Bioequivalence and Bioavailability Forum

Dear Helmut,

❝ I’m wondering what we can say about the precision of estimated CV_WR in different replicate designs. [...] Let’s look from how many subjects the value is estimated:

❝ TRTR|RTRT:   20 (100%)

❝ TRR|RTR|RRT: 30 (100%)

❝ TRT|RTR:     15 (50%)

❝ Heretic question: From TRT|RTR the estimate will be less precise (only half of the subjects used) ...

The 50% is only valid if you talk EMA .
Otherwise all the data are used for the fit of a (mixed) model.

Why not use the confidence intervals of the covariance parameter estimates from the fit of a mixed model as precision? Ok, this leaves out the partial replicate design because we are not aware if the σ²_WR is valid from fitting the mixed model, at least in the form of FDA code.

At least we can think in terms of intra-subject contrasts to estimate σ²_WR via an ANOVA with sequence group as the solely effect (as implemented in the FDA progesterone guidance in the framework of scaled ABE). The df for this analysis are n-seq where n is the number of intra-subject contrasts evaluable (=subject/2 in case of design TRT|RTR i.e. the 50% above are again correct).

Thus take formulas given by your own in the early days of this forum for obtaining a confidence interval for σ²_WR and then transformed to CV to obtain a measure of the precision of estimated CV_WR.

Lets go with the numbers of subjects given by you and assume that the estimated CV is obtained always as 20% (statistically only with vanishing probability ):
# R function upper confidence limit of CV - as one liner
CVUCL <- function(alpha=0.05, CV, df){
  sqrt(exp(log(1.0 + CV^2)*df/qchisq(alpha,df))-1)
}
gives
design         n   df  upper CL
TRTR|RTRT     20   18   27.94%
TRR|RTR|RRT   30   27   26.03%
TRT|RTR       15   13   30.07%

BTW: May it be that there is an error in this post in calculating SS-intra from MS-intra? The final result is again correct . That remains me on my old school days: Bad school grade (5) if final result correct but intermediate steps with errors .