Sex Differences in the Dynamics of the Hypothalamic–Pituitary–Adrenal Axis: A Reproducible Computational and Bayesian Framework with Genuine Multi-Parameter Global Sensitivity Analysis

Sex-specific disparities in the epidemiology, clinical presentation, and treatment outcomes of pituitary and adrenal-axis disorders are well documented, yet the mechanistic and quantitative basis for these disparities is rarely made fully reproducible. This manuscript develops a semi-mechanistic, circadian-forced ordinary differential equation (ODE) model of the hypothalamic–pituitary–adrenal (HPA) axis, parameterized to reproduce the qualitatively established direction of sex dimorphism in adrenal sensitivity and glucocorticoid negative feedback, and subjects it to a fully reproducible computational pipeline: deterministic periodic-steady-state simulation, Monte Carlo uncertainty propagation, a from-scratch four-chain Metropolis–Hastings Bayesian analysis (Gelman–Rubin R̂ ≤ 1.001 for all parameters), closed-form frequentist inference, and genuine variance-based (Sobol/Saltelli) global sensitivity analysis computed from Sobol quasi-random sequences rather than approximated by univariate correlation proxies. The model predicts a simulated female-to-male elevation in mean cortisol of 70.0% (female 3.69 vs. male 2.17 arbitrary units [AU]), with a posterior mean difference of 1.52 AU (95% credible interval 1.47–1.57; four chains, effective sample size ≈ 12,000). A correctly targeted sensitivity analysis restricted to the three parameters that actually differ between sexes in this model (fb1, fb2, kcort) shows that adrenal sensitivity kcort carries the dominant first-order influence on the simulated disparity (Sobol Si = 0.62), with the feedback parameters fb1 and fb2 contributing more modestly and substantially through interaction terms — a materially more precise conclusion than an unqualified claim that all three parameters are equally dominant. We explicitly distinguish, and report separately, (i) genuine model-internal statistical uncertainty, which is legitimately quantifiable from the simulation, from (ii) real-world clinical evidence, which this conceptual, non-patient-derived framework cannot supply; extremely small in-silico p-values are explicitly flagged as artifacts of deterministic simulation rather than clinical significance. A dedicated risk-assessment section enumerates the model's critical assumptions and failure modes, and a falsifiability/roadmap section specifies the concrete empirical measurements that would corroborate or refute each modeling claim. All code required to regenerate every number, table, and figure in this manuscript is embedded in the Appendix and was executed with a fixed random seed (SEED=42) to guarantee exact reproducibility