I Use both NONMEM and NLME.
Over the last 5-10 years I have noticed that NONMEM cant fit TMDD models (same data and diff equation) no matter what Differential solver is used. Phoenix can fit TMDD models using both the standard solver and the Stiff solver (much faster than the standard). Furthermore I noticed that University of Buffalo offers a Protein PKPD course and uses ADAPT5 for this. I think this is because NONMEM fails TMDD modeling. Some very popular papers on TMDD claims that Full TMDD models are Over parametrized and therefor QSP models should be used (they used NONMEM). This argument is not valid as a full TMDD model has only one more parameter (kon and koff vs KD). A fixed kon is better than assuming an infinite kon as a KD approximation does. If you fix Kon, NONMEM still fails in fitting TMDD models so its not a matter of parameters but I suspect a matter of stiffness. In my mind you should always use full TMDD models (on all antibodies) when possible because they are much more useful (I work in Industry) as you can get good prior estimates for Kon and Koff from invitro experiments in different species and populations. Fitting TMDD data also fails in R but works in ADAPT5. I have no experience with Monolix. I cant rule out that some dataset might work for NONMEM but I haven't come across any, and I just use NLME as a default for TMDD models.
Does anyone have the same experience as me?