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

Abstract

Neumann et al. [1] developed a widely used model for the analysis of hepatitis C virus (HCV) dynamics after the initiation of interferon therapy that assumes 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, leading to changes in drug effectiveness and viral rebounds. To investigate the appropriateness of the constant effectiveness (CE) model [1] for studies involving PEG-IFN, we simulated PEG-IFN treatment, using 294 sets of pharmacokinetic/pharmacodynamic (PK/PD) parameters that span observed ranges and fit the simulated data to the CE model. For most combinations of PK/PD parameters, the fits resulted in an infected cell loss rate, delta, that underestimates the true value used in the simulations and yielded over-estimates of the average effectiveness of PEG-IFN. In the setting of PEG-IFN therapy, the use of the CE model of HCV kinetics has to be reevaluated and the validity of its use depends on the amount of HCV RNA rebound observed between doses.

Figures

Fig. 1

Surrogate viral load data generated assuming PEG-IFN α-2b therapy starting at t = 0. Open circles are the data obtained by numerical simulation of equations (1a,b), (3a,b) and (4) with a 4th-order Runge-Kutta method. Solid lines are the best-fit of the CE model (equation 2) to the data. Note the CE model always predicts a monotonic decrease of HCV RNA. The parameters used to generate the surrogate data in the figure are: (A) ka = 0.19 day−1, EC50 = 0.01 μg/L, ke = 0.3 day−1, n = 1, (B) ka = 2 day−1, EC50 = 0.01 μg/L, ke = 0.8 day−1, n = 1 and (C–D) ka = 2.32 day−1, EC50 = 0.30 μg/L, ke = 0.48 day−1, n = 1 and n = 3, respectively. The other parameters are given in Table 1. The PK parameters used to generate panels (C) and (D) represent average values, while the parameters used to generate panels (A) and (B) represent plausible but less frequently observed values.

Fig. 2

The average of estimated effectiveness, ε^a, obtained by fitting the CE model to the surrogate data plotted against the average of actual effectiveness, εa, used to generate the data. Each point corresponds to the estimate obtained from analyzing one data set. Solid line indicates the ideal situation ε^a=εa. Data points above the line indicate that the average estimates are larger than the actual average effectiveness.

Fig. 3

Estimates of the viral clearance rate, c^ and the infected cell loss rate, δ^, obtained using the CE model. Dashed lines indicate the true values of c (9.9 day−1) and δ (0.32 day−1). The horizontal lines within the boxes denote the medians (c = 10.1 day−1 and δ = 0 day−1, which for δ is the same as the minimal value), while the lines at the bottom and top of the boxes show 25 and 75% quartiles, respectively. The whiskers show the 10 and 90% percentiles. Squares in the boxes denote the estimated averages (c = 13.2 day−1 and δ = 0.04 day−1).