# How translate the individual model equation obtained in Monolix into Pumas

**URL:** <https://discourse.pumas.ai/t/how-translate-the-individual-model-equation-obtained-in-monolix-into-pumas/1010>\
**Category:** maximum-likelihood\
**Created:** [April 10, 2024, 12:26am UTC](https://discourse.pumas.ai/t/how-translate-the-individual-model-equation-obtained-in-monolix-into-pumas/1010 "2024-04-10T00:26:33Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![anafunguetto](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/anafunguetto/32/455_2.png) [@anafunguetto](https://discourse.pumas.ai/u/anafunguetto)\
**Post date:** [April 10, 2024, 12:26am UTC](https://discourse.pumas.ai/t/how-translate-the-individual-model-equation-obtained-in-monolix-into-pumas/1010/1 "2024-04-10T00:26:33Z")

</div>

Hi!  
Would anyone help me translate the individual model equation obtained in Monolix into Pumas language? FC is my categorical covariable and the dose was given by iv.

```auto
[individual model – Model monolix]
log(Cl) = log(Cl_pop) + beta_Cl_FC_2*[FC = 2] + eta_Cl
log(V1) = log(V1_pop) + beta_V1_FC_2*[FC = 2] + eta_V1
log(Q) = log(Q_pop) + beta_Q_FC_2*[FC = 2] + eta_Q
log(V2) = log(V2_pop)

```

I tried to do this using the IF/ELSE command, based on pumas documentation, but some Gofs didn’t look good. In this case dFC2dcl sounds like beta values in monolix, right?

[Pumas model, 2 cmt model]

```auto
mdl_2cmp_prop = @ model begin
        @ param begin
            # model parameters
            tvcl ∈ RealDomain(lower = 0.001)
            tvv ∈ RealDomain(lower = 0.001)
            tvvp ∈ RealDomain(lower = 0.001)
            tvq ∈ RealDomain(lower = 0.001)
            Ω ∈ PDiagDomain(3)
            σ ∈ RealDomain(lower = 0.001)   
            dFC1dcl ∈ RealDomain(lower = 0.001) # FC effect on parameter
            dFC2dcl ∈ RealDomain(lower = 0.001)
            dFC1dv ∈ RealDomain(lower = 0.001)
            dFC2dv ∈ RealDomain(lower = 0.001)
            dFC1dq ∈ RealDomain(lower = 0.001)
            dFC2dq ∈ RealDomain(lower = 0.001)

        end
      @ pre begin
#https://tutorials.pumas.ai/html/introduction/covariate.html#categorical-covariates
            CL = if FC == 1
                tvcl * exp(η[1]) * dFC1dcl 
            elseif FC == 2
                tvcl * exp(η[1]) * dFC2dcl 
            end
    
            Vc = if FC == 1
                tvv * exp(η[2]) * dFC1dv 
            elseif FC == 2
                tvv * exp(η[2]) * dFC2dv 
            end
    
            Q = if FC == 1
                tvq * exp(η[3]) * dFC1dq 
            elseif FC == 2
               tvq * exp(η[3]) * dFC2dq  
            end
            Vp = tvvp

        end

```

I appreciate it!

---

<div class="post-metadata">

**Author:** ![vijay](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/vijay/32/96_2.png) [@vijay](https://discourse.pumas.ai/u/vijay)\
**Post date:** [April 10, 2024, 2:05am UTC](https://discourse.pumas.ai/t/how-translate-the-individual-model-equation-obtained-in-monolix-into-pumas/1010/2 "2024-04-10T02:05:04Z")

</div>

Dear @anafunguetto - welcome to the Pumas community. Glad to help you.

While your approach should work, you could start with a one to one translation of your monolix code and use something like this below.

```julia

@param begin
    ....
    beta_Cl_FC_2 in RealDomain()
    beta_V1_FC_2 in RealDomain()
    beta_Q_FC_2 in RealDomain()
    ....
end
@pre begin
    Cl = Cl_pop * beta_Cl_FC_2*(FC == 2) * exp(eta_Cl)
    V1 = V1_pop * beta_V1_FC_2*(FC == 2) * exp(eta_V1)
    Q = Q_pop * beta_Q_FC_2*(FC == 2) * exp(eta_Q)
    V2 = V2_pop
end

```

This means that `Cl_pop` is the population value of clearance for `FC==1`, `V1_pop` is the population value of volume for `FC==1` etc. Correspondingly `beta_Cl_FC_2` is the multiplicative difference in population clearance between `FC==1` and `FC==2`

Let me know if that is clear.

---

<div class="post-metadata">

**Author:** ![anafunguetto](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/anafunguetto/32/455_2.png) [@anafunguetto](https://discourse.pumas.ai/u/anafunguetto)\
**Post date:** [April 10, 2024, 6:05pm UTC](https://discourse.pumas.ai/t/how-translate-the-individual-model-equation-obtained-in-monolix-into-pumas/1010/3 "2024-04-10T18:05:14Z")

</div>

Thank you for your time! I did it, but now I have this error message in maximum LL estimation:

"ERROR: DomainError with Inf:  
The initial parameter values cause a negative log likelihood of Inf. This can be due to model mis-specification or bad initial parameter values.

