Bioequivalence and Bioavailability Forum

Dear Kevan!

❝ ❝ Run any normality test (Shapiro-Wilk, Anderson-Darling,…) on the intra-subject residuals of both the log-transformed and the untransformed data. If you don't have discordant outliers in the data set I bet that both tests will come up with a nonsignificant result.

❝ You means that i need to find each intra-subject residuals to run the normality test?

❝ How can I identify the outlier in the data set which consist the intra-subject residues?

The statistical model consists of a global mean µ ± effects (treatment, period, sequence,…) + ε.
ε is a the error term (normal distribution) with µ zero and variance σ.
In the general applied model the (unknown) ε is estimated by inter- and intra-subject residuals (in other words, the variability not 'explained' by effects).
In a cross-over design inter-subject variability has no influence on the BE assessment – only intra-subject variability (the higher CV_intra the wider the CI).

If you want to test for normality, intra-subject residuals are the term you should consider (neither the individual PK-responses nor the individual T/R-ratios).

❝ ❝ If it is not appropriate to analyse with transformed data, for example, when untransformed data shows normal distribution but transformed data shows non-normal distribution, you may state as such and use untransformed data for the assessment.

❝ Should I mention above statements in the protocol before start the study?

I guess that no country except Japan will accept such a statement!

❝ Anyway, the study already finished, what can I do now is to mention this phenomenon in report and conclude the treatments is not bioequivalence?

I don't know which country you are aiming at, but you should have stated the planned statistical model/methods in the protocol. You can run any method you like and show results in the report, but anything but log-transformed analyses most likely will not be accepted. I have seen a couple of reports 15+ years ago, where people tried to come up with an argument like this: the sample size is too low to make a clear decision between log-transformed and untransformed data analyses. Therefore the analysis with the narrower CI should be considered the “valid” one. The acceptance by regulatory authorities even at that time was close to zero. Nowadays: no chance.