Bioequivalence and Bioavailability Forum

Dear D. Labes,

thank you for your fruitful comments!
Unfortunately I’ll be out of office until 29 Feb, so just a few comments - I will jump into the details later.
I hope that other members of the forum will make some contributions in the meantime…

❝ […] within the context of BE studies we are not interested in the half life but rather in estimating the AUC part from tlast to infinity.

❝ Half live is only a vehicle to that end.

Definitely.

❝ Second: I have played around with adj. R2 (SAS code from Matos-Pita and Lillo (2005)) and cannot confirm your statement that too many points are included by this method in general. I on the contrary found many cases using the data from Sauter et al. that the method stops too early (starting with 3 points) if these points lie very good on the linear part.

❝ Which is the case especially the case for studies with low variability and 'good natured' concentration time courses.

Yes, but on the other hand if we observe low variability (which occurs rarely enough close to the LLOQ), why should we include more points than necessary to describe lambda_z? OK, the term 'necessary' is quite spongily…

❝ Third: …

I will come up to this point in March. Thanks for the references!

❝ By the way: I cannot verify numerical your results.

I must confess, this was just a quickshot in R. Obviously I made a mistake in coding (not using the correct extractAIC(lm)).

❝ Mine are (SAS Proc Reg, ln C versus time) :

❝ +----------+------------+-------------+------------+-------------+
❝ | n        |      3     |      4      |      5     |      6      |
❝ +----------+------------+-------------+------------+-------------+
❝ | RMSE     | 0.0299805  | 0.03428349  | 0.0285321  | 0.06775109  |
❝ | AIC 1    | -20.339    | -25.757     |  -34.121   |  -30.736    |
❝ | AIC 2    | -11.825    | -11.633     |  -14.439   |  - 5.391    |
❝ +----------+------------+-------------+------------+-------------+

❝ RSS=(RMSE*(n-2))^2

❝ AIC 1: n*ln(RSS/n)+4 (SAS AIC), AIC: full formula

❝

❝ Again 5 points will be chosen.

R (1) and WinNonlin (2) come up with:
+----------+------------+-------------+------------+-------------+
| n        |      3     |      4      |      5     |      6      |
+----------+------------+-------------+------------+-------------+
| AIC (1)  | -20.33909  | -25.75732   | -34.12138  |  -30.73577  |
| AIC (2)  | -17.04325  | -20.21214   | -26.07419  |  -19.98521  |
+----------+------------+-------------+------------+-------------+
... which again would pick 5 points (results from R coincide with SAS').

❝ … i wonder why you 5 points. Your criteria […] are fulfilled with 3,4,5 and 6 points. The rest is your opinion ('informed' view).

❝ This is the subjectivity factor i meant.

Absolutely.

❝ On the other hand i am convinced that man is the best pattern recognizer (at least in 3D ). If trained appropriate and has 'good will'. I have received a number of questions from people doing PK analyses to aid from a statistical view. Especially in cases of not so 'well behaved' concentration time curves.

Fully agree. I'm with you in the desire to establish some kind of statistically sound procedure which at least would support the ‘untrained eye’.

❝ For the presented example i think there is no substantial influence at all as we can see in regarding the lamdaZ. (By the way i think your lamdaZ is t1/2. )

Oops; I just corrected the original table.

❝ But for other curves it can make the difference.

Yes, and these are the nasty ones we have regularly to deal with.

❝ Your emphasis "It is the user's responsibility to evaluate the appropriateness of the estimated value" is totally correct but applies also to

❝ ❝ ‘eyeball-PK’

1. This emphasis was a quote from Pharsight.
   
2. Sure.

It just starts to become interesting; your suggestion of a stepwise procedure lead by AIC looks really promising! I think we should start with a couple of simulations:

• different ‘noise’ (type, degree)
  
• 2-compartment models
  
• &c &c ad libitum…