1 reply to this topic

[isaac_pirana]

Hi all,

 

I have a question regarding the control stream files generated by Pirana's Wizard tool. 

 

I have attached screenshots of part of a Wizard control stream and an example control stream format provided by Icon PLC (creators of NONMEM), and am confused about their differences in implementing the residual error model in the ERROR block.

 

In the NONMEM example, the proportional and additive error model is applied to F to produce Y. This process is applied to both PRED and IPRED estimates. Also, the error parameters are stored in the SIGMA block. 

 

However, in the Wizard control stream, IPRED is specified as F, meaning that the IPRED reported does not contain residual error as it should do, from my understanding. Then, a different form of error model is applied to F to attain Y (Y = F + W), and since sqrt(a^2 + b^2) is not equal to a + b, this does not equate to the usual formula for combined additive and proportional error. Finally, the error parameters are stored in the THETA block, meaning that NONMEM will treat them as fixed effects rather than random ones (for example, their shrinkage will not be calculated).

 

Is my understanding of the control stream correct? I would be grateful for any clarification anyone could provide, since I have seen the Wizard’s method of implementation throughout Pirana’s tutorials / documentation.

 

Many thanks,

Isaac

Attached Files

•  Wizard Control Stream .png   464.09KB   0 downloads
•  NONMEM Control Stream.png   313.92KB   0 downloads

[kniefort]

Hi Isaac,

 

The short answer is that the models indeed produce equivalent results, the difference being that the first example which uses a fixed EPS reports the error estimates as standard deviation, and the second that uses 2 EPS parameters reports error estimates as variances (run 1 is wizard model, run 2 is two epsilon model).

 compare.jpg   85.37KB   0 downloads

 

 

There are many different implementations of the combined proportional additive error model (e.g., see the excellent review series by Mould and Upton:  CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e38; doi:10.1038/psp.2013.14), some of which transform the problem space into a form that is more stable and less likely to crash.    

 

If you look at the 2 error models:

 

Two Epsilon Model:  Y=F*(1+EPS(1)) + EPS(2)

 

Wizard Model:  W=(THETA(1)^2 * F^2 + THETA(2)^2)^.5

                         take sqrt:

                         W=THETA(1) * F + THETA(2)

substitute:

Y = F + W

Y = F + THETA(1) * F + THETA(2) * 1 (eps fixed to 1)

Y = F*(1 + THETA(1)) + THETA(2)  -- This is the same as 2 epsilon model above

 

There may be someone on the board who can better describe the situations under which the wizard model is preferred, but the 2 models produce equivalent results.  See attached Pirana project.

Attached Files

•  WizardErrorModelCompare.zip   1.24MB   2 downloads

Edited by kniefort, 05 January 2024 - 10:51 PM.