See this page
for some discussion
of what convergence means.
Stuart Beal decided to use a criterion that all parameters
should have >= SIGDIG significant digits. Another criterion could have been an
OBJ value that changed by less than FOBJ where FOBJ might be 0.001. I would have
preferred the latter criterion because it seems like NONMEM wastes a lot of time
crunching through iterations with no reported change in OBJ. I dont believe the
parameter estimates are really any better after this activity.
Other similar programs
(e.g. WinBugs, Monolix) don't have a convergence criterion but ask the user to decide
by looking to see if they have found a fuzzy caterpillar rather then a wiggly worm
(strange but true!).
Picking a SIGDIG of 3 is just traditional - like using a Type
1 (alpha) error of 0.05 for hypothesis testing. For convenience, most people use
SIGDIG of 3 so they don't have to spend time explaining why they might prefer 2
or 4.
My own preference is 6 because I happened to come across a simple 2 cpt PK
problem with NONMEM V that got the right answer (which was known a priori) with
SIGDIG=6 but converged prematurely with SIGDIG=3. A SIGDIG of 5 was almost as good
as 6 but 4 was wrong but not as bad as 3. NONMEM VI does better than NONMEM V but
still terminates prematurely with SIGDIG=3. My conclusion from this one example
is that SIGDIG=3 is not a reliable convergence criterion even with NONMEM VI.
The
problem used data simulated with a mammillary model but estimation was done with
either a mammillary model (mam) or a model which assumed elimination from the peripheral
compartment (rec). These models are known to be exactly equivalent but with SIGDIG=3
the OBJ values were clearly different. With SIGDIG=6 the OBJ values were identical.
Intel 9.1 F77 Intel Pentium
METHOD=COND, additive residual error
+ means $COV ran
successfully
ADVAN9 TOL=5
| NONMEM V
|
|
|
|
|
Run |
Obj |
Eval |
Sig |
|
mam_mam_6 |
-1519.243 |
85 |
+6.5 |
|
mam_rec_6 |
-1519.243 |
78 |
+6.3 |
|
mam_mam_5 |
-1519.229 |
106 |
+5.3 |
|
mam_rec_5 |
-1519.228 |
78 |
+5.3 |
|
mam_mam_4 |
-1517.777 |
33 |
3.9 |
|
mam_rec_4 |
-1519.105 |
70 |
+4.7 |
|
mam_mam_3 |
-1517.777 |
30 |
+4.2 |
|
mam_rec_3 |
-1406.731 |
32 |
2.9 |
|
|
|
|
|
|
NONMEM VI |
|
|
|
|
Run |
Obj |
Eval |
Sig |
|
mam_rec_6 |
-1519.243 |
104 |
+8.7 |
|
mam_mam_6 |
-1519.243 |
101 |
+6.5 |
|
mam_rec_5 |
-1519.243 |
93 |
+5.2 |
|
mam_mam_5 |
-1519.243 |
101 |
+5.5 |
|
mam_rec_4 |
-1519.240 |
93 |
+4.3 |
|
mam_mam_4 |
-1519.241 |
92 |
+4.5 |
|
mam_rec_3 |
-1519.021 |
115 |
+3.1 |
|
mam_mam_3 |
-1518.920 |
49 |
+3.2 |
