## Parallel bears meeting at random in infinity [R for BE/BA]

Dear all, especially dear bears,

since I'm very interested in using R for evaluation of BE studies I had a closer look at the bear code for parallel group studies (code inspection as part of validation ).

If I got it right the code used is (f.i. AUC log-transformed):
lme(lnAUC0t ~ drug, random=~1|subj, data=TotalData, method="REML" )
I am wondering where this code comes from, what this code does an why it works anyhow .

IMHO this model, one (fixed) effect for the treatment and one (random) effect for the subjects must be over-specified. We have only one value for a distinct subject treated with Test or Reference and thus we are not able to separate this uniquely into 2 effects, one part for treatment and one attributed to the subject.

Nevertheless the lme() call produces a result.
Try it out in bear.

If I follow the strange and crude EMA suggestion and use all effects as fixed
lmModel <- lm(lnAUC0t ~ drug + subj, data=TotalData)
with the bear built-in dataset for parallel groups I get the anticipated result:
>summary(lmModel)
Call:
lm(formula = lnAUC0t ~ drug + subj, data = TotalData)

Residuals:
ALL 20 residuals are 0: no residual degrees of freedom! (over-specified!)

Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept)   7.3199         NA      NA       NA
drug2        -0.0622         NA      NA       NA
subj2        -0.5366         NA      NA       NA
[...]
>anova(lmModel)
Analysis of Variance Table

Response: lnAUC0t
Df  Sum Sq  Mean Sq F value Pr(>F)
drug       1 0.00127 0.001270
subj      18 1.17959 0.065533
Residuals  0 0.00000

BTW: I would go for a parallel groups study with exactly 2 groups with the 'simple' t-test (Welch variant as described by Helmut long ago) .
Is anybody out there who knows a generalization of the Welch test to more than 2 groups? Any hint would be very appreciated!
Or could we use pairwise Welch t-tests for that?

Regards,

Detlew