Clinical trial simulation to evaluate power to compare the antiviral effectiveness of two hepatitis C protease inhibitors using nonlinear mixed effect models: a viral kinetic approach

Abstract

Background: Models of hepatitis C virus (HCV) kinetics are increasingly used to estimate and to compare in vivo drug's antiviral effectiveness of new potent anti-HCV agents. Viral kinetic parameters can be estimated using non-linear mixed effect models (NLMEM). Here we aimed to evaluate the performance of this approach to precisely estimate the parameters and to evaluate the type I errors and the power of the Wald test to compare the antiviral effectiveness between two treatment groups when data are sparse and/or a large proportion of viral load (VL) are below the limit of detection (BLD).

Methods: We performed a clinical trial simulation assuming two treatment groups with different levels of antiviral effectiveness. We evaluated the precision and the accuracy of parameter estimates obtained on 500 replication of this trial using the stochastic approximation expectation-approximation algorithm which appropriately handles BLD data. Next we evaluated the type I error and the power of the Wald test to assess a difference of antiviral effectiveness between the two groups. Standard error of the parameters and Wald test property were evaluated according to the number of patients, the number of samples per patient and the expected difference in antiviral effectiveness.

Results: NLMEM provided precise and accurate estimates for both the fixed effects and the inter-individual variance parameters even with sparse data and large proportion of BLD data. However Wald test with small number of patients and lack of information due to BLD resulted in an inflation of the type I error as compared to the results obtained when no limit of detection of VL was considered. The corrected power of the test was very high and largely outperformed what can be obtained with empirical comparison of the mean VL decline using Wilcoxon test.

Conclusion: This simulation study shows the benefit of viral kinetic models analyzed with NLMEM over empirical approaches used in most clinical studies. When designing a viral kinetic study, our results indicate that the enrollment of a large number of patients is to be preferred to small population sample with frequent assessments of VL.

Figures

Figure 1

Time course of log10 HCV RNA after treatment initiation for one simulated dataset with one design (N = 30 patients per PI and n = 7 viral load measurements). A: assuming ϵ = 0.999; B1: assuming ϵ = 0.998; B2: assuming ϵ = 0.995; B3: assuming ϵ = 0.990. In bold, the mean curves predicted by the mean parameters of the model. LOD: limit of detection = log10(12) ≈ 1.08 log10 UI/mL; % < LOD: percentage of patients bellow the LOD at day 3, 7 and 14 estimated from 500 simulated datasets. The mean 14 days log drop were 6.56 log10 IU/mL with ϵ = 0.999, 6.25 log10 IU/mL with ϵ = 0.998, 5.85 log10 IU/mL with ϵ = 0.995 and 5.52 log10 IU/mL with ϵ = 0.990.

Figure 2

Boxplot of the relative estimation errors (REE) of the estimated parameters evaluated from 500 simulated datasets. Parameters were simulated assuming ϵA = 0.999, a limit of detection (“ML data”) and ϵB = 0.990 (β = 2.3), with N = 30 patients per PI and with n = 7 viral load (VL) measurements (in white) or n = 5 VL (sparse initial design in gray). On the left: fixed effects and on the right: inter-individual variances (ω²) and residual error (σ).

Figure 3

Evolution of the type I error of the Wald test according to the study design. Assuming ϵA = ϵB = 0.999, no limit of detection (“All data”, red line) or a limit of detection at 12 IU/mL (“ML”, blue line). N: number of patients per group of treatment; n: number of viral load measurements per patient; ntot: total numbers of observations per group of treatment.