TMDD QE model example and troubleshooting

Hi everyone,

I am trying to code a TMDD QE model (no Kon and Koff, just use KD). This is to fit a mAb targeting at an endogenous protein, and the assumption is the elimination rate of the bound complex is the same as that of free mAb (Ke) so no Kint is involved.

I did some research on internet and in the forum and complied the codes, however NLME just doesn’t run even verification is successful. I am attaching the Phoenix file and the PML codes here. Please feel free to suggest if I made any error.

Couple of notes:

  1. There are two readouts from the study, total mAb concentration and total target concentration. Both are set up as observations in the model.

  2. Target baseline concentration and KD were measured so they are both fixed in the model.

Thanks for any advice.

Hao

test(){
dosepoint(Atot)

deriv(Atot = -(Ke + K12) * C1 * V1 + K21 * A2 - Ke (Atot - C1 * V1))
deriv(A2 = K12 * C1 * V1 - K21 * A2)
deriv(Rtot = Kin - Kout * (Rtot - (Ctot - C1)) - Ke * (Ctot - C1))

Ctot = Atot / V1
C1 = 0.5 * ((Ctot - Rtot - KD) + sqrt((Ctot - Rtot - KD)**2 + 4 * KD * Ctot))
Kin = Kout * R0
sequence{Rtot = R0;}

error(CEps = 0.1)
observe(CObs = Ctot * (1 + CEps))
error(CEps_R = 0.1)
observe(CObs_R = Rtot * (1 + CEps_R))

stparm(V1 = tvV1 * exp(nV1))
stparm(Ke = tvKe * exp(nKe))
stparm(K12 = tvK12 * exp(nK12))
stparm(K21 = tvK21 * exp(nK21))
stparm(Kin = tvKin * exp(nKin))
stparm(Kout = tvKout * exp(nKout))
stparm(R0 = tvR0 * exp(nR0))
stparm(KD = tvKD * exp(nKD))

fixef(tvV1 = c(, 0.04, ))
fixef(tvKe = c(, 0.08, ))
fixef(tvK12 = c(, 0.6, ))
fixef(tvK21 = c(, 0.8, ))
fixef(tvKin = c(, 0.0133, ))
fixef(tvKout = c(, 0.0177, ))
fixef(tvR0 (freeze)= c(, 0.75, ))
fixef(tvKD (freeze)= c(, 0.0223, ))

ranef(diag(nV1, nK12, nK21, nKe, nKin, nKout, nR0, nKD) = c(1, 1, 1, 1, 1, 1, 1, 1))
}
TMDD QE model trial.phxproj (614 KB)

Dear colleague

In the first deriv statement , at the end you wrote Ke(Atot-C1*V1)

the multiplication sign is missing

should be

Ke*(Atot-C1*v1)

iF YOU DO THAT, ALL WILL WORK FINE

I am attaching the corrected verison (last model).

Best Regards

Serge

TMDD QE model trial.phxproj (1.24 MB)

Hi Serge,

Thanks so much for the quick troubleshooting! The missing of multiplication was indeed the error. The model runs like a charm after your fix.

I’ve played with the model for a few more days thereafter but not sure how Kin and Kout converges. The estimated Theta are as attached:

We define Kin = Kout * R0 and R0 is fixed as 0.75 in the model. But I am seeing the Theta of Kin and Kout doesn’t really comply with this equation. Any advice? Or I don’t really need to mind about it?

On the other end, I have trouble generating the results of Stderr, CV%, etc. There is nothing reported though I’ve tried all the Stderr settings in the “Run Options”. Any suggestions?

Thanks so much again!

Hao

Dear Hao

If Kin is fixed, then you can look at the code and delete the KIn stparm and if there is a random effect deleting it too. Usually it will not affect anything but you may waste time by trying estimating a parameter that is not sensitive.

For se’s, take the model and copy it to the workflow, shift to QRPEM and ask for 1 iteration with se request.

Best is to send me the project to check.

best

Serge

I would delete all the KIn part because I am not sure if the equation for Kin is used or if Kin is estimated (order issue).

Best

Serge

Thanks again Serge! Let me try all your suggestions and I’ll provide an update.