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Advanced Spatial Analysis

Source: vignettes/phenoscapR-03-spatial-analysis.Rmd
phenoscapR-03-spatial-analysis.Rmd

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Overview

phenoscapR provides a rich set of spatial statistics beyond basic nearest neighbours and density estimation. This vignette demonstrates:

  • Neighbourhood Enrichment — permutation test for phenotype co-localisation
  • Ripley’s K — global clustering / dispersion measure
  • Moran’s I — spatial autocorrelation of a continuous variable
  • Quadrat Analysis — complete spatial randomness test
  • Pair Correlation Function — scale-dependent g(r)
  • Cross Nearest-Neighbour Distance — inter-phenotype proximity
  • Delaunay Network — cell contact graph
  • Expression Clustering — marker-expression-based cell clusters

Setup: Simulated Tissue Data 

library(phenoscapR)

set.seed(42)
n <- 600

# Two spatially segregated populations
coords <- data.frame(
  x = c(rnorm(300, 250, 80), rnorm(300, 750, 80)),
  y = c(rnorm(300, 400, 80), rnorm(300, 400, 80))
)

counts <- matrix(
  c(
    c(rnorm(300, 900, 150), rnorm(300, 200, 100)),  # CD3 high in pop 1
    c(rnorm(300, 200, 100), rnorm(300, 800, 130)),  # CD8 high in pop 2
    abs(rnorm(600, 600, 150)),                       # PanCK background
    abs(rnorm(600, 400, 100))                        # DAPI
  ),
  nrow = n,
  dimnames = list(NULL, c("CD3", "CD8", "PanCK", "DAPI"))
)

obj <- CreateSpatialObject(counts, coords, project = "spatial-demo")
obj <- NormaliseData(obj, method = "zscore")
obj <- PhenotypeCells(obj, thresholds = list(CD3 = 0, CD8 = 0,
                                              PanCK = 0, DAPI = -99))
table(Idents(obj))
#> 
#> CD3+/CD8+/PanCK+/DAPI+             CD3+/DAPI+      CD3+/PanCK+/DAPI+ 
#>                      1                    126                    170 
#>             CD8+/DAPI+      CD8+/PanCK+/DAPI+                  DAPI+ 
#>                    159                    137                      4 
#>           PanCK+/DAPI+ 
#>                      3

Neighbourhood Enrichment

Tests whether phenotype pairs co-localise more (or less) than expected by random chance using a permutation approach:

# Run with n_perm = 100 or more for reliable p-values
ne <- NeighbourhoodEnrichment(obj, radius = 80, n_perm = 20)
ne

Ripley’s K

Assesses global spatial clustering across a range of radii. Values above the theoretical CSR line indicate clustering:

rk <- RipleysK(obj)
rk

Moran’s I

Quantifies the spatial autocorrelation of a continuous variable (e.g. a marker intensity). Values near +1 indicate strong spatial clustering of high/low values; values near −1 indicate regular spatial dispersion:

mi <- MoransI(obj, feature = "CD3", radius = 100)
mi

Quadrat Analysis

Divides the tissue into a regular grid and tests for Complete Spatial Randomness (CSR) using a chi-squared test. Significant results indicate non-random spatial distribution:

qa <- QuadratAnalysis(obj, nx = 4, ny = 4)
qa

Pair Correlation Function

The pair correlation function g(r) is the derivative of Ripley’s K and measures clustering or inhibition at a specific distance r. g(r) > 1 indicates clustering; g(r) < 1 indicates inhibition:

pcf <- PairCorrelation(obj)
pcf

Cross Nearest-Neighbour Distance

Measures the distance from each cell of phenotype A to the nearest cell of phenotype B, providing a directed measure of inter-phenotype proximity:

cn <- CrossNNDistance(obj, from = "CD3+CD8-", to = "CD3-CD8+")
summary(cn$cross_nn_distance)

Delaunay Triangulation Network

Constructs a cell contact graph based on Delaunay triangulation. Useful for cell-cell interaction analyses:

Expression Clustering

Cluster cells by their normalised marker expression profiles (k-means or hierarchical). Useful for discovering marker co-expression communities independently of spatial position:

obj <- ExpressionClusters(obj, k = 4)
table(obj$expr_cluster)
CellMap(obj, colour_by = "expr_cluster")

Summary

Function What it tests Key parameter
NeighbourhoodEnrichment() Co-localisation vs random radius, n_perm
RipleysK() Global clustering at multiple radii r_max, n_r
MoransI() Spatial autocorrelation of a feature feature, radius
QuadratAnalysis() CSR via chi-squared nx, ny
PairCorrelation() Scale-dependent g(r) r_max, n_r
CrossNNDistance() Inter-phenotype proximity from, to
DelaunayNetwork() Cell contact graph —
ExpressionClusters() Marker expression communities k, method

Next Steps