how to specify L2 data item and sigma block

Dear Certara forum users,

I am building a popPK model for a parent drug and its metabolite (rich data,single dose) using NLME. I want to estimate the correlation between the residual errors of parent drug and its metabolite, because their measurements were from a same blood sample. my questions are:

1. do I need to specify L2 data item, and if yes, how to do it in NLME? (could you please provide an example to demonstrate, including details like data format*); 2. how to add sigma block using PML, for example, I am using combined additive and proportional model for both parent and metabolite. 3. My codes* are shown as follows, I fix the fraction of parent metabolized (Fm=0.3) based on literature value to solve the identifiability issue. Any suggestion about my codes?

Thanks in advance,any suggestion is greatly appreciated.

Jing Niu

CTM

University of Maryland

test(){

deriv(A1 = - (Clr * C) + (Aa * Ka)- (Cl2 * (C - C2))- (CLpar2met * C))
urinecpt(A0 = (Clr * C))
deriv(Aa = - (Aa * Ka))
deriv(A2 = (Cl2 * (C - C2)))
deriv(Amet = (CLpar2met * C)- (CLmet * Cmet)- (Cl_met2 * (Cmet - Cmet2)))
urinecpt(Amet0 = (CLmet * Cmet))
deriv(Amet2 = (Cl_met2 * (Cmet - Cmet2)))
C = A1 / V
dosepoint(Aa, tlag = (Tlag), idosevar = AaDose, infdosevar = AaInfDose, infratevar = AaInfRate)
C2 = A2 / V2
error(CEps = 0.0365714)
observe(CObs = C + CEps * sqrt(1 + (C)^2 * (CMultStdev/sigma())^2))
Cmet = Amet / Vmet
error(CEps_met = 0.05)
observe(CObs_met = Cmet + CEps_met * sqrt(1 + (Cmet)^2 * (MultStdev/sigma())^2))
Cmet2 = Amet2 / Vmet2
stparm(Cl = tvCl)
stparm(Fm = tvFm)
stparm(Tlag = tvTlag * exp(nTlag))
stparm(Ka = tvKa * exp(nKa))
stparm(V = tvV (LBM/48)^dVdLBM * exp(nV))
stparm(Clr = tvCl * (1-tvFm) * (CrClcut120/95)^dClrdCrCl
exp(nClr))
stparm(CLpar2met = tvCl * tvFm * exp(nCLpar2met))
stparm(V2 = tvV2 * exp(nV2))
stparm(Cl2 = tvCl2 * exp(nCl2))
stparm(Vmet = tvVmet * exp(nVmet))
stparm(CLmet = tvCLmet * exp(nCLmet))
stparm(Vmet2 = tvVmet2 * exp(nVmet2))
stparm(Cl_met2 = tvCl_met2 * exp(nCl_met2))
stparm(CMultStdev = tvCMultStdev)
stparm(MultStdev = tvMultStdev)
fcovariate(Age)
fcovariate(Weight)
fcovariate(LBM)
fcovariate(Height)
fcovariate(BSA)
fcovariate(ECOG())
fcovariate(isFemale0F1M)
fcovariate(CrClnew)
fcovariate(CrClcut120)
fcovariate(Occ)
fixef(tvCl = c(0, 16.58102, ))
fixef(tvFm (freeze) = c(0, 0.3, ))
fixef(tvTlag = c(0, 0.225859, ))
fixef(tvKa = c(0, 2.28469, ))
fixef(tvV = c(0, 98.1745, ))
fixef(tvV2 = c(0, 57.4144, ))
fixef(tvCl2 = c(0, 19.6853, ))
fixef(tvVmet = c(0, 50, ))
fixef(tvCLmet = c(0, 25, ))
fixef(tvVmet2 = c(0, 20, ))
fixef(tvCl_met2 = c(0, 10, ))
fixef(dVdLBM(enable=c(0)) = c(0, 0.9, ))
fixef(dClrdCrCl(enable=c(0)) = c(0, 0.5, ))
fixef(tvCMultStdev = c(0, 0.237202, ))
fixef(tvMultStdev = c(0, 0.2, ))
ranef(diag(nKa, nTlag, nV, nV2, nCl2, nCLpar2met, nClr, nCLmet, nVmet, nCl_met2, nVmet2) = c(0.66896944, 0.5961447, 0.075934645, 0.19267901, 0.0656101, 0.16775341, 0.20547087, 0.18828786, 0.31245868, 1, 1))
ranef(diag() = c(), same(), same())
}

Hi Jing Niu,

Currently, Phoenix NLME (PML) does no support L2 or similar. There is no Epsilon “Matrix” each epsilon is independent to the other.

You might be able to do it using a trick where you model epsilon as thetas including the correlation between the two while keeping a dummy Ceps fixed at 1.

To be able to help more can you add a dummy/simulated version of your data so we can try the code above on it and se e how things are working ?

last ranef has no names in it.

Hi Samer,

I greatly appreciate your help!

Sure! I attached a proj file with simulated data. FYI, the simulated data took really long time to run (10 hr vs 1 hr of the original data) such that I didn’t finish a successful run with it.

Thanks again for willing to help!

Jing Niu

SigmaBlock_parentMetModel_test.phxproj (788 KB)

Hi Samer,

Any luck about my code?

If you have any reference with respect to this question, Could you please share that with me? This question seems like a rare case and can’t find resources for PML…

Thanks in advance for your help,

Jing