Modelling hepatitis C virus kinetics during treatment with pegylated interferon alpha-2b: errors in the estimation of viral kinetic parameters

In-host modeling

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.

Prediction of long-term treatment outcome in HCV following 24 day PEG-IFN alpha-2b therapy using population pharmacokinetic-pharmacodynamic mixture modeling and classification analysis

Mathematical models have been widely used for understanding the dynamics of the hepatitis C virus (HCV). We propose a method to predict final clinical outcome for 24 HIV-HCV - coinfected patients with the help of a mathematical model based on the first two weeks of PEG-IFN therapy. Applying a pharmacokinetic-pharmacodynamic (PKPD) approach, together with mixture models, to the adapted model of viral dynamics developed by Neumann et al., we have analyzed the influence of PEG-IFN on the kinetics and interaction of target cells, infected cells and virus mRNA. It was found that PEG-IFN pharmacokinetic parameters were similar in sustained virological responders and nonresponders, while the plasma PEG-IFN concentration that decreases HCV production by 50% (EC50) and the rate of infected cell death were different. The treatment outcome depended mainly on the initial viral mRNA concentration and the rate of infected cell death. The population PKPD approach with a mixture model enabled the determination of individual PKPD parameters and showed high sensitivity (93.5%) and specificity (97.4%) for the prediction of the treatment outcome.

A hepatitis C virus infection model with time-varying drug effectiveness: solution and analysis

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes of interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time.

Early dynamics of viremia in patients with genotype 1b chronic hepatitis C: Peg-IFNalpha2a shows earlier viral decline than peg-IFNalpha2b in combination therapy with ribavirin

Background

We aimed to assess differences in early viral dynamics following treatment with either peg-IFNα2a or peg-IFNα2b in combination with ribavirin in patients with chronic genotype 1b HCV infection.

Material/Methods

Sixty-one patients in the peg-IFNα2a + ribavirin treatment (group α2a) and 88 patients in the peg-IFNα2b + ribavirin treatment (group α2b) were retrospectively analyzed. The early dynamics of HCV RNA over 12 weeks were evaluated. Sustained virological response (SVR) was defined as undetectable HCV RNA at week 24 after end of therapy. First- (day 0–1) and second-phase (day 1–28) viral decline rates were calculated in accordance with theoretical formulae.

Results

Baseline HCV RNA concentrations were almost similar between the 2 groups. In group α2a, viral decline was significantly greater than in group α2b at weeks 4, 8, and 12. In group α2a, viral decline was significantly greater in SVR patients than in non-SVR patients at week 2, whereas significantly greater viral decline in SVR patients was found during weeks 1–12 in group α2b. The first-phase viral decline rate was significantly larger in group α2a than in group α2b (1.31±0.84 vs. 0.70±0.97 log IU/mL/day; p<0.0001). Within SVR patients, first-phase viral decline rate was significantly larger in group α2a compared with group α2b (1.45±0.85 vs. 0.78±1.0 log IU/mL/day; p<0.0001). Second-phase viral decline rate was comparable between the groups.

Conclusions

Peg-IFNα2a showed earlier viral decline than peg-IFNα2b and the difference was obvious, especially in the first-phase viral decline.

Using time-delayed mutual information to discover and interpret temporal correlation structure in complex populations

This paper addresses how to calculate and interpret the time-delayed mutual information (TDMI) for a complex, diversely and sparsely measured, possibly non-stationary population of time-series of unknown composition and origin. The primary vehicle used for this analysis is a comparison between the time-delayed mutual information averaged over the population and the time-delayed mutual information of an aggregated population (here, aggregation implies the population is conjoined before any statistical estimates are implemented). Through the use of information theoretic tools, a sequence of practically implementable calculations are detailed that allow for the average and aggregate time-delayed mutual information to be interpreted. Moreover, these calculations can also be used to understand the degree of homo or heterogeneity present in the population. To demonstrate that the proposed methods can be used in nearly any situation, the methods are applied and demonstrated on the time series of glucose measurements from two different subpopulations of individuals from the Columbia University Medical Center electronic health record repository, revealing a picture of the composition of the population as well as physiological features.

Hepatitis C virus viral kinetics during α-2a or α-2b pegylated interferon plus ribavirin therapy in liver transplant recipients with different immunosuppression regimes

BACKGROUND

Predictors of sustained virological response (SVR) to antiviral therapy post-liver transplantation (LT) for chronic hepatitis C are needed. In non-transplanted patients, viral kinetics can predict SVR.

OBJECTIVES

To determine the early viral kinetics in LT recipients with different immunosuppression (tacrolimus - Tac- vs. cyclosporine - CsA-) during treatment with peg-IFN+RBV.

