Questions about identifiability

Dear NONMEM users, The PK of the compound we are working on can be described by a 2-compartment model with non-linear protein binding in the central and in the peripheral compartment, which from a physiological point of view makes complete sense. The question we have is whether such model is identifiable having just total plasma concentration (no binding information is available). Therefore we want to simulate different kind of datasets and check if NONMEM is able to re-estimate them properly. * Our first question was: "Is the structure itself in principle identifiable?" We simulated a dataset with 100 time points per subject and no intra- or inter-individual variability and no residual error. ('ideal' data: plenty time points, no random error) Since under these conditions the parameters could be re-estimated (parameter estimates were nearly identical to the original ones, %SE is very small) we concluded that the structure in principle is identifiable. * Our second question was: "Are the time points of the given study sufficient to estimate all parameters assuming 'ideal' data?" We simulated the given dataset assuming no intra- or inter-individual variability and no residual error. The parameter estimates were again nearly identical to the original ones and %SE is still very small (below 0.3 %). * Our third question was: "Could the parameters still be re-estimated if we assume inter- and intra-subject variability for the simulation step?" We simulated the given dataset assuming IIV, IOV and residual error. Under these conditions, the parameter (fixed and random effect) estimates are again similar, but not identical to the original ones, %SE increased to about 9% (one exception is the SE% of the parameter for the amount of peripheral binding sites which were estimated to be 16%). However, when we re-estimate omitting the IIV and IOV, the estimated parameters differ from the original ones and estimates for the peripheral binding becomes difficult to estimate. The questions we have are: 1. Are these experiments sufficient to conclude on the model identifiability? 2. Does it make sense that the fixed effect parameters differ from the original ones when IIV and IOV are omitted in the estimation step in constrast to when they are included in the simulation step? Shouldn't the structure of the model remain stable? 3. How often would you simulate and re-estimate the third experiment? 4. Would you vary the initial estimates to check for any potential other set of parameters? (If yes how often?) 5. One problem is that the complete model with IIV and IOV has quite long run times (around 24h), do you think checking the model with just IIV would be enough? 6. Do you have any other proposal to check for the identifiability of a model? Your help is highly appreciated, thank you in advance, Silke Silke Dittberner PhD student Institute of Pharmacy University Bonn Germany