Population PK Post Hoc Analysis

Phoenix Certara Forums Modelling and Simulation
1

Hello,

I have a 2-cmpt pop PK model, and have generated the post-hoc output table by individual subject, which includes each of the thetas by ID. I also do have a corresponding eta table by ID.

My question is how do I setup my model to simulate exposures for each of the subjects in the study based on the individual post-hoc estimates for each subject. I would like to setup a fixed dose (126 mg given q3w for 6 cycles with PK simulations every 2 hours) for each of the subjects based on their (actual theta and eta) post-hoc estimates.

Previously I believe I was doing clinical trial simulations by accepting all fixed and random effects with my model, and adding a simulation table to include 50 random individuals, I added the dosing sheet, and put in seq (0,2260,2) with CObs as the output, I would then do descriptive stats on CObs and plot the median and also the shaded area band from the 5th to 95th percentiles (90% confidence). Feel free to see the image below.

This time around I am interested in the post-hoc analysis, but am not familiar with the approach for this. I would like to see the entire profiles, and generate PK parameters such as AUCtau for each actual subject ID based on the actual post-hoc theta and eta estimates (and not a random population of 50 theoretical subjects with the fixed population PK estimates as I had done before in the image above). You can see I also added the actual observations into the plot.

I imagine I will get a table (DV vs CObs) for each of the actual subject IDs, which I could then do a simple NCA with descriptive stats based on the post-hoc results.

Thanks a lot for your input, please see my model below. If you could please describe the process and also help me set this up in my model I would be much obliged.

https://www.dropbox.com/s/cm7orppqzxuud30/Post_hoc%20Analysis.phxproj?dl=0

2

Hi,

Try using individual eta estimates as the covariates instead of population eta, that way you would get Cobs adjusted to their eta for each individual subject- see the sample code:

test(){
cfMicro(A1, Cl / V, Cl2 / V, Cl2 / V2, first = (Aa = Ka))
dosepoint(Aa)
C = A1 / V
error(CEps = 0.268573)
observe(CObs = C * (1 + CEps))
stparm(Ka = tvKa * exp(nKa))
stparm(V = tvV * exp(nV))
stparm(V2 = tvV2 * exp(nV2))
stparm(Cl = tvCl * exp(nCl))
stparm(Cl2 = tvCl2 * exp(nCl2))
fcovariate(nV)
fcovariate(nCl)
fcovariate(nKa)
fcovariate(nV2)
fcovariate(nCl2)
fixef(tvKa = c(, 0.00871573, ))
fixef(tvV = c(, 6.42957, ))
fixef(tvV2 = c(, 900.051, ))
fixef(tvCl = c(, 0.0973144, ))
fixef(tvCl2 = c(, 0.0582446, ))
#ranef(diag(nV, nCl, nKa, nV2, nCl2) = c(0.46607611, 0.4057042, 0.044551053, 0.016906062, 0.46273008))
ranef(diag(ndumm) =c(0.0001))

}

hope this helps!

Thanks,

Soujanya

3

Thanks Soujanya for the quick reply.

What about the theta for each individual? The way the model is written above is using the fixed population estimates.

I would like to simulate based off the post-hoc estimates for each individual, theta + eta respectively (i.e. volumes and clearances for each subject are unique).

Thanks greatly.

4

Ok.. I tried following code as test case and it worked-

I have used the structural parameters from the post hoc estimates table from your model and removed the pop. estimates.

not sure if it is accurate or not though.

test(){
cfMicro(A1, Cl / V, Cl2 / V, Cl2 / V2, first = (Aa = Ka))
dosepoint(Aa)
C = A1 / V
error(CEps = 0.268573)
observe(CObs = C * (1 + CEps))
stparm(Ka = Ka)
stparm(V = V)
stparm(V2 = V2)
stparm(Cl = Cl)
stparm(Cl2 = Cl2)
#fixef(tvKa = c(, 0.00871573, ))
#fixef(tvV = c(, 6.42957, ))
#fixef(tvV2 = c(, 900.051, ))
#fixef(tvCl = c(, 0.0973144, ))
#fixef(tvCl2 = c(, 0.0582446, ))
#ranef(diag(nV, nCl, nKa, nV2, nCl2) = c(0.46607611, 0.4057042, 0.044551053, 0.016906062, 0.46273008))
ranef(diag(ndumm) =c(0.0001))
}

5

Thanks Soujanya for the the quick follow-up.

Could anyone confirm if this is the correct way to do post-hoc analysis of population pharmacokinetic data using NLME?

I am looking to simulate distinct individuals with the population PK model based on the individual post hoc PK parameters.

Thanks all, much obliged.