Bioequivalence and Bioavailability Forum

Dear Kevan!

❝ I faced a problem in calculation of CI of transformed and non-transformed data. The CI of transformed data was outside the accepted range (80-125) while the non-transformed data in the accepted range (80-120).

❝

❝ Most of the guidelines focus on the transformed data.

Right (at least for AUC, C_max,...). The use of the log-transformation is supported by two assumptions:

1. Pharmacokinetics
   Like many biological metrics AUC, C_max,… follow a log-normal distribution: skweded to the right and limited to the left. The definition of AUC = F × D / CL also supports a multiplicative model.
   
2. Bioanalytics
   Serial dilutions in the preparation of stock solutions lead to a multiplicative error model (propagation of uncertainty).

❝ Any statistical method to show that the transformed data is not valid in this case?

I hope you have stated a method in the protocol? It does not make sense to select between log-transformed and untransformed analyses. Give it a try. 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. In other words, you can not select the distribution based on a statistical test given the small sample size in a BE study. Therefore you have to stick with the log-transformed analysis.

The only exception I know comes from Japan (Q&A Document, November 2006, my private translation):

Q-32. Is logarithmic transformation always necessary? Is it not acceptable to carry out logarithmic transformation only when required?
(A) Based on the principle of international harmonisation, assessment should be made using values after logarithmic transformation. 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.

❝ How can I make conclusion for the study?

Your study was not able to demonstrate BE. Sorry.