Function calculate_interval_auc_per_observation 

pub fn calculate_interval_auc_per_observation(
    subject: &Subject,
    dense_times: &[f64],
    dense_predictions: &[f64],
    obs_times: &[f64],
) -> Vec<f64>

Calculate interval AUC for each observation independently

For each observation at time t_i, calculates AUC from the last dose before t_i to t_i. This is useful for calculating dosing interval AUC (AUCτ) in steady-state scenarios.

Arguments

• subject - Subject with doses and observations
• dense_times - Complete dense time grid covering all observations
• dense_predictions - Concentration predictions at dense_times
• obs_times - Observation times where interval AUC should be calculated

Returns

Vector of interval AUC values, one per observation

Algorithm

For each observation time:

1. Find the most recent dose (bolus or infusion) before that observation
2. Locate that dose time in the dense grid
3. Apply trapezoidal rule from dose time to observation time
4. Return the interval AUC

Example

let subject = Subject::builder("patient")
    .bolus(0.0, 100.0, 0)      // First dose
    .bolus(12.0, 100.0, 0)     // Second dose
    .observation(24.0, 200.0, 0)  // Want AUC from t=12 to t=24
    .build();

// Dense grid from 0 to 24 hours
let dense_times = vec![0.0, 1.0, 2.0, ..., 24.0];
let dense_predictions = simulate_at_dense_times(...);
let obs_times = vec![24.0];

let interval_aucs = calculate_interval_auc_per_observation(
    &subject, &dense_times, &dense_predictions, &obs_times
);
// interval_aucs[0] contains AUC from 12.0 to 24.0