Bioequivalence and Bioavailability Forum

Hi Antigoni,

❝ […] I discovered a defect in the calculation of univariate confidence intervals using WNL. I have already contacted Certara, who recognised the issue and shall proceed to relevant update. So, I would not recommend using the linear model 502 for confirmation of steady-state achievement for the time being.

Interesting. How did you discovered that? Using my example data in R:

t <- c(24, 48, 72, 96, 120)
c <- c(18.71, 22.24, 22.44, 25.63, 23.25)
m <- lm(c[3:5] ~ t[3:5]) # use only the last 3
summary(m)

Call:
lm(formula = c[3:5] ~ t[3:5])

Residuals:
      1       2       3
-0.9283  1.8567 -0.9283

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept) 22.15333    6.56431   3.375    0.183
t[3:5]       0.01687    0.06700   0.252    0.843

Residual standard error: 2.274 on 1 degrees of freedom
Multiple R-squared:  0.05966,   Adjusted R-squared:  -0.8807
F-statistic: 0.06344 on 1 and 1 DF,  p-value: 0.8429

anova(m)

Analysis of Variance Table

Response: c[3:5]
          Df Sum Sq Mean Sq F value Pr(>F)
t[3:5]     1 0.3280  0.3280  0.0634 0.8429
Residuals  1 5.1708  5.1708

confint(m, level=0.95)[2, ]
     2.5 %     97.5 %
-0.8343986  0.8681486

In Phoenix/WinNonlin 8.0:

Linear Model 502
Estimate        0.016875
StdError        0.066996687
UnivarCI_Lower -1.0886159
UnivarCI_Upper  1.1223659

Linear Mixed Effects
Estimate    0.016875
StdError    0.066996687
Conf_Level 95
Lower_CI   -0.74019547
Upper_CI    0.77394547

Even in bloody M$-Excel 2000 (!) I got an agreement with R up to the fifth significant digit:

 0.016875
 0.066996687
-0.834394981
 0.868144981