Getting this error. Can you please suggest any solution?
// Define functions for the 2-compartment ODE model
functions {
// Function defining the ODE system for amounts in compartments
// y[1]: amount in depot (for SC)
// y[2]: amount in central (Vc)
// y[3]: amount in peripheral (Vp)
// theta: parameters [CL, Vc, Vp, Q, ka]
// x_r: real data (not used in this ODE function, but required by signature)
// x_i: integer data (not used in this ODE function, but required by signature)
vector two_cmt_ode(real t, vector y, real[] theta, real[] x_r, int[] x_i) {
real current_CL = theta[1];
real current_Vc = theta[2];
real current_Vp = theta[3];
real current_Q = theta[4];
real current_ka = theta[5]; // Only used if depot has amount
// Add a small floor to volumes to prevent division by near-zero during integration
real safe_Vc = fmax(current_Vc, 1e-12); // Use 1e-12 or a similarly small positive number
real safe_Vp = fmax(current_Vp, 1e-12);
// Calculate concentrations in central and peripheral compartments
real conc_c = y[2] / safe_Vc; // Amount in central / Safe Volume of central
real conc_p = y[3] / safe_Vp; // Amount in peripheral / Safe Volume of peripheral
// Calculate rates of transfer and elimination
real rate_cl = current_CL * conc_c; // Elimination from central
real rate_q_out = current_Q * conc_c; // Transfer rate from central to peripheral
real rate_q_in = current_Q * conc_p; // Transfer rate from peripheral to central
real rate_abs = current_ka * y[1]; // Absorption rate from depot
// Rates of change for [Depot, Central, Peripheral]
vector[3] dydt = rep_vector(0.0, 3); // Correct syntax for declaring and initializing a sized vector
// Rate of change for Depot (only applies if there's drug in the depot)
dydt[1] = -rate_abs; // Drug leaves the depot by absorption
// Rate of change for Central compartment
dydt[2] = rate_abs // Absorption into central (if SC)
+ rate_q_in // Transfer from peripheral to central
- rate_q_out // Transfer from central to peripheral
- rate_cl; // Elimination from central
// Rate of change for Peripheral compartment
dydt[3] = rate_q_out - rate_q_in; // Transfer between central and peripheral
return dydt;
}
}
data {
int<lower=0> N; // Total number of observations (nIV + nSC)
int<lower=1> N_subjects; // Number of subjects
int<lower=1> N_drugs; // Number of drugs
int<lower=1, upper=N_subjects> subject[N]; // Subject index for each observation
int<lower=1, upper=N_drugs> drug[N]; // Drug index for each observation
int<lower=0, upper=1> route[N]; // Route (0 for IV, 1 for SC)
vector<lower=0>[N] time; // Time points for all observations
vector<lower=0>[N] conc; // Concentrations for all observations
vector<lower=0>[N] dose; // Dose for each observation (0 for non-dose points, actual dose for dose points)
vector<lower=0>[N_subjects] subject_wt; // Subject weight
real<lower=0> MEDWT; // <<-- Median weight (e.g., 70 kg)
// Remove ODE solver control parameters from data block
// They are moved to transformed data
}
transformed data {
// Declare and assign ODE solver control parameters here as fixed constants
real rel_tol = 1e-6;
real abs_tol = 1e-6;
int max_steps = 10000000; // Assign as integer literal (1e7)
}
parameters {
// Typical population parameters (log scale) for standard 2-cmt model
real log_CL; // Log of Typical elimination clearance
real log_Vc; // Log of Typical central volume
real log_Vp; // Log of Typical peripheral volume
real log_Q; // Log of Typical intercompartmental clearance
