N.I.M.R.O.D.  

PK1 : One-Compartment Pharmacokinetic model with absorption

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Model used in : M. Prague, C. Commenges, J. Guedj, J. Drylewicz and R. Thiebaut. NIMROD: A Program for Inference via Normal Approximation of the Posterior in Models with Random effects based on Ordinary Differential Equations. (Submitted)

-----> Download here : PK1.zip

Mathematical model (ode.f90)

PK1.png

\[ \frac{d A_{GI}(t)}{dt}=-k_a A_{GI} \]

\[ \frac{d C_{P}(t)}{dt}= \frac{k_a}{V_0} A_{GI} - k_e C_P \]

with

\[ A_{GI}(0)=Dose(0) \]

\[ C_P(0)=0 \]

Observational model (observationModelSpe.f90)

\[ Y^i_{1}(t_{ij})=C_P^i(X^i(t_{ij}))+\epsilon_{ij1}, \qquad \epsilon_{ij1}\sim \mathcal{N}\left(0,\sigma^2_{C_P}\right). \nonumber \]

Statistical model (parameterTransformation.f90)

All parameters are observed in log transformation. There is no additional covariates.

Data (inAndOutUser.f90 / pk.txt)

Data must be in this shape : "id" "time" "Cp" "dose(t=0)" (See the pk.txt file) If user want to account for multiple dosing, program must be modified. The input file used in this example is constituted of simulated data with :

\[\tilde{k}_a=log(k_a)=-4.60\]

\[\tilde{k}_e=log(k_e)=-5.56\]

\[\tilde{V}_0=log(V_0)=-4.19\]

\[\sigma_{k_a}=0.20\]

\[\sigma_{k_e}=0.25\]

\[\sigma_{V_0}=0.10\]

\[\sigma_{C_P}=0.3\]

Priors (Input.txt)

Priors are choosen in accordance with the litterature with rather small standard deviation for V0 to avoid the flip-flop paradox.

\[\tilde{k}_a\sim \mathcal{N}(-4.5;0.1)\]

\[\tilde{k}_e\sim \mathcal{N}(-6.0;5.0)\]

\[\tilde{V}_0\sim \mathcal{N}(-4.6;5.0)\]

\[\sigma_{k_a}\sim half-Cauchy(s=1.0)\]

\[\sigma_{k_e}\sim half-Cauchy(s=1.0)\]

\[\sigma_{V_0}\sim half-Cauchy(s=1.0)\]

\[\sigma_{C_P}\sim Jeffrey's\]

Results