Bioequivalence and Bioavailability Forum • Constraints, algebra, jommetry and such

Constraints, algebra, jommetry and such [RSABE / ABEL]

posted by ElMaestro – Denmark, 2015-03-31 14:16 (3313 d 03:58 ago) – Posting: # 14638
Views: 25,078

Hi Yung-jin,

❝ only to exclude "the period for that subject" or "all periods of that subject"? Which one is more acceptable? latter one? [edit: I mean when doing 90% CI and other stats.. The rest of periods of that subject will still perform NCA. Sorry about this.]

I think you don't have to worry about this. When I say it like I mean the statistics function like R's lm will take care of it.
Mathematically you have a myriad of constraints on effect estimates and in a sense this is what determines degrees of freedom.
For example, if I recall correctly -this is only from the top of my head and I could be somewhat off- when we do the linear model the average of the two "LSMeans" (booh! :-D

) must equal the grand mean, and so forth. There are constraints like for all factors. Also means that you can express the constraints as relationships between estimates of the factor levels across different factors (and that the histogram of residuals must be symmetric in a 222BE study???).
To satisfy these constraints you cannot include subjects from a 222BE study where one period is missing. I believe another way of saying this is that the model matrix cannot be inverted if we try to include such a subject.

This is why the lm, PROC GLM, lmer etc take the appropriate decision for you. These functions or procedures will exclude the subjects that need to be excluded - Those that do not allow estimation of their own treatment effect for both T and R (and note that with a mixed model you can include subjects with a missing period in a 222BE-study - but that is another discussion and has been debated on this forum a few times).

—
Pass or fail!
ElMaestro

Complete thread:

Statistical Analysis section of partial replicate BE study cher0424 2015-01-07 06:39 [RSABE / ABEL]
- Subjects to be considered in partial replicate BE study d_labes 2015-01-07 14:45
  - Subjects to be considered in partial replicate BE study cher0424 2015-01-07 15:35
  - Subjects to be considered in partial replicate BE study cher0424 2015-01-08 06:28
    - Subjects to be considered in partial replicate BE study d_labes 2015-01-08 09:03
      - Subjects to be considered in partial replicate BE study cher0424 2015-01-08 09:51
        
        Subjects to be considered in partial replicate BE study d_labes 2015-01-08 10:27
        
        Subjects in replicate BE study EU/FDA Shuanghe 2015-01-08 11:08
        
        Subjects in replicate BE study EU/FDA cher0424 2015-01-08 13:56
        Subjects in replicate BE study EU/FDA Relaxation 2015-03-02 09:46
        
        Subjects in replicate BE study EU/FDA d_labes 2015-03-02 11:38
        Subjects in replicate BE study EU mittyri 2015-03-19 20:12
  - Subjects to be considered in partial replicate BE study Dr_Dan 2015-01-08 08:59
    - Subjects to be considered in partial replicate BE study d_labes 2015-01-08 09:04
      - Subjects to be considered in partial replicate BE study Astea 2015-03-01 18:12
        
        Subjects to be considered in partial replicate BE study yjlee168 2015-03-01 19:01
        
        Subjects to be considered in partial replicate BE study Astea 2015-03-09 14:43
        
        NCA with bear? yjlee168 2015-03-09 15:24
        
        Bear and null PK parameters mittyri 2015-03-25 09:50
        
        to exclude or not to exclude the subjects with bear? yjlee168 2015-03-28 21:03
        
        to exclude or not to exclude - let the user decide mittyri 2015-03-29 19:04
        
        to exclude or not to exclude - let the user decide yjlee168 2015-03-30 11:28
        
        to exclude or not to exclude - let the user decide ElMaestro 2015-03-30 15:44
        
        to exclude or not to exclude - let the user decide yjlee168 2015-03-31 11:15
        
        Constraints, algebra, jommetry and suchElMaestro 2015-03-31 12:16
        
        Constraints, algebra, jommetry and such yjlee168 2015-03-31 13:13
        
        Constraints, algebra, jommetry and such ElMaestro 2015-03-31 14:26
        
        Constraints, algebra, jommetry and such mittyri 2015-04-01 08:25
        
        Proc GLM, lm() do not auto-exclude subjects d_labes 2015-04-01 09:15
        
        Proc GLM, lm() do not auto-exclude subjects ElMaestro 2015-04-01 16:29