Dual absorption 2 CMT model fitting error

1

Hello. I have been working on another model, with double absorption (KA1 and KA2) and two compartments. However, I get an error that has caused me problems before. The classic error of gradient = 0 and that a certain parameter is not identified.

OUTPUT: [ Info: Checking the initial parameter values.
[ Info: The initial negative log likelihood and its gradient are finite. Check passed.
Iter Function value Gradient norm
0 1.568802e+03 3.380961e+03

  • time: 0.0010001659393310547
    ERROR: gradient is exactly zero in tvlag. This indicates that tvlag isn’t identified.

MY MODEL:
mymodel = @model begin

@param begin
    tvcl ∈ RealDomain(lower=0)
    tvv ∈ RealDomain(lower=0)
    tvka1 ∈ RealDomain(lower=0.001)
    tvka2 ∈ RealDomain(lower=0)
    tvq ∈ RealDomain(lower=0)
    tvvp ∈ RealDomain(lower=0)
    tvlag ∈ RealDomain(lower=0)
    tvbio ∈ RealDomain(lower=0)
    Ω ∈ PDiagDomain(5)
    σ ∈ RealDomain(lower = 0.0001)
end

@random begin
    η ~ MvNormal(Ω)
end

@pre begin
    CL = tvcl*exp(η[1])
    Vc  = tvv*exp(η[2])
    Ka1 = tvka1*exp(η[3])
    Ka2 = tvka2*exp(η[4])
    lags = (SR = tvlag,)
    bioav = (IR = tvbio*exp(η[5]), SR = 1-tvbio*exp(η[5]))
    Q   = tvq
    Vp = tvvp
end

@dynamics begin
    IR'      = -Ka1*IR
    SR'      = -Ka2*SR
    Central' =  Ka1*IR + Ka2*SR - Central*CL/Vc - (Q/Vc)*Central + (Q/Vp)*Peripheral
    Peripheral' = (Q/Vc)*Central - (Q/Vp)*Peripheral
end

@derived begin
conc := @. Central/Vc
dv ~ @. Normal(conc, σ*abs(conc))
end

end

param = (
tvcl = 5, tvv = 50, tvka1 = 0.8, tvka2 = 0.6, tvlag = 1000, tvbio = 0.5,tvq=10,tvvp=100,
Ω = Diagonal([0.1,0.1,0.4,0.4,0.1]),
σ = 0.1
)

fit_results = fit(mymodel, pop, param, Pumas.FOCE())

2

Dear @chrisv

lags and bioav should go into the @dosecontrol block. So, please re-write your code this way


@pre begin
    CL = tvcl*exp(η[1])
    Vc  = tvv*exp(η[2])
    Ka1 = tvka1*exp(η[3])
    Ka2 = tvka2*exp(η[4])
    Q   = tvq
    Vp = tvvp
end

@dosecontrol begin
    lags = (SR = tvlag,)
    bioav = (IR = tvbio*exp(η[5]), SR = 1-tvbio*exp(η[5]))
end

you can read more in the documentation here

3

Thank you for your help! I have changed the code as I show below:

mymodel = @model begin

@param begin
    tvcl ∈ RealDomain(lower=0)
    tvv ∈ RealDomain(lower=0)
    tvka1 ∈ RealDomain(lower=0)
    tvka2 ∈ RealDomain(lower=0)
    tvq ∈ RealDomain(lower=0)
    tvvp ∈ RealDomain(lower=0)
    tvlag ∈ RealDomain(lower=0)
    tvbio ∈ RealDomain(lower=0)
    Ω ∈ PDiagDomain(5)
    σ ∈ RealDomain(lower = 0.0001)
end

@random begin
    η ~ MvNormal(Ω)
end

@pre begin
    CL = tvcl*exp(η[1])
    Vc  = tvv*exp(η[2])
    Ka1 = tvka1*exp(η[3])
    Ka2 = tvka2*exp(η[4])
    Q   = tvq
    Vp = tvvp
end

@dosecontrol begin
    lags = (SR = tvlag,)
    bioav = (IR = tvbio*exp(η[5]), SR = 1-tvbio*exp(η[5]))
end

@dynamics begin
    IR'      = -Ka1*IR
    SR'      = -Ka2*SR
    Central' =  Ka1*IR + Ka2*SR - Central*CL/Vc - (Q/Vc)*Central + (Q/Vp)*Peripheral
    Peripheral' = (Q/Vc)*Central - (Q/Vp)*Peripheral
end

@derived begin
conc := @. Central/Vc
dv ~ @. Normal(conc, σ*abs(conc))
end

end

Then I used my model, population and parameters to fit:
param = (
tvcl = 5, tvv = 50, tvka1 = 0.8, tvka2 = 0.6, tvlag = 1000, tvbio = 0.5,tvq=10,tvvp=100,
Ω = Diagonal([0.1,0.1,0.4,0.4,0.1]),
σ = 0.1
)

fit_results = fit(mymodel, pop, param, Pumas.FOCE())

Finally, I get the same error but now in KA2:
gradient is exactly zero in tvka2. This indicates that tvka2 isn’t identified.

4

Isn’t this particular initial value of tvlag too big?
What happens if you fit with something lower, e.g. 5?