Use of a stochastic model to develop understanding of the impact of different patterns of antiretroviral drug use on resistance development

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.

Basic PK/PD principles of drug effects in circular/proliferative systems for disease modelling

Disease progression modelling can provide information about the time course and outcome of pharmacological intervention on the disease. The basic PK/PD principles of proliferative and circular systems within the context of modelling disease progression and the effect of treatment thereupon are illustrated with the goal to better understand/predict eventual clinical outcome. Circular/proliferative systems can be very complex. To facilitate the understanding of how a dosing regimen can be defined in such systems we have shown the derivation of a system parameter named the Reproduction Minimum Inhibitory Concentration (RMIC) which represents the critical concentration at which the system switches from growth to extinction. The RMIC depends on two parameters (RMIC = (R₀ − 1) × IC₅₀): the basic reproductive ratio (R₀) a fundamental parameter of the circular/proliferative system that represents the number of offspring produced by one replicating species during its lifespan, and the IC₅₀, the potency of the drug to inhibit the proliferation of the system. The RMIC is constant for a given system and a given drug and represents the lowest concentration that needs to be achieved for eradication of the system. When exposure is higher than the RMIC, success can be expected in the long term. Time varying inhibition of replicating species proliferation is a natural consequence of the time varying inhibitor drug concentrations and when combined with the dynamics of the circular/proliferative system makes it difficult to predict the eventual outcome. Time varying inhibition of proliferative/circular systems can be handled by calculating the equivalent effective constant concentration (ECC), the constant plasma concentration that would give rise to the average inhibition at steady state. When ECC is higher than the RMIC, eradication of the system can be expected. In addition, it is shown that scenarios that have the same steady state ECC whatever the dose, dosage schedule or PK parameters have also the same average R₀ in the presence of the inhibitor (i.e. R_0-INH) and therefore lead to the same outcome. This allows predicting equivalent active doses and dosing schedules in circular and proliferative systems when the IC₅₀ and pharmacokinetic characteristics of the drugs are known. The results from the simulations performed demonstrate that, for a given system (defined by its RMIC), treatment success depends mainly on the pharmacokinetic characteristics of the drug and the dosing schedule.

Modelling imperfect adherence to HIV induction therapy

Background

Induction-maintenance therapy is a treatment regime where patients are prescribed an intense course of treatment for a short period of time (the induction phase), followed by a simplified long-term regimen (maintenance). Since induction therapy has a significantly higher chance of pill fatigue than maintenance therapy, patients might take drug holidays during this period. Without guidance, patients who choose to stop therapy will each be making individual decisions, with no scientific basis.

Methods

We use mathematical modelling to investigate the effect of imperfect adherence during the inductive phase. We address the following research questions: 1. Can we theoretically determine the maximal length of a possible drug holiday and the minimal number of doses that must subsequently be taken while still avoiding resistance? 2. How many drug holidays can be taken during the induction phase?

Results

For a 180 day therapeutic program, a patient can take several drug holidays, but then has to follow each drug holiday with a strict, but fairly straightforward, drug-taking regimen. Since the results are dependent upon the drug regimen, we calculated the length and number of drug holidays for all fifteen protease-sparing triple-drug cocktails that have been approved by the US Food and Drug Administration.

Conclusions

Induction therapy with partial adherence is tolerable, but the outcome depends on the drug cocktail. Our theoretical predictions are in line with recent results from pilot studies of short-cycle treatment interruption strategies and may be useful in guiding the design of future clinical trials.

