Grassmannian Geodesic Distance Predicts Cross-Cohort Classifier Degradation Under Analytical Heterogeneity, After Controlling for Source Classifier Quality

Geodesic distance on the Grassmannian manifold Gr(k, d) between cohort-specific PCA subspaces, after partialing out source classifier quality, predicts the residual AUC gap when a classifier is transferred to a new cohort. Raw geodesic–gap correlations are null on all seven datasets because the AUC gap conflates source internal performance with distribution shift. The confound-control step is essential.

The method is validated on a colorectal cancer microbiome meta-analysis (9 studies, 824 samples; partial rho = +0.61, clustered bootstrap 95% CI [−0.02, +0.80], 97% positive; Delta R^2 = +0.23) and on the QMDiab multi-biofluid metabolomics study (3 biofluids × 3 ethnicities, 356 participants; partial rho = +0.40, clustered CI [+0.04, +0.73]). Leave-one-study-out validation confirms out-of-sample utility (42% MAE reduction over baseline). QMDiab decomposition shows the signal reflects the contrast between cross-biofluid pairs (partial rho = −0.04) and within-biofluid cross-ethnicity pairs (partial rho = +0.14), consistent with the boundary-condition thesis rather than graded within-type prediction.

Five additional datasets (IBD microbiome, SPIROMICS COPD, breast cancer GEO, TCGA-BRCA, MTBLS7260 metabolomics) yield null results, identifying interpretable boundary conditions: the method requires analytical heterogeneity between cohorts. Centralized platforms or shared microarray platforms produce null results even across independent study sites. A formal power analysis shows 41% power to detect the CRC effect at the effective sample size of 9 studies; 19 studies would be needed for 80% power.

This deposit contains the PLOS ONE submission manuscript (LaTeX + PDF), cover letter, pre-registration document (frozen at commit 675290c before confirmatory analyses), confirmatory analysis scripts (power analysis, QMDiab decomposition), the full analysis codebase (Python), and all result files (JSON summaries, ordered-pair CSVs, figures) for all seven datasets. Raw data are publicly available from their respective repositories (curatedMetagenomicData, MetaboLights MTBLS59, GEO, TCGA) and are not included due to size.