STUDY DESIGN

Prospective pilot study in HCV-1b infected patients: (LT CsA n=8; Tac n=8; non-LT n=4), treated with IFN α-2a vs. α-2b (180 μg or 1.5 μg/kg, respectively) once weekly plus weight-based RBV. Median CsA or Tac baseline trough levels were 141 and 7.70 ng/mL, respectively. HCV-RNA was quantified before treatment and after 3, 6, 12h; days 1-6; and weeks 4, 12, 24, 48 and 78 (follow-up).

RESULTS

Different kinetics were observed: early viral load declines with shoulder phase (n=12), delayed monophasic without first phase (n=5, all CsA), and biphasic (n=1) or flat (n=1), without influence of IL28B rs12979860 donor/recipient alleles. In LT, median declines (log(10)UI/mL) at week 4 were -3.62 and -1.49 for Tac vs. CsA; and -2.10 vs.-1.50 for IFN α-2a vs. α-2b (NS), with a trend for faster declines in Tac patients. Generalized additive models suggested a cut-off for predicting response in LT patients of 30 days for Tac, but beyond day 40 for CsA.

CONCLUSION

In LT, the viral kinetics during peg-IFN+RBV treatment is delayed. HCV-RNA at 48 h. may not be predictive of response, and CsA-immunosupressed patients with delayed monophasic declines may potentially achieve ETVR and SVR despite unfavourable or absent early viral load declines.

IL28B genotype effects during early treatment with peginterferon and ribavirin in difficult-to-treat hepatitis C virus infection

BACKGROUND

Mathematical models of hepatitis C virus (HCV) during therapy may elucidate mechanisms of action for antiviral therapy. In genome-wide association studies, IL28B gene polymorphisms are highly predictive of therapeutic clearance of HCV.

METHODS

We collected sera from 20 chronically infected HCV participants at 13 points during the first 28 days of therapy. We assessed the presence of the C allele at single-nucleotide polymorphism rs12979860 using the ABI TaqMan allelic discrimination kit. We estimated dynamic parameters from the entire population using the Neumann model for HCV infection. Statistical methods for repeated nonlinear measures compared model parameters by established predictors of response.

RESULTS

The frequencies of IL28B genotypes were 6 (C/C), 11 (C/T), and 3 (T/T). The mean log decline in HCV RNA from 0 to 48 hours was more rapid among C/C genotype participants compared with C/T or T/T genotype participants (1.4 vs 0.7; P = .07), and from 2 days to 14 days (1.6 vs 0.7; P = .04). In the multivariate model, the C/C genotype predicted a steeper second-phase decline when adjusted for race (P = .01).

CONCLUSIONS

The presence of the C/C genotype at IL28B rs12979860 exerts its antiviral effect by increasing the infected hepatocyte death rate. This suggests that an immune-mediated mechanism is responsible.

A perspective on modelling hepatitis C virus infection

By mathematically describing early hepatitis C virus (HCV) RNA decay after initiation of interferon (IFN)-based antiviral therapy, crucial parameters of the in vivo viral kinetics have been estimated, such as the rate of production and clearance of free virus, and the rate of loss of infected cells. Furthermore, by suggesting mechanisms of action for IFN and ribavirin mathematical modelling has provided a means for evaluating and optimizing treatment strategies. Here, we review recent modelling developments for understanding complex viral kinetics patterns, such as triphasic HCV RNA declines and viral rebounds observed in patients treated with pegylated interferon and ribavirin. Moreover, we discuss new modelling approaches developed to interpret the viral kinetics observed in clinical trials with direct-acting antiviral agents, which induce a rapid decline of wild-type virus but also engender a higher risk for emergence of drug-resistant variants. Lastly, as in vitro systems have allowed a better characterization of the virus lifecycle, we discuss new modelling approaches that combine the intracellular and the extracellular viral dynamics.

Pegylated interferon and ribavirin promote early evolution of nonstructural 5A protein in individuals with hepatitis C who demonstrate a response to treatment

BACKGROUND

Hepatitis C virus (HCV) quasispecies diversity is more likely to affect early viral decline during treatment of hepatitis C than is having human immunodeficiency virus (HIV) infection. We evaluated the influence of HCV therapy on changes in the nonstructural 5A (NS5A) protein.

METHODS

Fifteen patients with HCV genotype 1 infection with or without HIV infection were recruited for the present study, and the decrease in the HCV RNA level was measured at early time points. The evolution of HCV NS5A quasispecies within the first week was analyzed by comparing the clones observed at later times in the study with the baseline consensus sequence of individual patients. The response to therapy was defined as an early response (ER; ie, an HCV RNA level <615 IU/mL at week 4) or a slow response (SR; ie, a detectable HCV RNA level at week 4).