The effect of intrinsic stochasticity on transmitted HIV drug resistance patterns

Estimates of transmitted HIV drug-resistance prevalence vary widely among and within epidemiological surveys. Interpretation of trends from available survey data is therefore difficult. Because the emergence of drug-resistance involves small populations of infected drug-resistant individuals, the role of stochasticity (chance events) is likely to be important. The question addressed here is: how much variability in transmitted HIV drug-resistance prevalence patterns arises due to intrinsic stochasticity alone, i.e., if all starting conditions in the different epidemics surveyed were identical? This 'thought experiment' gives insight into the minimum expected variabilities within and among epidemics. A simple stochastic mathematical model was implemented. Our results show that stochasticity alone can generate a significant degree of variability and that this depends on the size and variation of the pool of new infections when drug treatment is first introduced. The variability in transmitted drug-resistance prevalence within an epidemic (i.e., the temporal variability) is large when the annual pool of all new infections is small (fewer than 200, typical of the HIV epidemics in Central European and Scandinavian countries) but diminishes rapidly as that pool grows. Epidemiological surveys involving hundreds of new infections annually are therefore needed to allow meaningful interpretation of temporal trends in transmitted drug-resistance prevalence within individual epidemics. The stochastic variability among epidemics shows a similar dependence on the pool of new infections if treatment is introduced after endemic equilibrium is established, but can persist even when there are more than 10,000 new infections annually if drug therapy is introduced earlier. Stochastic models may therefore have an important role to play in interpreting differences in transmitted drug-resistance prevalence trends among epidemiological surveys.

Stochastic modelling of genotypic drug-resistance for human immunodeficiency virus towards long-term combination therapy optimization

MOTIVATION

Several mathematical models have been investigated for the description of viral dynamics in the human body: HIV-1 infection is a particular and interesting scenario, because the virus attacks cells of the immune system that have a role in the antibody production and its high mutation rate permits to escape both the immune response and, in some cases, the drug pressure. The viral genetic evolution is intrinsically a stochastic process, eventually driven by the drug pressure, dependent on the drug combinations and concentration: in this article the viral genotypic drug resistance onset is the main focus addressed. The theoretical basis is the modelling of HIV-1 population dynamics as a predator-prey system of differential equations with a time-dependent therapy efficacy term, while the viral genome mutation evolution follows a Poisson distribution. The instant probabilities of drug resistance are estimated by means of functions trained from in vitro phenotypes, with a roulette-wheel-based mechanisms of resistant selection. Simulations have been designed for treatments made of one and two drugs as well as for combination antiretroviral therapies. The effect of limited adherence to therapy was also analyzed. Sequential treatment change episodes were also exploited with the aim to evaluate optimal synoptic treatment scenarios.

RESULTS

The stochastic predator-prey modelling usefully predicted long-term virologic outcomes of evolved HIV-1 strains for selected antiretroviral therapy combinations. For a set of widely used combination therapies, results were consistent with findings reported in literature and with estimates coming from analysis on a large retrospective data base (EuResist).

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.

HIV recombination: what is the impact on antiretroviral therapy?

Retroviral recombination is a potential mechanism for the development of multiply drug resistant viral strains but the impact on the clinical outcomes of antiretroviral therapy in HIV-infected patients is unclear. Recombination can favour resistance by combining single-point mutations into a multiply resistant genome but can also hinder resistance by breaking up associations between mutations. Previous analyses, based on population genetic models, have suggested that whether recombination is favoured or hindered depends on the fitness interactions between loci, or epistasis. In this paper, a mathematical model is developed that includes viral dynamics during therapy and shows that population dynamics interact non-trivially with population genetics. The outcome of therapy depends critically on the changes to the frequency of cell co-infection and I review the evidence available. Where recombination does have an effect on therapy, it is always to slow or even halt the emergence of multiply resistant strains. I also find that for patients newly infected with multiply resistant strains, recombination can act to prevent reversion to wild-type virus. The analysis suggests that treatment targeted at multiple parts of the viral life-cycle may be less prone to drug resistance due to the genetic barrier caused by recombination but that, once selected, mutants resistant to such regimens may be better able to persist in the population.

Adherence to antiretroviral therapy and its impact on clinical outcome in HIV-infected patients

We analyse data on patient adherence to prescribed regimens and surrogate markers of clinical outcome for 168 human immunodeficiency virus infected patients treated with antiretroviral therapy. Data on patient adherence consisted of dose-timing measurements collected for an average of 12 months per patient via electronic monitoring of bottle opening events. We first discuss how such data can be presented to highlight suboptimal adherence patterns and between-patient differences, before introducing two novel methods by which such data can be statistically modelled. Correlations between adherence and subsequent measures of viral load and CD4+T-cell counts are then evaluated. We show that summary measures of short-term adherence, which incorporate pharmacokinetic and pharmacodynamic data on the monitored regimen, predict suboptimal trends in viral load and CD4+T-cell counts better than measures based on adherence data alone.