real log_ka; // Log of Absorption rate constant for SC
real<lower=0,upper=1> F; // Bioavailability for SC
real<lower=0,upper=100> sigma; // Residual error standard deviation (on log scale)
// Random effects (on log scale)
vector[N_drugs] eta_drug_CL;
vector[N_subjects] eta_subject_CL;
vector[N_drugs] eta_drug_Vc;
vector[N_subjects] eta_subject_Vc;
// Keep independent between-drug and between-subject Vp random effects
vector[N_drugs] eta_drug_Vp;
vector[N_subjects] eta_subject_Vp;
vector[N_drugs] eta_drug_Q; // Between-drug Q rand effects
vector[N_subjects] eta_subject_Q; // Between-subject Q rand effects
vector[N_drugs] eta_drug_ka; // Between-drug ka rand effects
vector[N_subjects] eta_subject_ka; // Between-subject ka rand effects
// Correlation structure (Expanded to include CL, Vc, Vp)
cholesky_factor_cov[3] L_drug_within_subject_cov; // Changed from [2] to [3] for CL, Vc, Vp
matrix[N_drugs, 3] z_drug_subject[N_subjects]; // Changed from [N_drugs, 2] to [N_drugs, 3]
// Covariate coefficients (on log scale) - Assuming weight on CL, Vc, and Vp
real beta_CL_WT;
real beta_Vc_WT;
real beta_Vp_WT; // Uncommented and added beta for Vp
// Add beta_Q_WT, beta_ka_WT priors if needed
}
transformed parameters {
// Population parameters (original scale)
real CL = exp(log_CL);
real Vc = exp(log_Vc);
real Vp = exp(log_Vp);
real Q = exp(log_Q);
real ka = exp(log_ka);
// Effective parameters for each observation
vector[N] CL_effective;
vector[N] Vc_effective;
vector[N] Vp_effective;
vector[N] Q_effective;
vector[N] ka_effective;
// Combined predictions for all observations
vector[N] pred_conc;
// Transform within-subject/drug deviates for CL, Vc, and Vp
vector[N_drugs] eta_drug_CL_within[N_subjects];
vector[N_drugs] eta_drug_Vc_within[N_subjects];
vector[N_drugs] eta_drug_Vp_within[N_subjects]; // Added within Vp
for (s in 1:N_subjects) {
for (d in 1:N_drugs) {
// Joint deviation vector now has size 3
vector[3] eta_drug_joint = L_drug_within_subject_cov * z_drug_subject[s, d]';
eta_drug_CL_within[s, d] = eta_drug_joint[1];
eta_drug_Vc_within[s, d] = eta_drug_joint[2];
eta_drug_Vp_within[s, d] = eta_drug_joint[3]; // Extract Vp component
}
}
// Calculate effective parameters for each observation
for (i in 1:N) {
real current_subject_wt = subject_wt[subject[i]];
real log_wt_ratio = log(current_subject_wt) - log(MEDWT);
// Effective CL (with all effects)
CL_effective[i] = CL * exp(eta_drug_CL[drug[i]] + eta_subject_CL[subject[i]] + eta_drug_CL_within[subject[i], drug[i]] + beta_CL_WT * log_wt_ratio);
// Effective Vc (with all effects)
Vc_effective[i] = Vc * exp(eta_drug_Vc[drug[i]] + eta_subject_Vc[subject[i]] + eta_drug_Vc_within[subject[i], drug[i]] + beta_Vc_WT * log_wt_ratio);
// Effective Vp (with all effects, including within Vp and weight)
// Combines population, between-drug, between-subject, within-subject/drug, and covariate effects
Vp_effective[i] = Vp * exp(eta_drug_Vp[drug[i]] + eta_subject_Vp[subject[i]] + eta_drug_Vp_within[subject[i], drug[i]] + beta_Vp_WT * log_wt_ratio);
// Effective Q and ka (with independent random effects, assuming no weight effect for now)
Q_effective[i] = Q * exp(eta_drug_Q[drug[i]] + eta_subject_Q[subject[i]]); // Add beta_Q_WT if needed
ka_effective[i] = ka * exp(eta_drug_ka[drug[i]] + eta_subject_ka[subject[i]]); // Add beta_ka_WT if needed
}
// --- Implement 2-Compartment Prediction using ODE Solver ---
// Solve ODEs for each observation point.