RESULTS

HIV infection did not affect early viral kinetics. At baseline, lower diversity was seen in NS5A and in the amino and carboxyl termini of patients with an ER, compared with those with an SR. Rapid evolution of the NS5A genetic region occurred in patients with an ER (P = .01) but not in those with an SR (P = .73). The evolution was the result of an increase in the number of amino acid substitutions in the carboxyl region (P = .02) in patients with an ER.

CONCLUSIONS

Selective pressure appears to result in more-marked changes in individuals with an ER than in those with an SR. The carboxyl terminus was subject to the most change and may be an important determinant of phenotypic resistance to interferon-based therapy.

Modeling HCV kinetics under therapy using PK and PD information

BACKGROUND

Mathematical models have proven helpful in analyzing the virological response to antiviral therapy in hepatitis C virus (HCV) infected subjects.

OBJECTIVE

To summarize the uses and limitations of different models for analyzing HCV kinetic data under pegylated IFN therapy.

METHODS

We formulate mathematical models and fit them by nonlinear least square regression to patient data to estimate model parameters. We compare the goodness of fit and parameter values estimated by different models statistically.

RESULTS/CONCLUSION

The best model for parameter estimation depends on the availability and the quality of data as well as the therapy used. We also discuss the mathematical models that will be needed to analyze HCV kinetic data from clinical trials with new antiviral drugs.

Modelling of viral dynamics in hepatitis B and hepatitis C clinical trials

In the recent years, studies of hepatitis B (HBV) and hepatitis C virus (HCV) dynamics have drawn great attention as they provide insight into the process of virus elimination/production and of infected cells decay during antiviral treatment. Estimates of viral dynamic parameters may be used to determine the lifetime of HCV/HBV virions and of infected cells, to estimate how long patients need to be treated and to evaluate antiviral therapies. The implementation of viral dynamics studies is difficult because they involve an intensive blood-sampling schedule and subsequent viral load quantification. In the majority of these studies, a model proposed by Neumann et al. (Science 1998; 282:103-107) is used under various assumptions, such as ignoring the delay in initial viral load decay, assuming time-constant treatment efficacy in reducing virion production and/or complete blocking of new infections, etc. However, only recently the effect of some of these assumptions on the estimated parameters has been evaluated. In this paper we provide a detailed review of the model, its underlying assumptions as well as the assumptions usually made by researchers during the design and analysis of viral dynamics studies. Then, we investigate the effect of these assumptions on the estimated parameters using simulations and draw useful conclusions concerning the analysis of these studies. Real data examples from a clinical trial on hepatitis B are provided as illustrations.

A Hepatitis C Viral Kinetic Model that Allows for Time-Varying Drug Effectiveness

Background

The standard model of hepatitis C virus (HCV) dynamics under high-dose daily interferon (IFN) therapy assumed that the drug effectiveness remains constant. However, for treatment with pegylated (PEG)-IFN-α2b dosed weekly, drug levels fall substantially and viral load rebounds have been observed toward the end of the weekly dosing interval, implying non-constant drug efficacy.

Methods

In this paper, we developed the decreasing effectiveness (DE) model, a new mathematical model that allows the drug effectiveness to change with time.

Results

The DE model can describe viral load rebounds as well as other viral kinetic patterns observed in clinical practice, such as biphasic viral declines. We applied the DE model to the HCV RNA kinetic data under PEG-IFN-α2b therapy. The average drug effectiveness during the first week of therapy estimated in the DE model agreed with the one estimated from HCV RNA kinetic data plus pharmacokinetic data.

Conclusions

We illustrated the usefulness of the DE model by analysing HCV RNA data from patients who received PEG-IFN-α2b once weekly plus daily ribavirin.

Modelling the kinetics of hepatitis C virus RNA decline over 4 weeks of treatment with pegylated interferon alpha-2b

Viral kinetic models for hepatitis C virus (HCV) have generally assumed that the effectiveness of therapy in blocking virion production, epsilon, is constant. However, with pegylated interferon alpha-2b (PEG-IFN) given weekly, there are significant changes in drug concentration between doses that may lead to changes in drug effectiveness and viral rebounds towards the end of the dosing interval. Here we investigate the effects of using a model that assumes a constant effectiveness for studies involving PEG-IFN. We simulated PEG-IFN treatment in a population of 294 computer simulated 'patients', each characterized by a different set of pharmacokinetic and pharmacodynamic parameters. We then sampled the simulated treatment data over 4 weeks with a schedule similar to that used in viral kinetic studies, and fitted a viral kinetic model assuming constant drug effectiveness, the CE model, to that data. Although the CE model was able to fit to the data well in most cases, the parameter estimates obtained scattered widely both above and below the true values. Thus, this model is less useful to analyse HCV RNA data during therapy with PEG-IFN than with standard IFN given daily. With PEG-IFN accurate estimation of viral dynamic parameters necessitates concomitant measurements of serum viral load and drug concentration.