[Clinical use of HIV-1 resistance genotyping. Predictive factors of poor virological evolution in salvage treatments]

OBJECTIVES

To describe the use of genotype resistance testing (GRT) for virological failure in clinical practice, and the long-term clinical and virological evolution in patients for whom it is requested. To identify the predictive factors of virological failure in patients with antiretroviral (ARV) salvage therapy.

METHODS

Observational study in HIV-infected patients for whom GRT was requested for virological failure (VF) in the period of 1 October 1999 to 31 December 2001. Logistic regression analysis was used to determine the predictive factors of virological progression.

RESULTS

Over the period studied, 196 patients required GRT for VF (15%) among those monitored in specific units. GRT was mainly requested for patients who had been extensively pretreated for a mean of 5 years and with a median of 5 ARV combinations. Half the patients presented 3 or more mutations associated with thymidine analogs (TAMs), mutations associated with non-nucleoside analogs (NNRTIs), and 5 or more mutations associated with protease inhibitors (PIs). In 143 (74%) patients, the RTV regimen was changed on the basis of GRT results. In the intent-to-treat analysis, the percentage of patients with plasma VL < 400 cop/mL at 6, 12 and 18 months was 41%, 29% and 17%, respectively. In the on-treatment analysis, the results were 50%, 48% and 46%, respectively. Mean CD4 lymphocyte increase was 59.74 and 94 cells/mm 3. The variables predicting virological failure (plasma VL > 400 cop/mL) at 12 months were plasma VL > 30,000 cop/mL (OR 6, 1.8-19.5) and accumulation of 3 or more TAMs (OR 4.4, 1.3-15) at the start of ARV salvage therapy.

CONCLUSION

Even though in clinical practice GRT is requested for patients with various treatment failures, when ART salvage treatment was started, plasma VL was undetectable and immunological response persisted in 40% of patients followed-up for 18 months. The factors best predicting virological evolution were VL and the number of baseline TAMs.

Adherence to antiretroviral HIV drugs: how many doses can you miss before resistance emerges?

The question of determining how many doses may be skipped before HIV treatment response is adversely affected by the emergence of drug-resistance is addressed. Impulsive differential equations are used to develop a prescription to minimize the emergence of drug-resistance for protease-sparing regimens. A threshold for the maximal number of missable doses is determined. If the number of missed doses is below this threshold, then resistance levels are negligible and dissipate quickly, assuming perfect adherence subsequently. If the number of missed doses exceeds this threshold, even for 24h, resistance levels are extremely high and will not dissipate for weeks, even assuming perfect adherence subsequently. After this interruption, the minimum number of successive doses that should be taken is determined. Estimates are provided for all protease-sparing drugs approved by the US Food and Drug Administration. Estimates for the basic reproductive ratios for the wild-type and mutant strains of the virus are also calculated, for a long-term average fractional degree of adherence. There are regions within this fraction of adherence where the outcome is not predictable and may depend on a patient's entire history of drug-taking.

Monte Carlo estimates of natural variation in HIV infection

We describe a Monte Carlo simulation of the within-host dynamics of human immunodeficiency virus 1 (HIV-1). The simulation proceeds at the level of individual T-cells and virions in a small volume of plasma, thus capturing the inherent stochasticity in viral replication, mutation and T-cell infection. When cell lifetimes are distributed exponentially in the Monte Carlo approach, our simulation results are in perfect agreement with the predictions of the corresponding systems of differential equations from the literature. The Monte Carlo model, however, uniquely allows us to estimate the natural variability in important parameters such as the T-cell count, viral load, and the basic reproductive ratio, in both the presence and absence of drug therapy. The simulation also yields the probability that an infection will not become established after exposure to a viral inoculum of a given size. Finally, we extend the Monte Carlo approach to include distributions of cell lifetimes that are less-dispersed than exponential.

