PD marker with a bimodal distribution

Phoenix Certara Forums Modelling and Simulation
1

Hi,

I am trying to fit a PK-PD model (the PD being a TGI model with e.g. linear conc effect, see below), but I realized the Basline PD data shows a bimodal distribution. A number of subjects have a quite high Tumor Baseline, another type of subjects has a quite low PD basline. How could I introduce this fact into my PD model?

Any help is very appreciated.

Thanks

Frank

deriv(Tumor = growthTumor-CTumor*kill0)

error(EEps=5)
observe(EObs = Tumor+EEps,bql)

sequence{Tumor=BASE
}

stparm(kill0 = tvkill0 * exp(nkill0)

stparm(growth = tvgrowthexp(ngrowth))
stparm(BASE = tvBASEexp(nBase))

fixef(tvkill0 = c(,))
fixef(tvgrowth = c(,))
fixef(tvBASE = c(,))

ranef(diag(nBase,ngrowth,nkill0) = c(1,1,1))

2

Dear Frank

Unless you know the distribution to which each row of data belong to, we do not have mixture distribution implemented in Phoenix at this stage. What I do suggest you to try to do is to look at all your baseline values and decide to which distribution each baseline value belong to. It will be a 0, 1 column and you define it as categorical covariate linked to the baseline. Then you can fit that model to the data.

That is the only way I can see so far with Phoenix.

best Regards

Serge

3

Thanks Serge, I guess manually deciding to which Baseline category the pt belongs will work.

That would mean I would implement the 0,1 column that you describe like this?

stparm(BASE = tvBASEexp(nBase) exp(dBase*(PDcat==1))

Does that then mean the tvBase I get is the Basline of the “0” patients, and the (tvBASE* exp(dBase*(PDcat==1))) is the basline of the “1” pateints?

4

Dear Frank, Dear Serge,

Does that then mean the tvBase I get is the Basline of the “0” patients, and the (tvBASE* exp(dBase*(PDcat==1))) is the basline of the “1” pateints?

exactly

“0” patients tvBase (with lognormal distribution in population)

“1” patients tvBase*exp(dBase)

I’m wondering regarding some crazy stuff like this:

stparm(Base = tvBaseexp(nBase)exp(dBase((tvBaseexp(nBase))>Terminator)))
fixef(Terminator = c(,tvBase_value,))

I think it shouldn’t be a problem for EM algo

Hope it helps,

Mittyright