Bioequivalence and Bioavailability Forum

Dear HS

thank you for your concise and elaborate answer and opinion.
As i knew the thread in the PKPD list from 2002 i had expected this to a certain extent .

I agree to you not in all respects. First of all i think 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.

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.

Third: I am not your opinion regarding AIC. Akaikes information criterion
is not only used for model discrimination (with different numbers of model parameters) also this is the commonly known usage.

Below you can find 2 references on usage as outlier test.

Genshiro Kitagawa
On the Use of AIC for the Detection of Outliers
Technometrics, Vol. 21, No. 2 (May, 1979), pp. 193-199

Pynnönen, S. (1992).
Detection of outliers in regression analysis by information criteria.
Proceedings of the University of Vaasa. Discussion Papers 146, 8 p.
http://lipas.uwasa.fi/~sjp/Abstracts/dp146.pdf

Google "outlier AIC" to find many more references.

Based on this one can imagine a method for choosing stepwise the lineare part based on the test if the next included point is an 'outlier' to the linear model.
Begin with a maximum number of points, leave one point (with lowest time) out. IF AIC decreases leave one more out and so on.
This should fulfill your demand on parsimony.

Your formula for AIC in the reply to Ohlbe is only correct for comparing
AICs with the same number of data points n.
From the original definition
  AIC =-2*log likelihood +2*p
we derive
  AIC =n*(ln(2*pi*RSS/n)+1)+2*p    (2)
(http://en.wikipedia.org/wiki/Akaike_information_criterion)
      =n*(ln(2*pi)+1)+n*ln(RSS/n)+2*p
where RSS=residual sum of squares of errors

The first term is only constant if models are compared with same n.
But most references on regression use AIC=n*ln(RSS/n)+2*p.

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

Fourst: Regarding your method of choosing the points i wonder why you choose
5 points. Your criteria
- at least 3 points
- not including tmax, Cmax
- fit with p(r)<0.05
are fulfilled with 3,4,5 and 6 points. The rest is your opinion ('informed' view).
This is the subjectivity factor i meant.
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.

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. )
But for other curves it can make the difference.

Fifth and last comment:
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’

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Edit: References linked. [HS]