A stochastic version of corticosteriod pharmacogenomic model

The purpose of this study was to develop a stochastic version of corticosteriod fifth generation pharmacogenomic model. The Gillespie algorithm was used to generate the independent time courses of the receptor messenger RNA (mRNA). Initial parameters for the stochastic simulation were adapted from the study by Jin et al. The result obtained from the proposed stochastic model showed an overall agreement with the deterministic fifth generation model. This study suggested that because the stochastic model takes into account the "noise" nature of gene regulation, it would have potential application in pharmacogenomic modeling.

Understanding HIV resistance, fitness, replication capacity and compensation: targeting viral fitness as a therapeutic strategy

The increasingly prevalent emergence of drug-resistant virus strains in patients being treated with highly active antiretroviral regimens and the increasing rates of transmission of drug-resistant virus strains have focused attention on the critical need for additional antiretroviral agents with novel mechanisms of action and enhanced potency. Furthermore, novel means of employing highly active antiretroviral therapy are needed to reduce or eliminate the virological treatment failures that currently occur. Over the past several years, evidence has mounted supporting the fact that the emergence of resistant strains is associated with reductions in viral fitness, yielding decreases in plasma virus load in treated patients harbouring resistant populations of the virus. Additional mutations that serve to modify fitness (compensatory mutations) and mutations that impact the viral replication capacity also emerge under the selective pressure of drug treatment, and have both negative and positive effects on virus growth. Fitness is generally accepted to refer to the ability of HIV to replicate in a defined environment and thus is used to describe the viral replication potential in the absence of the drug. Although viral fitness and replication capacity are related in some ways, it is important to recognise that viral fitness is not the same as viral replication capacity. This review will assess the recent literature on antiviral drug resistance, viral fitness and viral replication capacity, and discuss means by which the adaptability of HIV to respond rapidly to antiviral treatment through mutation may be used against it. This would be done by treating patients with an aim to lock the deleterious mutations into the resistant virus genome, resulting in a positive therapeutic outcome despite the presence of resistance to the selecting agents. The review will specifically discuss the literature on nucleoside and non-nucleoside reverse transcriptase inhibitors, protease inhibitors, integrase inhibitors, fusion inhibitors, as well as other biological factors involved in viral fitness.

High prevalence of antiretroviral resistance in treated Ugandans infected with non-subtype B human immunodeficiency virus type 1

This study examined the emergence and prevalence of drug-resistant mutations in reverse transcriptase and protease coding regions in human immunodeficiency virus type 1 (HIV-1)-infected Ugandans treated with antiretroviral drugs (ARV). Genotypic resistance testing was performed on 50 and 16 participants who were enrolled in a cross-sectional and longitudinal observational cohort, respectively. The majority of the 113 HIV-1 PR-RT sequences were classified as subtypes A and D. Drug resistance mutations were prevalent in 52% of ARV-experienced individuals, and 17 of 27 ARV-resistant isolates had three mutations or more in reverse transcriptase. Resistance mutations in protease were less prevalent but only 17 of the 50 patients were receiving a protease inhibitor upon sample collection. Mutations conferring drug resistance were also selected in 3 of 16 participants in the longitudinal cohort, i.e., less than 8 months after the initiation of ARV treatment. Rapid emergence of ARV resistance was associated with poor adherence to treatment regimens, which was related to treatment costs. ARV resistance did, however, appear at a slightly higher prevalence in HIV-1 subtype D (21 of 33) than subtype A (7 of 25) infected individuals. Overall, this observational study suggests that ARV-resistant HIV-1 isolates are emerging rapidly in ARV-treated individual in Uganda and possibly other developing countries.

