Bioequivalence and Bioavailability Forum

Hi Mohamed Yehia,

❝ What to do if Normality shapiro-wilk test on Ln transformed Auc and cmax are non normal?. Can we proceed using parametric analysis test "Anova"?. As according to my knowledge, we can't use any parametric analysis tests on non normal data.

You don't have much choice in practice, generally.
BE data from human trials are always -as far as I know- analysed using parametric testing (linear model for the effects and residuals, derivation of 90% CI via the model residual, typically an ANOVA on top of all that). You are not even supposed to do a SW-test or similar. Any test for distributional departure will not have impact on the choice of method.

Hi Mohamed,

❝ What to do if Normality shapiro-wilk test on Ln transformed Auc and cmax are non normal?

Given the sample sizes commonly seen in BE, it is very (very!) unlikely that you will see a significant result. See this presentation (slides 5–6).
The problem with Shapiro-Wilk (and any other test for distributional assumptions like Kolmogorov–Smirnov, Anderson–Darling, …) is that they test against a reference probability distribution. If you run two concurrent tests (one against the normal and the other one against the log-normal) you may end up with two nonsignificant results (as in slide 6) – which is contradictory. These tests cannot support you in deciding which distribution fits the data “better”. Hence, you are left out in the rain. Theoretically you could assess the Kullback–Leibler divergence, but I have never seen that in practice.

❝ Can we proceed using parametric analysis test "Anova"?. As according to my knowledge, we can't use any parametric analysis tests on non normal data.

The t-test is pretty robust against deviations from normality. Howver, it is very sensitive against imbalance (hence, in crossovers always use the formula given there and not the simple σ_w√2∕n; in parallel designs with unequal group sizes Sattertwaite’s approximation). However, only the model’s residuals have to be normally distributed. Even for IIDs (assumed in ANOVA) which are non-normal, their difference will be (central limit theorem).

❝ I want any references or guidelines regarding that?

A test for normality should not be performed. Justification of the multiplicative model is based on:

• The basic equation of PK (AUC = F·D∕CL) which – after taking logs – will be transformed into an additive model (as required in ANOVA).
  • Negative concentrations are not possible.
    
  • The distribution of raw data is skewed to the right (see slide 5).
• Serial dilutions in bioanalytics lead to multiplicative errors.

Already stated 25 (‼) years ago in the FDA’s guidance (Section III).

Only in the Japanese Q&A-document (Feb 2012) something is stated:

Q-32  Is logarithmic transformation always necessary? Is it acceptable to carry out logarithmic transformation only if necessary?
(A)     Based on the principle of international harmonization, assessment should be made using logarithmically transformed values. However, when it is not appropriate to conduct an analysis with transformed data, assessment can be made with untransformed data. For example, the assessment can be made using untransformed data if the parameters are normally distributed or transformed data can be used with non-normally distributed data.