GPSNorm: Gaussian Process Spatial Normalization for Spatial Transcriptomics

Key results

1. SuggestedWhen the group contrast tracks latent spatial structure, two-stage normalization yields overconfident differential expression intervals, whereas joint estimation widens them and keeps coverage near nominal, in a reduced null simulation (true effect 0).

   Over 100 replicates per level of spatial SD σu, two-stage interval widths stayed nearly flat and empirical 95% coverage fell toward zero as σu grew; joint 95% credible intervals widened monotonically, keeping coverage near nominal 0.95 for most σu levels apart from a transient dip at low σu. The two coincided at σu = 0, as predicted by a law-of-total-variance argument. · 3.1 Theoretical Motivation; 3.2 Empirical Demonstration Under Spatial…; Figure legends

2. SuggestedIn simulations anchored to empirical count data, GPSNorm recovered the simulated technical spatial field and gave the most accurate log fold-change estimates, with its advantage growing as slide-level and spatial technical variation increased.

   Correlation of estimated with true technical field: 0.921 ± 0.021 over 25 runs of the hardest scenario (F_hard). Mean log fold-change RMSE over 30 replicates was lowest for GPSNorm in all six scenarios, with minimal bias; DE-ranking AUC was similar across methods in low-confounding regimes and higher for GPSNorm under technical confounding. · 4.3.1 Recovery of Technical Spatial Structure; 4.3.2 Differential Expression Performance; Figure legends

3. SuggestedIn a GeoMx COVID-19 lung dataset of 46 areas of interest (AOIs), only GPSNorm called genes differentially expressed between severe and mild-to-moderate damage, including chemokines consistent with the original study; other methods followed by limma with FDR control called none.

   Up in severe AOIs: CCL18, CXCL10, CCL2; up in milder AOIs: SCGB1A1. GPSNorm calls used a region-of-practical-equivalence rule, P(|βg| > 0.10 | y) ≥ 0.95; comparators used limma FDR, which the authors note is a different inferential quantity. SpaNorm and scran gave no valid estimates with so few AOIs. No dataset-specific preprocessing or tuning was applied. · 6.2 GeoMx COVID-19 Lung Damage Dataset; Figure legends

4. SuggestedGPSNorm kept expected contrasts: white-matter MOBP enrichment in Visium dorsolateral prefrontal cortex (DLPFC), as SpaNorm also did, and high ranking of both glomerular and proximal tubule markers in GeoMx kidney, where several other methods ranked tubule markers lower and SpaNorm did not show this advantage.

   DLPFC sample 151672: unnormalized MOBP counts hid white-matter enrichment; GPSNorm (percentile-adjusted counts and posterior median) and SpaNorm showed it within white matter and at its boundary. Kidney: mean evidence percentile of marker sets including NPHS1, PODXL, SYNPO, WT1 and LRP2, CUBN, AQP1, SLC22A6, SLC22A8, glomerular vs other nephron AOIs. Shown in figures only; no numbers in the text. · 6.1 10x Visium Human DLPFC Dataset; 6.3 GeoMx Spatial Organ Atlas Kidney Dataset; Figure legends

5. ShownClustering neighboring AOIs within each slide for fitting, then projecting estimates back, cut runtime substantially while largely preserving log fold-change magnitudes and the order of top-ranked genes relative to the full-resolution fit.

   Simulation (F_hard, 25 replicates; 0.5x and 0.25x levels): about 50% less runtime with moderate and about four-fold speedup with stronger aggregation, log fold-change (logFC) shifts of a few hundredths, lower global but higher top-gene rank agreement. Kidney: over five-fold faster at the coarsest level, logFC shifts on the order of 10^−3, high agreement among the top 10% of genes. · 5 AOI Clustering and Computational Scaling; Tables