Competitive fitness of nevirapine-resistant human immunodeficiency virus type 1 mutants

Determining the fitness of drug-resistant human immunodeficiency virus type 1 (HIV-1) strains is necessary for the development of population-based studies of resistance patterns. For this purpose, we have developed a reproducible, systematic assay to determine the competitive fitness of HIV-1 drug-resistant mutants. To demonstrate the applicability of this assay, we tested the fitness of the five most common nevirapine-resistant mutants (103N, 106A, 181C, 188C, and 190A), with mutations in HIV-1 reverse transcriptase (RT), singly and in combination (for a total of 31 variants) in a defined HIV-1 background. For these experiments, the 27 RT variants that produced viable virus were cocultured with wild-type virus without nevirapine. The ratios of the viral species were determined over time by utilization of a quantitative real-time RT-PCR-based assay. These experiments revealed that all of the viable variants were less fit than the wild type and demonstrated that the order of relative fitness of the single mutants tested was as follows: 103N > 181C > 190A > 188C > 106A. This order correlated with the commonality of these mutants as a result of nevirapine monotherapy. These investigations also revealed that, on average, the double mutants were less fit than the single mutants and the triple mutants were less fit than the double mutants. However, the fitness of the single and double mutants was often not predictive of the fitness of the derivative triple mutants, suggesting the presence of complex interactions between the closely aligned residues that confer nevirapine resistance. This complexity was also evident from the observation that all three of the replication-competent quadruple mutants were fitter than most of the triple mutants, and in some cases, even the double mutants. Our data suggest that, in many cases, viral fitness is the determining factor in the evolution of nevirapine-resistant mutants in vivo, that interactions between the residues that confer nevirapine resistance are complex, and that these interactions substantially affect reverse transcriptase structure and/or function.

Can structured treatment interruptions (STIs) be used as a strategy to decrease total drug requirements and toxicity in HIV infection?

Structured treatment interruptions (STIs) are a new strategy under investigation in clinical trials involving a number of different HIV-infected populations. These populations include patients with prolonged HIV RNA suppression who were treated in either seroconversion or later in disease, and patients with virologic failure despite HAART, prior to the initiation of a salvage regimen. The goals of STI vary in each of these groups. Until the results of clinical trials are available, the use of STIs must be considered experimental. There are a number of potential risks, including the loss of a significant number of CD4 cells with the development of opportunistic infections, rebound of HIV RNA, emergence of drug resistance, and reseeding of viral reservoirs. However, STIs also hold the promise for decreasing antiretroviral drug burden and toxicity, and improving quality of life. Given that much of the world's population infected with HIV does not have access to continuous HAART, the development of strategies that could decrease overall drug burden and cost is important. This paper provides an update of the recently published and presented studies on the use of STIs in various populations of HIV-infected patients. In particular, it discusses what is known and unknown about the relative risks and benefits of this approach, and what studies are ongoing. Lastly, it identifies how the use of STIs could decrease drug burden and toxicity in patients receiving therapy.

Theoretical rationale for the use of sequential single-drug antiretroviral therapy for treatment of HIV infection

BACKGROUND

Subpopulations of HIV with mutations associated with resistance to antiretroviral drugs often have reduced replicative capacity, so virus with resistance mutations for all existing and new antiretroviral drugs is likely to be appreciably impaired. Issues of toxicity, quality of life and economics mean that the simultaneous use of all these drugs in combination is unrealistic. We aimed to explore the use of sequential monotherapy regimens using a mathematical model of quasi-species dynamics, to see if these could take advantage of the poor replicative capacity of highly resistant virus.

METHODS

We assume for each of seven drugs that a single mutation is associated with the ability to replicate (effective reproductive ratio, R > 1) in the presence of that drug as monotherapy. Parameters included were drug efficacy, the cost of resistance mutations and the number of new target cells arising daily.

RESULTS

The use of seven drugs in a daily/weekly sequential monotherapy cycle led to substantial viral suppression (in the presence of all resistant viral subpopulations) for a wider range of parameter values than a continuous five-drug regimen. Although on any one day/week there is a viral subpopulation with R > 1 (e.g. that with resistance only to the current drug), this subpopulation does not have time to grow sufficiently during the short period when that drug is being taken.

CONCLUSION

These results provide a rationale for trials of sequential regimens, using as wide a number of drugs with different resistance-associated mutations as possible, as a potential 'resistance-proof' strategy for achieving significant viral load suppression.