergence of resistant viruses and treatment failure. These difficulties are especially acute in resource-poor settings, where antiretroviral agents are limited. This has prompted an interest in induction–maintenance (IM) treatment strategies, in which brief intensive therapy is used to reduce host viral levels. Induction is followed by a simplified and more easily tolerated maintenance regimen. IM approaches remain an unproven concept in HIV therapy. We have developed a mathematical model to simulate clinical responses to antiretroviral drug therapy. We account for latent infection, partial drug efficacy, cross-resistance, viral recombination, and other factors. This model accurately reflects expected outcomes under single, double, and standard three-drug antiretroviral therapy. When applied to IM therapy, we find that (1) IM is expected to be successful beyond 3 y under a variety of conditions; (2) short-term induction therapy is optimally started several days to weeks after the start of maintenance; and (3) IM therapy may eradicate some preexisting drug-resistant viral strains from the host. Our simulations may help develop new treatment strategies and optimize future clinical trials.

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.

Modeling HIV infection dynamics: the role of recombination in the development of drug resistance

The benefit of recombination to HIV remains unclear because just as recombination can induce the association of favorable mutations and accelerate the development of multidrug resistance, it can also dissociate favorable combinations of mutations. The confounding influences of mutation, random genetic drift, selection and epistatic interactions between multiple resistance loci render the role of recombination difficult to unravel experimentally. Mathematical models provide valuable insights into the influence of recombination on the genomic diversification of HIV and the development of drug resistance in patients undergoing therapy, capture several recent experimental observations of HIV recombination quantitatively, and set the stage for the establishment of a robust framework for the identification of improved treatment protocols and guidelines for drug development.

Short-term safety and tolerability of a once-daily fixed-dose abacavir-lamivudine combination versus twice-daily dosing of abacavir and lamivudine as separate components: findings from the ALOHA study

STUDY OBJECTIVE

To evaluate the short-term (12 wks) safety and tolerability of a once-daily, fixed-dose abacavir-lamivudine combination versus twice-daily dosing of the separate components, both with background antiretroviral therapy.

DESIGN

Phase IIIB, randomized, open-label, parallel-group, multicenter study.

SETTING

One hundred forty-six human immunodeficiency virus (HIV) clinics.

PATIENTS

Six hundred eighty antiretroviral therapy-naïve patients with HIV type 1 RNA greater than 1000 copies/ml at baseline.

INTERVENTION

Patients were randomly assigned in a 2:1 manner to receive either abacavir 600 mg-lamivudine 300 mg once/day or abacavir 300 mg twice/day and lamivudine 150 mg twice/day. Subjects were stratified based on choice of third or fourth antiretroviral drug (nucleoside reverse transcriptase inhibitor [NRTI], NNRTI, or protease inhibitor), assigned before randomization.

MEASUREMENTS AND MAIN RESULTS

The primary end point was occurrence of grades 2-4 adverse events and serious adverse events; abacavir hypersensitivity reactions were considered serious adverse events. Baseline characteristics were similar between the once-daily (455 patients) and twice-daily (225 patients) groups. The rates of all grades 2-4 adverse events were similar: once-daily 33% (150 patients), twice-daily 31% (69). A slightly larger proportion of patients in the twice-daily group experienced drug-related grades 2-4 adverse events: once-daily 10% (47), twice-daily 16% (36). Rates of all serious adverse events (once-daily 11% [49], twice-daily 10% [22]) and drug-related serious adverse events (once-daily 5% [21], twice-daily 8% [17]) were similar. The rate of suspected abacavir hypersensitivity reaction was 5.3% (once-daily 4.4% [20], twice-daily 7.1% [16]), with a higher rate for the NNRTI stratum of the twice-daily group (8.6% [10]) than in any other stratum (once-daily, NNRTI 4.3% [10]; twice-daily, protease inhibitor 5.6% [6]; once-daily, protease inhibitor 4.6% [10]).

CONCLUSION

In the short-term, the rates of adverse events in the once-daily and twice-daily groups appeared to be similar. The rate of suspected abacavir hypersensitivity reaction in the once-daily group was lower than the rate in the twice-daily group.

