In this model, emax is patient-specific maximal efficacy, EC50 is the individual 50% effective concentration of IFN, and Nhill is the Hill coefficient representing the second-order sensitivity to changes in IFN levels for blocking production, or the steepness of the e(IFN) saturation curve. Nonlinear fitting was performed using the log-transformed 90% effective IFN concentration (log10[EC90]), which can be derived by:
EC90 was used instead of EC50 since the fits proved to be more sensitive to estimation of an antiviral effect that produces a 1–2-log10 viral decline, as observed in the present and previous studies.11,12
Since e(t) is not constant in time, the ordinary differential equations model (Eq 3–Eq 5) was used, together with the pharmacodynamic equation (Eq 6) and the pharmacokinetic model (Eq 1), for parameter estimation, rather than the analytical solution used in a previous study by Neumann et al.5
Estimation of viral kinetic and pharmacodynamic parameters. Virologic response at Day 28 (Week 4) was defined as a = 2-log10 IU/mL reduction in HCV RNA. First-phase viral decline was defined as maximal decline (log10 IU/mL) during the first 4 days of treatment. A sliding window was used to calculate the second-phase decline (log10 IU/mL/wk) by the means of the log-linear viral decline between Day 4 and Day 18 and between Day 7 and Day 21.
Viral clearance rate was defined as c = 6/d, based on previous results5; this value was verified to be consistent with the first-phase decline in the present study. Initial infected cell and target cell concentrations (I0 and T0, respectively) were calculated based on steady-state conditions and initial viral load, and the parameter ß was set accordingly. The following parameters were set to fixed values, according to the literature5,6,14: p = 10 (virus/cell production rate), d = 0.01 (day–1, target cell death rate), and s = 1e–9 (target cells/day production rate). It was verified that changing these parameters over a number of orders of magnitude did not significantly change the results of the estimates. Finally, emax was fixed to 0.9999, allowing the maximal individual efficacy value observed during treatment, since no need for a limiting factor on effectiveness could be identified.
Using nonlinear regression analysis (Berkeley Madonna), pharmacokinetic data for each patient were fitted and individual profiles were obtained. Based on individual pharmacokinetic parameters, the viral kinetic data for the first 2 weeks (until the second injection) were fitted with the free viral kinetic and pharmacodynamic parameters d, log(EC90), and Nhill, and the model simulation was extrapolated to 28 and 42 days. In most patients, the same parameters were used for the full 42 days; in 8 patients, a change in EC90, Nhill, or both was needed between Day 14 and Day 28 to fit the viral kinetics, or the trend of the extrapolation was different from that observed. In some patients, transient viral rebound on Day 1 or Day 4 was observed, followed by resolution within a few days and continued viral decline over the dosing interval. The current model is not adequate to explain such nonpharmacokinetic-related transient rebounds. These rebounds could be due to variability in assay measurement, since they always involved only 1 HCV-RNA time point or could reflect more complex dynamics. Given the small sample size, testing of the latter hypothesis was not pursued in this study. Therefore, the Jackknife procedure, in which the algorithm performs non-linear fits on the M possible sets of data with 1 of M data-points removed each time and is allowed to select the best fit when none or one of the data points is removed, was used to fit the viral kinetics. In most cases, this procedure resulted in exclusion of the single time point where a transient rebound was observed and allowed an adequate fit of the rest of the data points.
Additional parameters combining pharmacodynamics with pharmacokinetics were also generated: maximal antiviral quotient (MQ), defined as maximal concentration (Cmax)/EC90; inhibitory quotient (IQ), defined as concentration on Day 14 (C[d14]/EC90), reflective of drug level at the end of the dosing interval relative to the effective level for the individual patient, and number of days alb-IFN drug levels remained > EC90 (ie, duration for which e[t] was > 90%).
Statistical analysis. Descriptive statistics were used to summarize the data. Means, medians, and standard deviations were calculated for all pharmacokinetic and pharmacodynamic parameters. Fisher’s exact nonparametric test was used for categorical variables. The nonparametric Mann-Whitney U test was used to test the significance of differences in distribution of continuous pharmacokinetic and pharmacodynamic variables between dose groups and virologic response groups. The nonparametric Spearman test was used to test the significance of correlation between continuous variables. All statistical tests were 2-sided and significance was assumed at P < .05. Results are presented as median (25%, 75%) values.
Pharmacokinetic and viral kinetic parameters. Table 1 shows the baseline characteristics and pharmacokinetic parameters for the 26 patients enrolled in the 900 µg and 1200 µg treatment groups. All patients had a high baseline HCV RNA (> 800,000 IU/mL), with a median value of 7.16 log10 IU/mL.
Table 1. Baseline Patient Characteristics and Pharmacokinetics Parameters Per Dose Arm
Comparably high levels of alb-IFN were maintained during the 14-day dosing intervals in both the 900 µg and 1200 µg groups (Figure 1A). Following the second dose on Day 14, drug was detectable on Day 42 in 96% of patients.
Figure 1. Median serum albinterferon alfa-2b (Alb-IFN) pharmacokinetics (A) and hepatitis C virus (HCV) RNA viral kinetics (B) for the 42-day study duration. Alb-IFN was injected subcutaneously at Day 0 and Day 14. Blue diamonds, 900 µg; red circles, 1200 µg.
The magnitude of HCV-RNA reductions over the study duration was similar between the 900 µg and 1200 µg dose groups (Figure 1 and Table 2). The median HCV-RNA reduction from baseline after 4 weeks of treatment in all patients combined was 3.03 log10 IU/mL (25%, 75% quartiles: 1.56, 4.36). Virologic response (= 2-log10 viral load decline from baseline) was observed in 69% (n = 18) of patients at both Day 28 and Day 42. Modeling of the HCV-RNA decline showed comparable biphasic responses in the 2 dose groups. In all patients, the median first-phase HCV-RNA decline was 1.68 log10 IU/mL and the second-phase slope of viral decline was 0.48 log10 IU/mL/wk (Table 2).
Table 2. Summary of Viral Kinetic and Pharmacodynamic Parameters*