Helmut ★★★ Vienna, Austria, 20070417 17:16 Posting: # 674 Views: 9,677 
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Hi everybody! In this post I wrote: » You never know when rounding will hit you  and don't dare asking the software vendor for the algorithm... OK, it’s getting even worse! According to FDA’s Guidance For parallel designs, the confidence interval for the difference of means in the log scale can be computed using the total betweensubject variance. As in the analysis for replicated designs (section VI. B.1.b), equal variances should not be assumed. (my emphasis)In other words, naïve pooling of variances – as given in this post – is not appropriate (at least with the FDA). Degrees of freedom should be corrected by e.g. the WelchSatterthwaiteApproximation, and the confidence interval calculated accordingly. Therefore df=21.431 (M$Excel rounds down to the nearest integer 21) instead of df=22. Below is a comparison of results (90% CI) for period 1 of the example data set, using different software packages (general purpose statistics, and ‘spezialized’ packages for PK/BE). ┌────────────────────────┬─────────────────┬────────────────┐ For unequal variances in the manual calculation I used the Satterthwaite approximation, R uses the Welch approximation, NCCS: AspinWelch, STATISTICA: MillikenJohnson. WinNonlin, Kinetica, and EquivTest calculate the CI based on the assumption of equal variances (naïve pooling) only, which:
If assumption(s) are violated, the ‘classical’ ttest becomes liberal (i.e., the CI is too tight; patient’s risk is higher than the nominal 5%). Whereas for equal group sizes this inflation of the αrisk may be small, the more imbalanced a study gets the more liberal the test becomes. As an example I multiplied AUCvalues of subjects 46 (test) by three, and removed subjects 2224 (test). Now we have an imbalanced data set (N_{test}: 9, N_{reference}: 12) with unequal variances (test: 0.564, ref: 0.129; Fratio test p 0.0272, modified Levene test p 0.107). equal variances: 81.21%  190.41% Nothing about the methods used is documented in the ‘specialized’ programs’ manuals and online help. Making things even worse, WinNonlin has an option field for ‘Degrees of Freedom’, where ‘Satterthwaite’ is checked by default. Anyhow, for parallel groups it should be noted, that exactly the same results are obtained as for the other method ‘Residual’! Wang H and SC Chow A practical approach for comparing means of two groups without equal variance assumption Statist Med 21, 3137–51 (2002) online resource Edit: Link corrected for FDA’s new site. [Helmut] — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Helmut ★★★ Vienna, Austria, 20070418 17:05 @ Helmut Posting: # 675 Views: 8,352 

Hi everybody! I prepared some code in R (v2.4.1) to be used with an example data set (actually data from a 2×2 crossover, but only data of period 1 are used). Save the datafile to the bin folder below the main Rapplication (you may use any other location, but then you will have to tell R where to look for it (in R’s GUI: File > Change directory...).
disply < function() { Results should be:
Two Sample ttest Have fun, and don’t trust in commercial software! — Cheers, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 