Development of a population simulation model for HIV monotherapy virological outcomes using lamivudine

Current highly active antiretroviral therapy (HAART) requires the use of combinations of three drugs to minimize the early emergence of drug-resistant HIV strains. Therefore, long-term monotherapy data with new agents are unavailable. However, the development of computer models for Monte-Carlo-type simulations of antiviral monotherapy, which incorporate HIV infection dynamic distributions from previously studied populations, together with pharmacokinetics and pharmacodynamic parameters of the new agent, could serve as an important tool. The nucleoside lamivudine (3TC) was used as a representative drug to standardize an improved pharmacodynamic and infection dynamic monotherapy model. 3TC plasma concentration versus time profiles was used to drive the cellular accumulation of 3TC-triphosphate (TP) in primary human lymphocytes in the model, over a 16 week period. The fraction of HIV reverse transcription inhibited was calculated using the median inhibitory concentration and intracellular 3TC-TP levels. Virus loads and activated CD4+ T-cell counts were generated for 2,200 theoretical individuals and compared with the outcomes of an actual 3TC monotherapy trial at the same dose. Pharmacokinetic variance alone did not account for the interindividual HIV-load variability. However, selection of appropriate distributions of the various pharmacokinetic and infection dynamics parameters produced a similar range of virus load reductions to actual observations. Therefore, once parameter and variance distributions are standardized, this modelling approach could be helpful in planning clinical trials and predicting the antiviral contribution of each agent in a HAART modality.

Bayesian Experimental Design for Long-Term Longitudinal HIV Dynamic Studies

The study of HIV dynamics is one of the most important developments in recent AIDS research for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. Currently a large number of AIDS clinical trials on HIV dynamics are in development worldwide. However, many design issues that arise from AIDS clinical trials have not been addressed. In this paper, we use a simulation-based approach to deal with design problems in Bayesian hierarchical nonlinear (mixed-effects) models. The underlying model characterizes the long-term viral dynamics with antiretroviral treatment where we directly incorporate drug susceptibility and exposure into a function of treatment efficacy. The Bayesian design method is investigated under the framework of hierarchical Bayesian (mixed-effects) models. We compare a finite number of feasible candidate designs numerically, which are currently used in AIDS clinical trials from different perspectives, and provide guidance on how a design might be chosen in practice.

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.

Optimal drug treatment regimens for HIV depend on adherence

Drug therapies aimed at suppressing the human immunodeficiency virus (HIV) are highly effective, often reducing the viral load to below the limits of detection for years. Adherence to such antiviral regimens, however, is typically far from ideal. We have previously developed a model that predicts optimal treatment regimens by weighing drug toxicity against CD4+ T-cell counts, including the probability that drug resistance will emerge. We use this model to investigate the influence of adherence on therapy benefit. For a drug with a given half-life, we compare the effects of varying the dose amount and dose interval for different rates of adherence, and compute the optimal dose regimen for adherence between 65% and 95%. Our results suggest that for optimal treatment benefit, drug regimens should be adjusted for poor adherence, usually by increasing the dose amount and leaving the dose interval fixed. We also find that the benefit of therapy can be surprisingly robust to poor adherence, as long as the dose interval and dose amount are chosen accordingly.

Emergence of HIV-1 Drug Resistance During Antiretroviral Treatment

Treating HIV-infected patients with a combination of several antiretroviral drugs usually contributes to a substantial decline in viral load and an increase in CD4(+) T cells. However, continuing viral replication in the presence of drug therapy can lead to the emergence of drug-resistant virus variants, which subsequently results in incomplete viral suppression and a greater risk of disease progression. In this paper, we use a simple mathematical model to study the mechanism of the emergence of drug resistance during therapy. The model includes two viral strains: wild-type and drug-resistant. The wild-type strain can mutate and become drug-resistant during the process of reverse transcription. The reproductive ratio [Symbol: see text](0) for each strain is obtained and stability results of the steady states are given. We show that drug-resistant virus is more likely to arise when, in the presence of antiretroviral treatment, the reproductive ratios of both strains are close. The wild-type virus can be suppressed even when the reproductive ratio of this strain is greater than 1. A pharmacokinetic model including blood and cell compartments is employed to estimate the drug efficacies of both the wild-type and the drug-resistant strains. We investigate how time-varying drug efficacy (due to the drug dosing schedule and suboptimal adherence) affects the antiviral response, particularly the emergence of drug resistance. Simulation results suggest that perfect adherence to regimen protocol will well suppress the viral load of the wild-type strain while drug-resistant variants develop slowly. However, intermediate levels of adherence may result in the dominance of the drug-resistant virus several months after the initiation of therapy. When more doses of drugs are missed, the failure of suppression of the wild-type virus will be observed, accompanied by a relatively slow increase in the drug-resistant viral load.

