Sensitivity Analysis Results

Global sensitivity analysis uses Sobol indices computed via Saltelli’s sampling scheme. For each output of interest (e.g., steady-state ATP, PEM severity after standardized exertion), the first-order index \(S_i\) quantifies the fraction of output variance attributable to parameter \(\theta_i\) alone, and the total-order index \(S_{T i}\) includes contributions from all interactions involving \(\theta_i\):

\[ \begin{aligned} S_i &= \frac{\text{Var}(\mathbb{E}[Y | \theta_i])}{\text{Var}(Y)} \\ S_{T i} &= 1 - \frac{\text{Var}(\mathbb{E}[Y | \mathbf{\theta}_{\sim i}])}{\text{Var}(Y)} \end{aligned} \tag{1}\]

where \(\mathbf{\theta}_{\sim i}\) denotes all parameters except \(\theta_i\). A sample size of \(N(2p+2)\) model evaluations is required, where \(p\) is the number of parameters and \(N >= 1000\) for convergent estimates. For the full 42-variable model with approximately 60 parameters, this requires ~122,000 model evaluations—computationally feasible given the sub-second integration time per evaluation.

Parameters with \(S_{T i} < 0.01\) are classified as insensitive and can be fixed at nominal values without affecting model predictions. Parameters with \(S_i > 0.1\) are classified as influential and are prioritized for experimental measurement.