Bioequivalence and Bioavailability Forum • Not understood

Not understood [🇷 for BE/BA]

posted by PharmCat – Russia, 2020-08-05 18:37 (1531 d 19:26 ago) – Posting: # 21825
Views: 16,231
(edited on 2020-08-06 00:34)

Hello!

❝ Sounds neat, will check if I can somehow do such a thing.

I found Lindstrom&Bates, equation 3.4 or J. GURKA, 2006, equation 5.

Some experiment:

m = matrix(c(5, 1, 0, 0, 1, 2, 0, 0, 0, 0, 5, 3, 0, 0, 3, 4), nrow = 4, ncol = 4)

m

     [,1] [,2] [,3] [,4]


[1,]    5    1    0    0

[2,]    1    2    0    0

[3,]    0    0    5    3

[4,]    0    0    3    4

log(det(m))

[1] 4.59512

log(det(m[1:2, 1:2])) + log(det(m[3:4, 3:4]))

[1] 4.59512

solve(m)

           [,1]       [,2]       [,3]       [,4]


[1,]  0.2222222 -0.1111111  0.0000000  0.0000000

[2,] -0.1111111  0.5555556  0.0000000  0.0000000

[3,]  0.0000000  0.0000000  0.3636364 -0.2727273

[4,]  0.0000000  0.0000000 -0.2727273  0.4545455

solve(m[1:2, 1:2])

           [,1]       [,2]


[1,]  0.2222222 -0.1111111

[2,] -0.1111111  0.5555556

solve(m[3:4, 3:4])

           [,1]       [,2]


[1,]  0.3636364 -0.2727273

[2,] -0.2727273  0.4545455

So V_i can be result of function ƒ(Z_i, θ); Z_i is known for all subjects, θ - vector of optimizables parameters.

❝ My approach is very simple: I make a case for saying that when T is not replicated while R is

❝ replicated, then it is not possible to make a meaningful model when V=ZGZt+R (as long as we count on R having the withins and G having the betweens).

Mmm... I can't say that ZGZ'+R is meaningful. If you construct V manualy it can still be represented as ZGZ'+R if ρ not equal 0. If used random model with covariation (ρ≠0) nondiagonal elements of G depends on diagonal and when you construct V some nondiagonal elements depends on both variance parameters. Then we add diagonal R matrix and have combination (parts of V): σ²_BT+σ²_WT, σ²_BR+σ²_WR, σ²_BR, σ_BT*σ_BR*ρ (we have no σ²_BT) so we can estimate σ²_WT from σ²_BT+σ²_WT and σ²_BT is stable because it is part of σ_BT*σ_BR*ρ (Yes estimate of σ²_WT is indirect). If ρ = 0 we have σ_BT*σ_BR*ρ = 0, and we can estimate only σ²_BT+σ²_WT.

And I think that V can be decomposed to ZGZ'+R if you know Z, ρ (ρ≠0) and σ²_BR in model with covariance and diagonal R.

Complete thread:

Semireplicated + REML in R ElMaestro 2020-07-10 13:19 [🇷 for BE/BA]
- Semireplicated + REML in R Helmut 2020-07-10 19:03
  - Semireplicated + REML in R ElMaestro 2020-07-10 19:24
    - Avoid partial replicate designs, pleeeze! Helmut 2020-07-11 11:57
      - Avoid partial replicate designs, pleeeze! ElMaestro 2020-07-11 14:43
        
        Braveheart! Helmut 2020-07-11 15:38
        
        Who can help? ElMaestro 2020-07-12 12:28
        
        Who can help? ElMaestro 2020-07-12 13:26
        Update II ElMaestro 2020-07-12 21:36
        
        Update III ElMaestro 2020-07-12 21:46
        
        Final update today ElMaestro 2020-07-12 22:27
        
        Medium rare. Helmut 2020-07-13 13:52
        
        took just 52 hrs to do it :-) ElMaestro 2020-07-13 14:18
        
        Will take much more hours still… Helmut 2020-07-13 15:34
        
        Negative determinant ElMaestro 2020-07-14 03:22
        
        Are we loosers? Helmut 2020-07-14 13:58
        
        "we"? Loosers? ElMaestro 2020-07-14 15:07
        
        Misunderstanding? Helmut 2020-07-14 15:32
        
        Braveheart! ElMaestro 2020-07-13 10:13
        
        Braveheart! Helmut 2020-07-13 14:16
        Braveheart! PharmCat 2020-07-15 14:19
        
        Braveheart! ElMaestro 2020-08-02 17:39
- We were all blind (except Detlew) Helmut 2020-07-15 14:27
  - It is the opposite way around for me ElMaestro 2020-07-15 16:25
    - Desultory thoughts Helmut 2020-07-15 17:33
      - FDA RSABE is ISC d_labes 2020-07-15 18:13
        
        FDA RSABE is ISC Helmut 2020-07-16 11:11
      - Desultory thoughts ElMaestro 2020-07-15 23:06
        
        Desultory thoughts Helmut 2020-07-16 10:59
  - Phoenix - which template? mittyri 2020-07-19 00:42
    - FDA RSABE Project template_ v1.4.phxproj Helmut 2020-07-19 01:45
- "By popular demand": likelihood ElMaestro 2020-07-24 10:07
  - And by the way.... ElMaestro 2020-07-24 12:52
    - And by the way.... PharmCat 2020-08-03 14:24
      - Not understood ElMaestro 2020-08-03 22:55
        
        Not understood PharmCat 2020-08-05 01:41
        
        Not understood ElMaestro 2020-08-05 08:13
        
        Not understoodPharmCat 2020-08-05 16:37
        
        Open issues ElMaestro 2020-08-06 21:11
        
        Open issues PharmCat 2020-08-07 00:02
        
        Open issues ElMaestro 2020-08-07 07:49
        
        Open issues PharmCat 2020-08-07 11:29
        
        Still can't make it work ElMaestro 2020-08-07 13:08
        
        Still can't make it work PharmCat 2020-08-07 15:42
        
        Still can't make it work ElMaestro 2020-08-07 16:44
        
        Still can't make it work PharmCat 2020-08-07 18:14
        
        Still can't make it work ElMaestro 2020-08-07 18:23
        
        And now it works ElMaestro 2020-08-07 21:31
        Still can't make it work PharmCat 2020-08-08 01:08
        
        Speed improvement ElMaestro 2020-08-08 12:25
        
        Speed improvement PharmCat 2020-08-08 17:27
        Speed improvement ElMaestro 2020-08-08 18:10
        
        Speed improvement PharmCat 2020-08-09 18:22
        Some tests... PharmCat 2020-08-10 11:48