// This approach solves from t=0 for each observation, handling dose at t=0
// It's a simplification; a more accurate approach solves per subject with dose events at actual times.
for (i in 1:N) {
// Parameters for the ODE system: [CL, Vc, Vp, Q, ka]
real theta[5] = {CL_effective[i], Vc_effective[i], Vp_effective[i], Q_effective[i], ka_effective[i]};
// Integer data for ODE (not used by ODE function, but required by signature)
int x_i[1] = {0};
// Real data for ODE (not used by ODE function, but required by signature)
real x_r[1] = {0.0};
// Initial amounts at time 0: [Depot, Central, Peripheral]
// Add dose instantly to the target compartment at t=0 based on route and F for SC
real y0[3] = {0.0, 0.0, 0.0};
if (route[i] == 0) { // IV Bolus
y0[2] = dose[i]; // Add dose to Central (y[2])
} else { // SC
y0[1] = dose[i] * F; // Add dose*F to Depot (y[1])
}
// Solve ODE from time 0 up to observation time time[i]
// The solver returns amounts at the requested output times (only time[i] in this case)
real ts[1]; // Array of output times for the solver
ts[1] = time[i];
// amount_solution is a matrix: rows correspond to output times, columns to compartments
matrix[rows(ts), cols(y0)] amount_solution =
integrate_ode_bdf(two_cmt_ode, y0, 0.0, ts, theta, x_r, x_i,
rel_tol, abs_tol, max_steps);
// Extract amount in Central compartment at time[i]
// If time[i] == 0, amount_solution will contain y0
real amount_central_at_obs_time = amount_solution[1, 2];
// Calculate concentration (Mass/Volume)
// Need to handle potential division by zero if Vc_effective is extremely small (should be positive)
pred_conc[i] = amount_central_at_obs_time / Vc_effective[i];
// Check for non-positive or NaN predictions from ODE solver output
// This check helps identify problematic parameter values that lead to bad predictions
// A check in the model block likelihood is also recommended.
if (!is_finite(pred_conc[i])) {
target += -1e18; // Penalize non-finite predictions
} else if (pred_conc[i] < 0) {
target += -1e18; // Penalize negative predictions
}
}
// --- END OF ODE IMPLEMENTATION ---
}
model {
// Priors for typical log parameters (Normal, centered at log(median))
log_CL ~ normal(log(0.2), 1); // Prior for log of typical CL (elimination), median 0.2 L/time
log_Vc ~ normal(log(4), 1); // Prior for log of typical Vc (central), median 4 L
log_Vp ~ normal(log(10), 1); // Example Prior for log of typical Vp, median 10L
log_Q ~ normal(log(5), 1); // Example Prior for log of typical Q, median 5 L/time
log_ka ~ normal(log(0.4), 1); // Prior for log of typical ka, median 0.4 1/time
// Prior for bioavailability
F ~ beta(7, 3); // Example Beta prior centered around 0.7
// Prior for residual error
sigma ~ normal(0, 1); // Half-normal prior for sigma (due to lower=0 constraint)
// Priors for covariance structure (Expanded to include CL, Vc, Vp correlation)
L_drug_within_subject_cov ~ lkj_corr_cholesky(3); // Changed dimension
// Priors for raw deviates (CL, Vc, Vp)
for (s in 1:N_subjects) {
to_vector(z_drug_subject[s]) ~ std_normal(); // Applies to the new [N_drugs, 3] matrix
}
// Priors for independent random effects (Q, ka)
eta_drug_Q ~ normal(0, 0.5);
eta_subject_Q ~ normal(0, 0.5);
eta_drug_ka ~ normal(0, 0.5); // Prior for ka random effects
eta_subject_ka ~ normal(0, 0.5); // Prior for ka random effects
// Priors for between-drug and between-subject random effects (CL, Vc, Vp)
eta_drug_CL ~ normal(0, 0.5);
eta_subject_CL ~ normal(0, 0.5);
eta_drug_Vc ~ normal(0, 0.5);
eta_subject_Vc ~ normal(0, 0.5);
eta_drug_Vp ~ normal(0, 0.5); // Prior for between-drug Vp
eta_subject_Vp ~ normal(0, 0.5); // Prior for between-subject Vp
// Priors for covariate coefficients (CL, Vc, Vp)
beta_CL_WT ~ normal(0, 0.5);
beta_Vc_WT ~ normal(0, 0.5);
beta_Vp_WT ~ normal(0, 0.5); // Prior for weight effect on Vp
// Likelihood for ALL data (using combined prediction vector)
for (i in 1:N) {
if (time[i] > 0) { // Only include observations after time 0 in likelihood
// Check if prediction is positive before taking log
// A robust ODE solver implementation should ideally not return non-positive for positive time.
