74  Degrees of Freedom when Assessing OMEGAs

Introduction to NONMEM 7.6.0

Previous to nm751, for EM methods and MCMC Bayesian methods, the default correction for degrees of freedom was

\[\frac{M}{M-\text{LDF}}\]

where M is the number of subjects, and LDF is the loss of degrees of freedom. The LDF for EM/BAYES methods was 1 by default. Such a correction was not used in FOCE/Laplace analysis. Normally, this correction is very small, as M should be at least 10 for a proper population analysis. However, a difference in FOCE versus EM analysis may be noticed if the number of subjects is less than 10.

Because the correction is very small, for most problems, the LDF need not be adjusted. However, on the occasions where there are very few subjects, it would be most accurate to have LDF(I) be the number of to-be-estimated THETAs involved in MU_I. For example, you could enter the following (note the LDF must be accessed with verbatim code):

" LDF(3)=2.0
MU_3=THETA(4)+LOG(BWT)*THETA(5)
CL=EXP(MU_3+ETA(3))

As of nm751, the default LDF for EM/BAYES is 0, and you need to purposely add in degrees of freedom with LDF, and it will act on all analysis methods.

Or, you can ask NONMEM to evaluate the most appropriate LDF for you by setting the LDF to a negative value, for example:

" LDF(1:4)=-1.0

This will specify LDF according to the number of non-fixed THETAs associated with a particular MU reference. Therefore, when setting LDF=-1, it is necessary to have proper mu referencing, even for FOCE/Laplace. If you are curious about what the NONMEM assessed LDF values are, you can access them with:

$PK
Include nonmem_reserved_general
…
" write(*,*) TLDF(1),TLDF(2)

The LDF=-1 will correct for all analysis methods. If you set LDF>0, this will use that degrees of freedom for all methods. You can of course filter as follows:

Include nonmem_reserved_general
LDF(3)=2.0
If(IBMETHOD==EST_BAYES) LDF(3)=0.0

In summary, for nm751 and higher, if you wish to correct for degrees of freedom loss, let NONMEM determine the best values and for which methods, and make sure THETAs are mu referenced. So, for example:

$PK
LDF=-1
MU_1=THETA(1)+THETA(2)*LOG(AGE)
MU_2=THETA(3)

Etc.

will determine the correct degrees of freedom loss, and impose this correction for EM/FOCE/Laplace.

If there is a reason that you need your problem to handle LDF’s in the manner of previous NONMEM versions, insert the following after $PROBLEM:

$LDFOLD

and this will revert to the old default handling of LDF’s. Only the new methods (ITS/IMP/SAEM/BAYES) are affected by a change in default behavior regarding LDF’s of NONMEM version 7.5.0 to 7.5.1.