01.12.2013  Research article  Ausgabe 1/2013 Open Access
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
 Zeitschrift:
 BMC Medical Research Methodology > Ausgabe 1/2013
Electronic supplementary material
Competing interests
Authors’ contributions
Background
Methods
Viral kinetic model
Statistical model

f is the nonlinear model,

Φ _{ i } is the vector of individual parameters of length p where p is the number of parameters,

e _{ ij } is the residual error assumed to follow a normal distribution with mean 0 and variance σ ^{2},

h is the transformation of the vector of parameters that make them normally distributed,

μ is the vector of fixed effects,

β is the vector of coefficient of the only covariate studied i.e. the difference of effectiveness between PIA and PIB (with T _{ i } = 0 if treatment is PIA and T _{ i } = 1 if treatment is PIB),

η _{ i } is the vector of random effects independent of e _{ i }, and are supposed to be independent, with diagonal variancecovariance matrix $\mathrm{\Omega}=\mathit{diag}\phantom{\rule{0.5em}{0ex}}\left({\omega}_{1}^{2},\dots ,{\omega}_{p}^{2}\right)$.
Parameter values
V
_{
0
}(IU/mL) 
c(day^{1}) 
δ(day^{1}) 
ϵ
 σ (log_{10}IU/mL)  

Fixed effect  2.68 10^{6}
 13.4  0.58  0.999  0.19 
Transformation  lognormal  lognormal  lognormal  logisticnormal   
Interindividual standard deviation (ω)  1.09  0.25  0.25  0.61   
Clinical trial simulation
Parameter estimation
Detection of a difference in antiviral effectiveness
Results
Parameter estimation
All data (n = 7 VL)  ML (n = 7 VL)  ML (n = 5 VL)  

RB (%)  RRMSE (%)  RB (%)  RRMSE (%)  RB (%)  RRMSE (%)  
log_{10}(V
_{
0
}) (IU/mL)  0.1  1.0  0.2  1.0  0.1  1.0 
c (day^{1})  1.0  4.3  0.6  4.1  34.1  78.8 
δ (day^{1})  0.2  3.2  0.8  3.7  0.6  3.7 
log_{10}(1ϵ)  0.1  3.2  0.4  3.1  0.3  3.6 
β
 0.4  8.5  −0.5  8.5  0.4  9.9 
_{ω}
^{2}
_{vo}
 −0.4  18.9  −1.0  19.0  −0.5  19.3 
_{ω}
^{2}
_{c}
 −4.6  31.5  −10.9  32.9  236.6  358.3 
_{ω}
^{2}
_{δ}
 −3.0  19.8  −2.3  24.5  −2.4  24.9 
_{ω}
^{2}
_{ϵ}
 −2.6  32.2  −4.5  32.0  −9.9  36.3 
σ
 −0.03  5.3  −0.7  6.2  −1.3  8.0 
Type I error of the Wald test
Power to detect a difference in antiviral effectiveness
ϵ
^{B}
 0.998  0.995  0.990  0.998  0.995  0.990  0.998  0.995  0.990  

Small sample size  Design*  N = 10 and n = 7  N = 14 and n = 5  N = 10 and n = 5  
n_{tot} = 70  n_{tot} = 70  n_{tot} =50  
Wald test (uncorrected)  62.2  99.8  100  61.8  100  100  55.2  98.8  100  
Wald test (corrected)  44.2  98.4  100  50.4  100  100  35.8  95.8  100  
Wilcoxon test  6.6  11.2  26.8  4.4  15.6  39.0  6.6  11.2  26.8  
Design*  N = 20 and n = 7  N = 28 and n = 5  N = 20 and n = 5  
n_{tot} = 140  n_{tot} = 140  n_{tot} = 100  
Middle sample size  Wald test (uncorrected)  83.4  100  100  86.8  100  100  77.8  100  100 
Wald test (corrected)  69.0  100  100  78.0  100  100  58.8  100  100  
Wilcoxon test  7.0  23.0  50.4  6.8  30.4  64.6  7.0  23.0  50.4  
Large sample size  Design*  N = 30 and n = 7  N = 42 and n = 5  N = 30 and n = 5  
n_{tot} = 210  n_{tot} = 210  n_{tot} = 150  
Wald test (uncorrected)  94.0  100  100  86.8  100  100  89.4  100  100  
Wald test (corrected)  89.2  100  100  82.6  100  100  82.6  100  100  
Wilcoxon test  7.4  31.0  67.0  9.2  43.8  85.0  7.4  31.0  67.0 