Frequently Asked Questions

Do I need to use MU-referencing in my model definitions, like in NONMEM / nlmixr2?

No. FeRx does not require MU-referencing.

In NONMEM and nlmixr2, MU-referencing is a convention in which each random effect ETA(i) is linearly associated with a single MU_i term (typically MU_i = LOG(THETA(i))), so individual parameters look like:

MU_1 = LOG(THETA(1))
CL = EXP(MU_1 + ETA(1))

This structure is required by those tools' SAEM implementations because they rely on conjugate Gibbs updates that are only valid when the MU_i → ETA(i) relationship is strictly linear (and typically on a log scale). If you deviate — for example by writing CL = THETA(1) * EXP(ETA(1)) without going through an intermediate MU_1, or by mixing multiple etas into one parameter — NONMEM SAEM will either reject the model or silently produce biased estimates.

FeRx's SAEM implementation uses Metropolis-Hastings sampling for the E-step rather than Gibbs, which does not require MU-referencing. You can write individual parameters in any form you like:

# All of these work fine in ferx:
CL = TVCL * exp(ETA_CL)
CL = TVCL + ETA_CL                              # additive eta
CL = TVCL * (WT/70)^0.75 * exp(ETA_CL)          # with covariates
CL = TVCL * exp(ETA_CL + ETA_CL_OCC)            # multiple etas
VMAX = TVVMAX * exp(ETA_VMAX)
KM   = TVKM                                      # no eta at all

The FOCE / FOCEI estimators have no MU-referencing requirement in any NLME tool — they use MAP optimization over etas regardless of parameterization. This is equally true in ferx.

Performance implication

The main tradeoff is that MH sampling is slightly less efficient per iteration than conjugate Gibbs for MU-referenced models. In practice:

  • For models with a few random effects, the difference is negligible
  • For models with many (>10) random effects, conjugate Gibbs would converge in fewer iterations — but in exchange you gain flexibility to write models that don't fit the MU-referenced mold

If you have a NONMEM model that uses MU-referencing and want to port it to ferx, you can drop the MU intermediate step and write the individual parameters directly — the results will be equivalent.