Bioequivalence and Bioavailability Forum

Dear Ram!

❝ … that all biological samples follow normal distribution before or after log transformation of data, in present context PK data.

It’s a common consensus that some metrics follow a normal distribution (untransformed data, additive model), e.g., A_e (amount excreted), whilst others follow a log-normal distribution (multiplicative model), e.g., AUC, C_max,…
Due to the sampling schedule the theoretical continous metric t_max has to be assessed by nonparametric methods (valid for discrete data).

Rationale behind assuming a multiplicative model (i.e., performing the analysis on log-transformed data):

• F = AUC × Clearance / Dose
  
• Propagation of error in bioanalytics (serial dilutions)

Since parametric statistical methods (ANOVA, GLM, t-test, F-test,…) call for normally distributed data, additivity of effects, etc. and some metrics follow a log-distribution, data have to be transformed before analysis.

❝ when I see a statistical report, I won't understand the statistical report after log tranformation of Pk data, like point estimate, CV, ANOVA, p-value, t-test, least square mean (LSM) etc.

What are you problems in particular? Maybe the report is not clearly written. Generally PE and the confidence interval should be back-transformed into the linear domain. Example:
Acceptance range [0.80, 1.25] (Napierian log: [-0.2231, +0.2231])
Unity 1.0 (log: 0)
PE [CI] from study's ANOVA on log-data: -0.02314 [-0.1231, +0.07686] Back-transformation:
PE: ℯ^–0.02314 = 0.9771 (or 97.7%)
CI: ℯ^–0.1231 = 0.8841 (88.4%), ℯ^+0.07686 = 1.080 (108%)

❝ can you give me algorithm of calculation of data.

Please refer to this post. As a starter I would recommend Hauschke et al. (2007), Patterson & Jones (2006), and Chow & Liu (2000).

❝ I think it is very difficult question for you to answer

No, not at all…
… but not within even a couple of posts!