Stacktrace:

1. `_optim_check_initial_values(costf::Pumas.var"#621#625"{PumasModel{(tvcl = 1, tvv = 1, tvvp = 1, tvq = 1, Ω = 3, σ = 1, beta_Cl_FC_2 = 1, beta_V1_FC_2 = 1, beta_Q_FC_2 = 1), 3, (:Central, :Peripheral), (Symbol("##A##"), Symbol("##b##")), ParamSet{NamedTuple{(:tvcl, :tvv, :tvvp, :tvq, :Ω, :σ, :beta_Cl_FC_2, :beta_V1_FC_2, :beta_Q_FC_2), Tuple{RealDomain{Float64, TransformVariables.Infinity{true}, Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}, PDiagDomain{PDMats.PDiagMat{Float64, Vector{Float64}}}, RealDomain{Float64, TransformVariables.Infinity{true}, Float64}, RealDomain{Int64, TransformVariables.Infinity{true}, Int64}, RealDomain{Int64, TransformVariables.Infinity{true}, Int64}, RealDomain{Int64, TransformVariables.Infinity{true}, Int64}}}}, var"#81#88", Pumas.TimeDispatcher{var"#82#89", var"#83#90"}, Nothing, var"#85#92", Pumas.LinearODE, var"#86#93", var"#87#94", ModelingToolkit.ODESystem, Pumas.PumasModelOptions}, Vector{Subject{NamedTuple{(:DV,), Tuple{Vector{Union{Missing, Float64}}}}, Pumas.ConstantCovar{NamedTuple{(:FC,), Tuple{Int64}}}, Vector{Pumas.Event{Float64, Float64, Float64, Float64, Float64, Float64, Int64}}, Vector{Float64}}}, FOCE{Optim.NewtonTrustRegion{Float64}, Optim.Options{Float64, Nothing}}, EnsembleThreads, NamedTuple{(), Tuple{}}, TransformVariables.TransformTuple{NamedTuple{(:tvcl, :tvv, :tvvp, :tvq, :Ω, :σ, :beta_Cl_FC_2, :beta_V1_FC_2, :beta_Q_FC_2), Tuple{TransformVariables.ShiftedExp{true, Float64}, TransformVariables.ShiftedExp{true, Float64}, TransformVariables.ShiftedExp{true, Float64}, TransformVariables.ShiftedExp{true, Float64}, Pumas.PDiagTransform, Vararg{TransformVariables.ShiftedExp{true, Float64}, 4}}}}, Vector{Vector{Float64}}, Vector{Vector{Float64}}, Vector{Float64}}, vparam::Vector{Float64}, verbose::Bool)` at likelihoods.jl"

I guess It is because of my initial values, so a changed but it didn’t work.  
I’m working on this code now:

mdl\_2cmp\_prop = @ model begin  
@ param begin  
# Parâmetros do modelo  
tvcl ∈ RealDomain(lower = 0.001)  
tvv ∈ RealDomain(lower = 0.001)  
tvvp ∈ RealDomain(lower = 0.001)  
tvq ∈ RealDomain(lower = 0.001)  
Ω ∈ PDiagDomain(3)  
σ ∈ RealDomain(lower = 0.001)  
beta\_Cl\_FC\_2 in RealDomain(lower = -100)  
beta\_V1\_FC\_2 in RealDomain(lower = -100)  
beta\_Q\_FC\_2 in RealDomain(lower = -100)

@ random begin  
η ~ MvNormal(Ω)  
end

```
    @ covariates FC

    @ pre begin
        # https://tutorials.pumas.ai/html/introduction/covariate.html#categorical-covariates
        CL = tvcl * beta_Cl_FC_2*(FC == 2) * exp(η[1])
        Vc = tvv * beta_V1_FC_2*(FC == 2) * exp(η[2])
        Q = tvq * beta_Q_FC_2*(FC == 2) * exp(η[3])
        Vp = tvvp

    end

    @ dynamics begin
        # https://docs.pumas.ai/stable/model_components/dynamical_types/
        Central' = -(CL+Q)/Vc*Central + Q/Vp*Peripheral
        Peripheral' = Q/Vc*Central - Q/Vp*Peripheral

    end

    @ derived begin
        # https://docs.pumas.ai/stable/model_components/error_models/
        cp := @. Central / Vc
        DV ~ @. Normal(cp, cp * σ)
    end 
end

```

#initial estimates values  
params\_2cmp\_prop = (  
tvcl = 7119.54,  
tvv = 1795.2,  
tvq = 3471.5,  
Ω = Diagonal([0.1, 0.1, 0.1]),  
tvvp =7124.9,  
σ = 0.1,  
beta\_Cl\_FC\_2 = 1,  
beta\_V1\_FC\_2 = 1,  
beta\_Q\_FC\_2 = 1,  
)

# maximum likelihood estimation

pkfit\_2cmp\_prop= fit(mdl\_2cmp\_prop, pop1, params\_2cmp\_prop, Pumas.FOCE())

thank you!

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/mohamed82008/32/127_2.png) [@mohamed82008](https://discourse.pumas.ai/u/mohamed82008)\
**Post date:** [May 10, 2024, 4:52am UTC](https://discourse.pumas.ai/t/how-translate-the-individual-model-equation-obtained-in-monolix-into-pumas/1010/4 "2024-05-10T04:52:23Z")

</div>

> [@vijay](#):
>
> ```auto
> Cl = Cl_pop * beta_Cl_FC_2*(FC == 2) * exp(eta_Cl)
> V1 = V1_pop * beta_V1_FC_2*(FC == 2) * exp(eta_V1)
> Q = Q_pop * beta_Q_FC_2*(FC == 2) * exp(eta_Q)
> 
> ```

Can you try it with this instead?

```julia
    Cl = Cl_pop * exp(beta_Cl_FC_2*(FC == 2)) * exp(eta_Cl)
    V1 = V1_pop * exp(beta_V1_FC_2*(FC == 2)) * exp(eta_V1)
    Q = Q_pop * exp(beta_Q_FC_2*(FC == 2)) * exp(eta_Q)

```