Simultaneously estimating IIV and IOV estimate for first cycle in pharmacokinetic NLME model using Torsten

[marianklose]

@yizhang Thanks a lot for your answer!

@yizhang

Apologize for being late to the thread.

No worries. I also just returned to office after one week of absence.

@yizhang

As pointed out the additive IIV & IOV pose unidentifiability. For the first dose cycle, you don’t need to add IOV as the rest observations of this subject can be anchored to the first one, in order to account for the variation between the visits.

I agree that we face some unidentifiability issues in the first cycle and that we have to deal with it somehow. However, I am not sure if I agree with the suggested solution. To my understanding, NONMEM is estimating the variance of the IOV part based on all cycles available and is not taking the first cycle as some kind of reference (which would result in KAP_CL = 0 for the first cycle). I just had a look into the sdtab file and there we can see that ETA1 (EBE for IIV) remains constant within one ID (as expected) and that KAP_CL (EBE for IOV) changes per cycle and that it is unequal to 0 for the first cycle:

ID             CYCLE             CL             ETA1               KAP_CL 
1.0000E+00     1.0000E+00        1.2525E+00     -2.4793E-02        1.6011E-02
(...)
1.0000E+00     2.0000E+00        1.0585E+00     -2.4793E-02       -2.3082E-02
(...)
1.0000E+00     3.0000E+00        1.2750E+00     -2.4793E-02       -7.0252E-03

The underlying equation for CL is:

TVCL = THETA(1) * (EGFR_I/84)**THETA(7) * EXP(ETA(1) + KAP_CL)

Of course ETA1 and KAP_CL are based on all observations and cycles, so during model building we do not have that unidentifiability issue. To my understanding I would underestimate the variability on CL if I simply discard the IOV part for the first part and simply focus on the IIV part. I would rather suggest to sum up the variances of IIV and IOV for the first cycle and then estimate only one posterior for the joint ETA(1) + KAP_CL part. Once we have informative data in the second cycle, I would estimate the posterior seperately for IIV and IOV. Any objections or am I missing something?

@yizhang

Since we are focusing on personalized prediction, I wonder if it makes sense to use EBE pred from NONMEM instead of the population TVs. This way the IIV becomes unnecesary and we only need to focus on subject param and IOV around it.

Of course we could switch to the mode of the posterior (EBE) for IIV, but then we would miss out important parts of the variability driven by IIV. I am not sure how to interpret the resulting posterior predictions if some parts are fixed to the mode of the posterior (IIV) and some parts represent the full posterior (IOV).

@yizhang

Depends on dosing schedule I guess it’s also worth to think over if there is indeed IOV of CL, or it’s just caused by observation noise.

Good point. But in our clinical use-case inter-occasion variability is quite plausible and gos beyond normal observations noise. There I am quite confident that it is needed in the model.