self-define model structure with if, else

Phoenix Certara Forums Modelling and Simulation
1

Hi Everyone,

I am trying to code a self-define model structure with ifelse statements in Phoenix nlme for a pop Pk model.

I would like to have a statement like this:

t_0=10
Ac_0=y0

if t < Tin
ddt_Ac = k * Ac - kel * Ac
else
ddt_Ac = - kel * Ac

Q1: Ac is target PK concentration, starting at day 10, and initial value should be fixed as a regression variable with subject ID which could be read from inputs.
How should I code to define start time and its subject dependent initial value?

k, kel and Tin are parameters needed to be fitted.

Q2: How to code if else statement with a uncertain condition (Tin needs to be fitted)?

I wrote a partial code for this model structure, please give me some suggestions for these two questions.

test(){

covariate(Time)

stparm (Ac = Time=10? Ac=y0)

stparm(Dev = Time<Tin ? kAc-kelAc: -kel*Ac)

deriv(Ac = Dev)

error(AcEps = 1)

observe(AcObs(Time) = Ac+ AcEps )

fixef(tvTin= c(,1,))

fixef(tvk = c(, 1, ))

fixef(tvkel = c(, 1, ))

stparm(Tin = tvTin * exp(nTin))

stparm(kel = tvkel * exp(nkel))

stparm(k = tvk* exp(nk))

ranef(diag(nTin, nk, nkel) = c(1, 1, 1))

}

Best,

Linda

2

Hi Linda,

there is something a bit unclear about your model:

you are defining Dev as structural parameter:

stparm(Dev = Time<Tin ? kAc-kelAc: -kel*Ac)

This should actually be a deriv() statement, since you are coupling concentrations (Ac) with micro constants (k, kel)

Should Ac be fixed until Time=10 ?

When you have a first order input (k*Ac) what is the dose?

Perhaps, you can provide more details?

Thanks,

Bernd

3

Hi Bernd,

Thank you for your reply. I agree that I should use deriv(), instead of stparm()

The model is just a kinetics model, where is no dose. The model is used to fitting the data with two phases, production phase with k and decay phase with kel. I can solve the Q1 by chaning the initial time points. But I still need help for Q2, which is how to sturcture a two phase model.

I rewrote a code, but still couldn’t run successfully.

test(){

covariate(Time)

deriv(Ac = Time<Tin ? kAc-kelAc: -kel*Ac)

error(AcEps = 1)

observe(AcObs(Time) = Ac+ AcEps )

fixef(tvTin= c(,1,))

fixef(tvk = c(, 1, ))

fixef(tvkel = c(, 1, ))

stparm(Tin = tvTin * exp(nTin))

stparm(kel = tvkel * exp(nkel))

stparm(k = tvk* exp(nk))

ranef(diag(nTin, nk, nkel) = c(1, 1, 1))

}

Thanks,

Linda

4

Hi Linda,

please try this as a first draft:

test(){
deriv(Ac = kAc-kelAc)
error(AcEps = 1)
observe(AcObs(t) = Ac+ AcEps )
sequence{Ac=10}
fixef(tvTin= c(,10,))
fixef(tvk = c(, 1.5, ))
fixef(tvkel = c(, 1, ))
stparm(Tin = tvTin * exp(nTin))
stparm(kel = tvkel * exp(nkel))
stparm(k = t<Tin? tvk* exp(nk):0)
ranef(diag(nTin, nk, nkel) = c(1, 1, 1))
}

It will produce a two-phase curve:

[attachment=3890:Ac.png]

Bernd

Ac.png
Ac.png1152×720 8.18 KB

5

Hi Berna,

Thank you for your quick reply. The code can execute. What is sequence{Ac=10}, is that for set an initial value? I would like to set initial value at time 0 from data. Is that possible? I attached input dataset to make you more clear.

Thanks,

Linda

6

Sequence{AC=0} sets the initial value for Ac, you are right.

You can read in values from a file with:

covariate(Ac0)

then you can read those in through:

sequence{Ac=Ac0}

Here is the output:

ac0.png
ac0.png1152×720 14.6 KB

7

Hi Berna,

Thank you so much. The initial question Q1 is solved.

However, when I check the fitted population parameters, I found a problem:

I used Monolix for this fitting before. They can support if else statement as

if t < Tin
ddt_Ac = k * Ac - kel * Ac
else
ddt_Ac = - kel * Ac

And I found our approach gets a smaller value of k. I am thinking whether because we have some timepoints setting k as 0. Whether we have another way for coding this?

Bests,
Linda

8

Hi Linda,

the implementation of if-else condition in Phoenix is just using a different syntax:

stparm(k = t<Tin? tvk* exp(nk):0)

means, that while time is smaller than Tin, the value of k is estimated, e.g. tvk. When time is greater or equal to Tin the value of k =0

When you look at the differential equation, the first term, k*Ac will be 0 when k=0:

deriv(Ac = kAc-kelAc)

Hope, this helps.

Bernd

9

Hi Bernd,

Thank you for your answer. I think if we set k =0 for phase 1, I will effect the population estimation value of k because theotically there should be no k value on phase1.

Thanks,

Linda