Reduced local effective rank of the whole-blood transcriptome in sepsis: a permutation-tested, composition-adjusted structural correlate across public case-control cohorts

Sepsis whole blood is reproducibly structured but lacks a stable single-marker signature, so this study tests a marker-agnostic structural property — the local effective rank of each sample's whole-blood transcriptomic covariance neighbourhood — across four public Gene Expression Omnibus case–control cohorts, each analysed cohort-natively. Sepsis showed a lower local effective rank than healthy controls in all three testable cohorts (mean differences −0.034, −0.170, −0.282 bits), and the direction passed a dependence-respecting label-permutation null in every cohort (one-sided p ≈ 0.005). The effect is composition-entangled (deconvolved cell-type fractions explain 3–58% of entropy variance) and persists under a full reference-based EPIC cell-type-composition sensitivity analysis: the disease coefficient stays negative and significant after adjusting for neutrophil, lymphocyte, and monocyte fractions, and slightly strengthens. Because that adjustment uses an off-label estimator on two of the three cohorts, the effect is composition-entangled but not composition-explained; it is composition-adjusted but not demonstrated composition-robust. Honest boundaries are stated plainly: the statistic is not novel (it equals effective rank / PC1-dominance), it is not established as sepsis-specific (a sepsis-versus-healthy design that cannot rule out generic severe illness), and no clinical, diagnostic, or treatment use is supported — the contribution is a real, cross-platform, permutation-tested but modest structural correlate of the whole-blood host response.