Modeling within-host HIV-1 dynamics and the evolution of drug resistance: trade-offs between viral enzyme function and drug susceptibility

There are many biological steps between viral infection of CD4(+) T cells and the production of HIV-1 virions. Here we incorporate an eclipse phase, representing the stage in which infected T cells have not started to produce new virus, into a simple HIV-1 model. Model calculations suggest that the quicker infected T cells progress from the eclipse stage to the productively infected stage, the more likely that a viral strain will persist. Long-term treatment effectiveness of antiretroviral drugs is often hindered by the frequent emergence of drug resistant virus during therapy. We link drug resistance to both the rate of progression of the eclipse phase and the rate of viral production of the resistant strain, and explore how the resistant strain could evolve to maximize its within-host viral fitness. We obtained the optimal progression rate and the optimal viral production rate, which maximize the fitness of a drug resistant strain in the presence of drugs. We show that the window of opportunity for invasion of drug resistant strains is widened for a higher level of drug efficacy provided that the treatment is not potent enough to eradicate both the sensitive and resistant virus.

Design in nonlinear mixed effects models: Optimization using the Fedorov–Wynn algorithm and power of the Wald test for binary covariates

We extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi-exponential model. We first show the relevance of the predicted standard errors (SEs) given by the computation of the population Fisher information matrix using the R function PFIM, in comparison to those computed with the stochastic approximation expectation-maximization algorithm, implemented in the Monolix software. We then highlight the usefulness of the Fedorov-Wynn (FW) algorithm for designs optimization compared to the Simplex algorithm. From the predicted SE of PFIM, we compute the predicted power of the Wald test to detect a treatment effect as well as the number of subjects needed to achieve a given power. Using the FW algorithm, we investigate the influence of the design on the power and show that, for optimized designs with the same total number of samples, the power increases when the number of subjects increases and the number of samples per subject decreases. A simulation study is also performed with the nlme function of R to confirm this result and show the relevance of the predicted powers compared to those observed by simulation.

Density-dependent decay in HIV-1 dynamics

The decay of HIV-1-infected cell populations after treatment with antiretroviral therapy has been measured using simple exponential decay models. These models are unlikely to be realistic over periods longer than a few months, however, because the population dynamics of HIV are complex. We considered an alternate model developed by Perelson and colleagues that extends the standard model for biphasic viral load decline and allows for nonlinear log decay of infected cell populations. Using data from 6 children on highly active antiretroviral therapy (HAART) and a single parameter in the new model, the assumption of log linear decay of infected cell populations is tested. Our analysis indicates that the short-lived and long-lived infected cell populations do not decay according to a simple exponential model. Furthermore, the resulting estimates of time to eradication of infected cell compartments are dramatically longer than those previously reported (eg, decades vs. years for long-lived infected cell populations and years vs. weeks for short-lived infected cell populations). Furthermore, estimates of the second-phase decay rates are significantly different than 0 for most children when obtained using the Perelson biphasic decay model. In contrast, this rate is not significantly different than 0 when the density-dependent decay model is used for parameter estimation and inference. Thus, the density-dependent decay model but not the simple exponential decay model is consistent with recent data showing that even under consistent HAART-mediated suppression of viral replication, decay rates of infected cell reservoirs decay little over several years. This suggests that conclusions about long-term viral dynamics of HIV infection based on simple exponential decay models should be carefully re-evaluated.