sd on eta

[FelicienLL]

I should study the possibility to compute a standard deviation on parameters (computed from the Hessian etc...)

• See Kang et al, Korean J Physiol Pharmacol, 2012

[FelicienLL]

Something like this:

final_eta %>%
  hessian() %>% # <- find a way to compute it
  solve() %>%
  multiply_by(2) %>%
  diag() %>%
  sqrt()

[FelicienLL]

Was not convinced of my previous attempt

• Set (hessian = TRUE) in the control list as default rather than adding a new argument to mapbayest().
• Maybe return the var-cov matrix instead of the SE, FIM or whatever... Whether in the form of :
  • a list of matrices ; to be consistent with $final_eta ; with an associated get_cov() method ?
  • a vector with low-triangle elements; as in NM root.phi.

[mattfidler]

Nlmixr has an exported hessian method that is more similar to what NONMEM uses. In tests the standard errors without using that method were off.

[FelicienLL]

Hello, thanks for your comment @mattfidler. That's good to know ; I'll definitely have a look into it and keep you informed. Félicien

[FelicienLL]

Hello @mattfidler I tested nlmixrHess vs optimHess on a few patients, and it turns that results were often very close between each other, but still (somewhat) different from NONMEM. Don't know if there is something I did wrong. Nevermind. I'll probably push with optimHess nevertheless, and just keep in mind that it is not as reliable as I could hope. Maybe I'll investigate it later. Thanks again for your feedback.

$optimHess
# A tibble: 10 x 6
       ETC11       ETC12        ETC13     ETC22        ETC23     ETC33
       <dbl>       <dbl>        <dbl>     <dbl>        <dbl>     <dbl>
 1 0.0136825  0.00503530 -0.000305194 0.0237150  0.0213066   0.132214 
 2 0.0290800  0.0283385  -0.00732591  0.177288   0.00126383  0.201054 
 3 0.0186945  0.0245448  -0.0187729   0.0369761 -0.0148816   0.186758 
 4 0.0487145  0.0789953  -0.00700705  0.167763   0.00308537  0.196837 
 5 0.0275728 -0.00573297 -0.0101148   0.0243365  0.0293306   0.138650 
 6 0.0601378  0.0897458  -0.00532107  0.151483   0.00332034  0.197242 
 7 0.0108475  0.00915594  0.00758177  0.0415659  0.0267983   0.134075 
 8 0.0321328  0.0444571  -0.00774746  0.189320   0.00192683  0.199362 
 9 0.0121780  0.00824785  0.00577110  0.0235335  0.0230167   0.0804586
10 0.0302423  0.00718001 -0.00776195  0.156584   0.000421537 0.202562 

$nlmixrHess
# A tibble: 10 x 6
       ETC11       ETC12        ETC13     ETC22        ETC23     ETC33
       <dbl>       <dbl>        <dbl>     <dbl>        <dbl>     <dbl>
 1 0.0136827  0.00503522 -0.000305312 0.0237151  0.0213068   0.132215 
 2 0.0290801  0.0283382  -0.00732593  0.177288   0.00126394  0.201054 
 3 0.0186941  0.0245439  -0.0187722   0.0369748 -0.0148803   0.186757 
 4 0.0487147  0.0789951  -0.00700703  0.167763   0.00308553  0.196837 
 5 0.0275732 -0.00573320 -0.0101150   0.0243370  0.0293311   0.138651 
 6 0.0601327  0.0897369  -0.00532115  0.151468   0.00332050  0.197243 
 7 0.0108476  0.00915586  0.00758176  0.0415660  0.0267983   0.134075 
 8 0.0321329  0.0444570  -0.00774745  0.189320   0.00192690  0.199362 
 9 0.0121781  0.00824780  0.00577102  0.0235335  0.0230168   0.0804588
10 0.0302425  0.00717970 -0.00776197  0.156584   0.000421609 0.202562 

> phi1
# A tibble: 4,000 x 7
      ID     ETC11        ETC21     ETC22        ETC31         ETC32     ETC33
   <dbl>     <dbl>        <dbl>     <dbl>        <dbl>         <dbl>     <dbl>
 1     1 0.0128120  0.00540869  0.0231664  0.000469547  0.0219134    0.125253 
 2     2 0.0315751  0.0278753   0.195386  -0.00716980   0.00118665   0.199695 
 3     3 0.0170443  0.0220648   0.0333487 -0.0197813   -0.0154167    0.195512 
 4     4 0.0476201  0.0768924   0.161199  -0.00698803   0.00352623   0.199680 
 5     5 0.0349610 -0.00818342  0.0270017 -0.0123977    0.0305114    0.150705 
 6     6 0.0587815  0.0872319   0.146116  -0.00540675   0.00333980   0.199793 
 7     7 0.0107253  0.00879663  0.0403477  0.00614566   0.0246981    0.137189 
 8     8 0.0326341  0.0442259   0.188313  -0.00772443   0.00204115   0.199643 
 9     9 0.0120836  0.00887946  0.0240298  0.00632080   0.0234488    0.0816501
10    10 0.0370990  0.000563275 0.199998  -0.00732788   0.0000253381 0.199670 

[mattfidler]

To be clear, when we did the vaidation of nlmixr against nonmem and monolix optimHess provided poorer estimates than nlmixrHess. That is not to say that I had the exact same vaules as nonmem.

This I think the accuracy of the two methods depends on you minization surface. Often they were comparable. In some lost reference they proposes that optimHess is a good method when you know the derivatives ot the surface well. The nlmixrHess method procided better results when you dont know the derivatives.

[mattfidler]

With sd eta perhaps optimHess is enough