## Empiric distributions [PK / PD]

❝ this thread gave me an idea (sorry for going a bit off topic now):

That’s perfect

**on**topic!

❝ The whole general use of log transformation is quite unjustified from a biological perspective, but has a lot of appeal from a mathematical perspective in that it rectifies an assumption that must hold for normal dists and which can strictly be said to be violated with untransformed values. But other empirical transformations might have appeal as well.

Yep.

❝ Someone should therefore make an Al Gore Rhythm which could find the 'best' transformation among a set of possible transformations (this would by nature have to be a limited number of known transformations) on a limited number of datasets and see if there's anything useful, like consensus, coming out for whichever parameters are of interest.

Right. \(1/\sqrt{x}\) is a nice one. I think there are different parties out there:

- What the heck are you talking about?

- Not being aware about assumptions and/or stick to what the majority does.

- Don’t test assumptions, although:
*“Sponsors and/or applicants are not encouraged to test for normality of error distribution after log-transformation, nor should they use normality of error distribution as a reason for carrying out the statistical analysis on the original scale. Justification should be provided if sponsors or applicants believe that their BE study data should be statistically analyzed on the original rather than on the log scale.”*(FDA 2001)

- I don’t care. Asymptotics will save me.

- Log-transformation is based on PK grounds. Reasonable for AUC (and C
_{max}?) – but other metrics?

- Log-transform or not (if justified) or even go with a nonparametric method (Japan 2006)

❝ Of course, there's trouble ahead: It might not be easy to define an objective function that gives a clearcut winner.

Yep. Generally the sample size is much too small. Whilst log-transform is a clear winner in the 405 subjects (slide 43) I would not bet on the SW’s in the next slide (12 subjects; p 0.29668 vs. 0.85764). Normality tests are no decision tools

*between*two transformations.

❝ I am myself in uncharted territory here but I would perhaps naïvely start with something like the Shapiro-Wilks statistic or a regression goodness-of-fit statistic from the QQ plot, and then make sure not to compare it between datasets but only within.

What do you mean by

*“only within”*? If we run them on the single studies, power will be too low (see the example above) and inconclusive. That’s why Volker Steinijans looked at the distribution of historical data and defined the method of a particular study

*a priori*. I think that’s the way to go. But: Requires data, data, data.

So here we are – 10 studies on MR methylphenidate formulations (designs 2×2, 6×3, 4×4; 10–60 mg, 12–24 subjects/study, 174 subjects total; t

_{75%}, HVD, MRT

_{t}, C

_{max}/AUC

_{t}):

Tails are amazing. We use a pretty sensitive method; LLOQ <1% of C

_{max}, residual AUC <5%, residual AUMC <15%…

❝ Just another useless idea from ElMaestro... I should perhaps just stick to poetry?!?

Have you tried that before? Far more complicated.

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

- Empiric distributions Helmut 2012-03-21 16:18 [PK / PD]
- nitpicking ElMaestro 2012-03-21 17:32
- nitpicking Helmut 2012-03-22 16:06

- Empiric distributions martin 2012-03-21 21:16
- QQ-Plots Helmut 2012-03-22 01:17
- Transform or not transform d_labes 2012-03-22 09:31
- Transform or not transform Helmut 2012-03-22 13:27

- Transform or not transform d_labes 2012-03-22 09:31

- QQ-Plots Helmut 2012-03-22 01:17
- Empiric distributions ElMaestro 2012-03-22 18:16
- Empiric distributionsHelmut 2012-03-23 01:50

- nitpicking ElMaestro 2012-03-21 17:32