// This check penalizes problematic predictions during sampling.
if (!is_finite(pred_conc[i]) || pred_conc[i] <= 0) {
target += -1e18; // Add a large penalty for non-positive prediction
} else {
conc[i] ~ lognormal(log(pred_conc[i]), sigma);
}
}
}
}
generated quantities {
// Declare vectors and arrays for output
vector[N] pred_conc_subj_drug; // Combined posterior predictive concentrations
int subject_output[N]; // Subject indices for combined output
int drug_output[N]; // Drug indices for combined output
int route_output[N]; // Route for combined output
vector[N] time_output; // Time for combined output
vector[N] dose_output; // Dose for combined output
vector[N] conc_output; // Observed concentration for combined output
// Effective parameters for output
vector[N] effective_CL_output = CL_effective;
vector[N] effective_Vc_output = Vc_effective;
vector[N] effective_Vp_output = Vp_effective;
vector[N] effective_Q_output = Q_effective;
vector[N] effective_ka_output = ka_effective;
// Typical parameters for output
real typical_CL = exp(log_CL);
real typical_Vc = exp(log_Vc);
real typical_Vp = exp(log_Vp);
real typical_Q = exp(log_Q);
real typical_ka = exp(log_ka);
// Weight-related quantities (combined size)
vector[N] obs_wt;
vector[N] obs_log_wt_ratio;
vector[N] obs_CL_wt_factor;
vector[N] obs_Vc_wt_factor;
vector[N] obs_Vp_wt_factor; // Added weight factor for Vp
// Loop to populate weight-related outputs
for (i in 1:N) {
real current_subject_wt = subject_wt[subject[i]];
real log_wt_ratio = log(current_subject_wt) - log(MEDWT);
obs_wt[i] = current_subject_wt;
obs_log_wt_ratio[i] = log_wt_ratio;
obs_CL_wt_factor[i] = exp(beta_CL_WT * log_wt_ratio);
obs_Vc_wt_factor[i] = exp(beta_Vc_WT * log_wt_ratio);
obs_Vp_wt_factor[i] = exp(beta_Vp_WT * log_wt_ratio); // Calculate Vp weight factor
}
// Generate posterior predictive samples and store original data/indices
for (i in 1:N) {
subject_output[i] = subject[i];
drug_output[i] = drug[i];
route_output[i] = route[i];
time_output[i] = time[i];
dose_output[i] = dose[i];
conc_output[i] = conc[i]; // Store observed concentration
if (time[i] > 0) {
// Use the pred_conc calculated in transformed parameters
if (!is_finite(pred_conc[i]) || pred_conc[i] <= 0) {
pred_conc_subj_drug[i] = -99.0; // Indicate problematic prediction
} else {
pred_conc_subj_drug[i] = lognormal_rng(log(pred_conc[i]), sigma);
}
} else {
// Indicator for time <= 0 points
pred_conc_subj_drug[i] = -99.0;
}
}
}
```
> # Compile and fit the Stan model
> compiled_model <- cmdstan_model(write_stan_file(stan_model_code))
SYNTAX ERROR, MESSAGE(S) FROM PARSER:
Variable "real" does not exist.
error in '/tmp/Rtmp1s9jms/model-3fc52455e4d9.stan' at line 196, column 9
-------------------------------------------------
194: // Solve ODE from time 0 up to observation time time[i]
195: // The solver returns amounts at the requested output times (only time[i] in this case)
196: real ts[1]; // Array of output times for the solver
^
197: ts[1] = time[i];
-------------------------------------------------