# Population PK Post Hoc Analysis **URL:** \ **Category:** Modelling and Simulation\ **Created:** [April 1, 2018, 4:18pm UTC](https://forum.certara.com/t/population-pk-post-hoc-analysis/3301 "2018-04-01T16:18:57Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![csheme](https://avatars.discourse-cdn.com/v4/letter/c/7993a0/32.png) [@csheme](https://forum.certara.com/u/csheme)\ **Post date:** [April 1, 2018, 4:18pm UTC](https://forum.certara.com/t/population-pk-post-hoc-analysis/3301/1 "2018-04-01T16:18:57Z")
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](https://www.dropbox.com/s/cm7orppqzxuud30/Post_hoc%20Analysis.phxproj?dl=0) ---
**Author:** ![soujanya234](https://avatars.discourse-cdn.com/v4/letter/s/96bed5/32.png) [@soujanya234](https://forum.certara.com/u/soujanya234)\ **Post date:** [April 2, 2018, 3:44pm UTC](https://forum.certara.com/t/population-pk-post-hoc-analysis/3301/2 "2018-04-02T15:44:50Z")
> [@csheme](#): > > 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](https://www.dropbox.com/s/cm7orppqzxuud30/Post_hoc%20Analysis.phxproj?dl=0) 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 ---
**Author:** ![csheme](https://avatars.discourse-cdn.com/v4/letter/c/7993a0/32.png) [@csheme](https://forum.certara.com/u/csheme)\ **Post date:** [April 2, 2018, 4:51pm UTC](https://forum.certara.com/t/population-pk-post-hoc-analysis/3301/3 "2018-04-02T16:51:40Z")
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. ---
**Author:** ![soujanya234](https://avatars.discourse-cdn.com/v4/letter/s/96bed5/32.png) [@soujanya234](https://forum.certara.com/u/soujanya234)\ **Post date:** [April 2, 2018, 7:06pm UTC](https://forum.certara.com/t/population-pk-post-hoc-analysis/3301/4 "2018-04-02T19:06:07Z")
> [@csheme](#): > > 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. 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)) } ---
**Author:** ![csheme](https://avatars.discourse-cdn.com/v4/letter/c/7993a0/32.png) [@csheme](https://forum.certara.com/u/csheme)\ **Post date:** [April 6, 2018, 12:37am UTC](https://forum.certara.com/t/population-pk-post-hoc-analysis/3301/5 "2018-04-06T00:37:11Z")
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.