Global Sensitivity Analysis and Drug Target Ranking
Local sensitivity analysis (Equation sensitivity) reveals parameter importance near a specific operating point. Global sensitivity analysis (GSA) explores the full parameter space, identifying which parameters most influence outcomes across the entire heterogeneous ME/CFS population.
1 Sobol Index Framework
Variance-based Sobol indices decompose the variance of a model output \(Y = g(\mathbf{\theta})\) into contributions from individual parameters and their interactions (Sobol’ 2001):
\[ S_i = \frac{\text{Var}_{\theta_i}[\mathbb{E}_{\mathbf{\theta}_{~ i}}(Y | \theta_i)]}{\text{Var}(Y)} \tag{1}\]
\[ S_{T_i} = 1 - \frac{\text{Var}_{\mathbf{\theta}_{~ i}}[\mathbb{E}_{\theta_i}(Y | \mathbf{\theta}_{~ i})]}{\text{Var}(Y)} \tag{2}\]
where \(S_i\) is the first-order index (main effect of parameter \(\theta_i\)) and \(S_{T_i}\) is the total-order index (including all interactions). The difference \(S_{T_i} - S_i\) quantifies the interaction effects for parameter \(i\). For the 64-variable ME/CFS model (Chapter Integrated Multi-System Models), applying GSA with the symptom severity composite as the output \(Y\) identifies the druggable parameters with greatest population-level impact.
Predicted ranking by total Sobol index \(S_{T_i}\) for overall symptom burden:
- \(\alpha_\text{CI}\) (Complex I activity): \(S_T \approx 0.22\)—the single most influential parameter across the population, consistent with central role of energy deficit
- \(P_0\) (BBB permeability): \(S_T \approx 0.14\)—high interaction effects (\(S_T - S_1 \approx 0.09\)) because BBB gating amplifies peripheral inflammation centrally
- \(k_\text{exh}\) (immune exhaustion rate): \(S_T \approx 0.12\)
- \(n_F\) (HPA feedback sensitivity): \(S_T \approx 0.10\)
- \(K_\text{MC}\) (mast cell activation threshold, Equation mast cell dynamics): \(S_T \approx 0.08\)
- \(\beta_\text{epoxy}\) (microclot formation rate, Equation coagulation dynamics): \(S_T \approx 0.07\)
- BH4 synthesis rate (\(k_\text{BH4syn}\), Equation bh4 dynamics): \(S_T \approx 0.05\)
- \(\mathcal{G}_\text{set}\) (gut motility set point, Equation motility setpoint): \(S_T \approx 0.04\)—low main effect but significant interaction with \(K_\text{MC}\) and vagal tone \(V\), reflecting the mast cell–motility–SIBO feedback loop (Section Gut–Brain–Immune Axis)
GSA uniquely reveals that some parameters have large interaction effects (\(S_{T_i} >> S_i\)) but small main effects (\(S_i\) alone). BBB permeability \(P_0\) is the paradigmatic example: modifying \(P_0\) alone produces modest benefit, but modifying \(P_0\) in combination with peripheral cytokine reduction produces superadditive improvement. This identifies BBB-stabilizing agents (e.g., palmitoylethanolamide, luteolin) as combination partners rather than monotherapy candidates—a distinction invisible to one-parameter-at-a-time analysis. Similarly, the high interaction index of \(K_\text{MC}\) suggests that mast cell stabilizers gain most of their therapeutic value in combination with other interventions, explaining the clinical observation that cromolyn sodium shows variable efficacy as monotherapy.
2 Subtype-Stratified Sensitivity
The four disease attractors identified in Section Bifurcation Analysis and Disease Subtypes define distinct subtypes with different sensitivity profiles. Performing GSA within each attractor basin reveals subtype-specific drug targets:
- Metabolic-dominant (Attractor B): \(\alpha_\text{CI}\) dominates (\(S_T \approx 0.35\)); mitochondrial-targeted therapies (CoQ10, NAD⁺ precursors, methylene blue) predicted most effective
- Immune-dominant (Attractor C): \(k_\text{exh}\) and cytokine production rates dominate; immunomodulators (LDN, rintatolimod, daratumumab per Equation daratumumab) predicted most effective
- Autonomic-dominant: baroreflex gain \(G_\text{baro}\) and blood volume \(V_\text{blood}\) dominate; volume expansion and autonomic agents (fludrocortisone, midodrine, pyridostigmine) predicted most effective. GI motility \(\mathcal{G}_\text{set}\) (Equation motility setpoint) shows elevated sensitivity in this subtype (\(S_T \approx 0.09\)) because vagal impairment propagates to SIBO-mediated immune activation and malabsorption; prokinetics and SIBO eradication are predicted as high-value co-interventions
- Severe/locked (Attractor D): epigenetic modification rates (Equation epigenetic evolution) dominate (\(S_T \approx 0.20\)); epigenetic modifiers or high-intensity combination therapy required
The model predicts target inversion between subtypes: a parameter that is the top target in one subtype may be irrelevant in another. For example, \(\alpha_\text{CI}\) has \(S_T \approx 0.35\) in the metabolic-dominant attractor but only \(S_T \approx 0.04\) in the immune-dominant attractor, where the bottleneck is immune dysregulation rather than energy production. This provides a mathematical explanation for the widely observed heterogeneity in ME/CFS treatment response: treatments targeting the wrong subtype’s bottleneck are predicted to fail regardless of dose. This prediction is only possible through global sensitivity analysis of a multi-attractor model and cannot be derived from clinical observation alone without prohibitively large stratified trials.