Function calculate_cost 

pub fn calculate_cost(
    problem: &BestDoseProblem,
    candidate_doses: &[f64],
) -> Result<f64>

Calculate cost function for a candidate dose regimen

This is the core objective function minimized by the Nelder-Mead optimizer during Stage 2 of the BestDose algorithm.

Arguments

• problem - The BestDoseProblem containing all necessary data
• candidate_doses - Dose amounts to evaluate (only for optimizable doses)

Returns

The cost value (1-λ) × Variance + λ × Bias² for the candidate doses. Lower cost indicates better match to targets.

Dose Masking

Only doses with amount == 0.0 in the target subject are considered optimizable. Doses with non-zero amounts remain fixed at their specified values.

The candidate_doses parameter contains only the optimizable doses, which are substituted into the target subject before simulation

Cost Function Details

Variance Term

Expected squared prediction error using posterior weights:

Variance = Σᵢ P(θᵢ|data) × Σⱼ (target[j] - pred[i,j])²

For each support point θᵢ:

1. Simulate model with candidate doses
2. Calculate squared error at each observation time j
3. Weight by posterior probability P(θᵢ|data)

Bias Term

Squared deviation from population mean:

Bias² = Σⱼ (target[j] - E[pred[j]])²
where E[pred[j]] = Σᵢ P(θᵢ) × pred[i,j]  (prior weights)

The population mean uses prior weights, not posterior weights, to represent population-typical behavior independent of patient-specific data.

Target Types

• Concentration (Target::Concentration): Predictions are concentrations at observation times

• AUC ([Target::AUC]): Predictions are cumulative AUC values calculated via trapezoidal rule on a dense time grid (controlled by settings.predictions().idelta)

Example

// Internal use by optimizer
let cost = calculate_cost(&problem, &[100.0, 150.0])?;

Errors

Returns error if:

• Model simulation fails
• Prediction length doesn’t match observation count
• AUC calculation fails (for AUC targets)