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update poppk model example #45

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100 changes: 59 additions & 41 deletions example-models/twocpt_population/twocpt_population.stan
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Original file line number Diff line number Diff line change
Expand Up @@ -10,30 +10,30 @@ functions {
real V1 = parms[3];
real V2 = parms[4];
real ka = parms[5];

// Re-parametrization
real k10 = CL / V1;
real k12 = Q / V1;
real k21 = Q / V2;

// Return object (derivative)
vector[3] y; // 1 element per compartment of
// the model

// PK component of the ODE system
y[1] = -ka * x[1];
y[2] = ka * x[1] - (k10 + k12) * x[2] + k21 * x[3];
y[3] = k12 * x[2] - k21 * x[3];

return y;
}
}
data {
int<lower=1> np; /* population size */
int<lower=1> nt; // number of events
int<lower=1> nt; // num ber of events per subj, assuming all subj have same number of events
int<lower=1> nObs; // number of observations
array[nObs] int<lower=1> iObs; // index of observation

// NONMEM data
array[np * nt] int<lower=1> cmt;
array[np * nt] int evid;
Expand All @@ -43,23 +43,20 @@ data {
array[np * nt] real time;
array[np * nt] real rate;
array[np * nt] real ii;

array[np * nObs] real<lower=0> cObs; // observed concentration (dependent variable)
}
transformed data {
array[np * nObs] real logCObs;
array[np] int<lower=1> len;
array[np] int<lower=1> len_theta;
array[np] int<lower=1> len_biovar;
array[np] int<lower=1> len_tlag;


int nTheta = 5; // number of parameters
int nCmt = 3; // number of compartments
array[np * nt, nCmt] real biovar;
array[np * nt, nCmt] real tlag;

logCObs = log(cObs);

for (id in 1 : np) {
for (j in 1 : nt) {
for (i in 1 : nCmt) {
Expand All @@ -68,45 +65,59 @@ transformed data {
}
}
len[id] = nt;
len_theta[id] = nt;
len_biovar[id] = nt;
len_tlag[id] = nt;
}
}

parameters {
array[np] real<lower=0> CL;
array[np] real<lower=0> Q;
array[np] real<lower=0> V1;
array[np] real<lower=0> V2;
array[np] real<lower=0> ka;
array[np] real<lower=0> sigma;
// population mean
real<lower=0> CL;
real<lower=0> Q;
real<lower=0> V1;
real<lower=0> V2;
real<lower=0> ka;

// residual error
real<lower=0> sigma;

// inter-individual variance scale
vector<lower=0>[nTheta] tau;

// cholesky decompositino of inter-individual correlation
cholesky_factor_corr[nTheta] L_Omega;

matrix[nTheta, np] z;
}

transformed parameters {
array[np * nt, nTheta] real theta;
vector[nTheta] theta_pop;
matrix[nTheta, np] theta_dev;
array[np, nTheta] real theta_subj;
array[np] vector<lower=0>[nt] cHat;
array[np * nObs] real<lower=0> cHatObs;
matrix[3, nt * np] x;

matrix[nCmt, nt * np] x;

theta_pop = [CL, Q, V1, V2, ka]';
theta_dev = diag_pre_multiply(tau, L_Omega) * z;


for (id in 1 : np) {
theta_subj[id, ] = to_array_1d(theta_pop + theta_dev[, id]);
for (it in 1 : nt) {
theta[(id - 1) * nt + it, 1] = CL[id];
theta[(id - 1) * nt + it, 2] = Q[id];
theta[(id - 1) * nt + it, 3] = V1[id];
theta[(id - 1) * nt + it, 4] = V2[id];
theta[(id - 1) * nt + it, 5] = ka[id];
theta[(id - 1) * nt + it, ] = theta_subj[id, ];
}
}

x = pmx_solve_group_bdf(twoCptModelODE, 3, len,
time, amt, rate, ii, evid, cmt, addl, ss,
theta, biovar, tlag);

for (id in 1 : np) {
for (j in 1 : nt) {
cHat[id][j] = x[2, (id - 1) * nt + j] ./ V1[id];
cHat[id][j] = x[2, (id - 1) * nt + j] ./ theta_subj[id, 3];
}
}

for (id in 1 : np) {
for (i in 1 : nObs) {
cHatObs[(id - 1) * nObs + i] = cHat[id][iObs[i]]; // predictions for observed data records
Expand All @@ -115,17 +126,24 @@ transformed parameters {
}
model {
// informative prior
CL ~ lognormal(log(10), 0.25);
Q ~ lognormal(log(15), 0.5);
V1 ~ lognormal(log(35), 0.25);
V2 ~ lognormal(log(105), 0.5);
ka ~ lognormal(log(2.5), 1);
sigma ~ cauchy(0, 1);

to_vector(z) ~ std_normal();

// non-informative prior
L_Omega ~ lkj_corr_cholesky(2);
tau ~ cauchy(0, 2);

// likelihood
for (id in 1 : np) {
CL[id] ~ lognormal(log(10), 0.25);
Q[id] ~ lognormal(log(15), 0.5);
V1[id] ~ lognormal(log(35), 0.25);
V2[id] ~ lognormal(log(105), 0.5);
ka[id] ~ lognormal(log(2.5), 1);
sigma[id] ~ cauchy(0, 1);

for (i in 1 : nObs) {
logCObs[(id - 1) * nObs + i] ~ normal(log(cHatObs[(id - 1) * nObs + i]),
sigma[id]);
sigma);
}
}
}