MI_spatialAnalysis

Transcript

1. Julia Wrobel, PhD
   Department of Biostatistics and Informatics
   Spatial analysis of multiplex imaging data
   

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2. • Spatial summary statistics are extracted to describe spatial relationship
   amongst cells in an image
   • Also often separated by tumor/stroma
   • Univariate spatial summary metrics
   • Clustering or dispersion of cells of one type
   • Bivariate spatial summary metrics
   • Co-expression or co-clustering of two cell types
   • Methods based on spatial point processes
   • Analyze number of neighbors: K-function, L-function
   • Analyze distance to nearest neighbor: G-function
   Spatial summary statistics
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3. • Locations of cells are considered random and
   to follow a point process
   • Marked point patterns have covariates (cell
   shape, area, expression of CD3) associated
   with each point
   • Multitype point patterns have multiple types
   of points
   • Gray are tumor cells, red are immune cells
   • Specifically interested in spatial arrangement of
   immune cells
   Spatial point patterns
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4. • Green cells are in tumor tissue
   area
   • Pink cells are in stromal tissue
   area
   • Black cells are macrophages
   • Quantify macrophage clustering
   in tumor and stromal areas
   Another example: macrophages in ovarian cancer
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5. • Capture important features of the point pattern
   • Assume location of points in point pattern are random variables
   • Typically number of points n is also a random variable
   • Often to detect deviations from complete spatial randomness (CSR)
   • Clustering or repulsion
   Spatial summary functions based on point processes
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6. • Homogeneity: 𝐸 𝑛(𝑋 ∩ 𝐴) = 𝜆|𝐴|
   • The expected number of points falling in
   a given region A should be proportional
   to the area of the region
   • Spatial independence
   • The counts in disjoint subregions of R are
   independent random variables
   Then, the number of points falling in R
   follows a Poisson distribution
   • Homogeneous Poisson point process
   • Deviations from Homogeneous Poisson
   point process represent spatial clustering
   Complete Spatial Randomness
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   𝑃 𝑛 𝑋 ∩ 𝐴 = 𝑘 = 𝑒!|#|
   𝜆 𝐴 $
   𝑘!
   𝜆 is the intensity, or expected number of
   random points per unit area
   

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7. • K-function is a popular metric for analyzing spatial correlation in point patterns
   • Essentially the standardized average number of neighbors of a cell within radius r
   /
   𝐾 𝑟 =
   |𝐴|
   𝑛(𝑛 − 1)
   4
   %
   &
   4
   %'(
   𝐼 𝑑 𝑐%, 𝑐) ≤ 𝑟 𝑒%)
   • Assumes homogeneity
   • Has theoretical value under CSR
   • Compare observed to theoretical value to assess clustering
   𝐸!"#
   "
   𝐾 𝑟 = 𝜋𝑟$
   Ripley’s K-function
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8. Ripley’s K function for simulated cells
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9. Transformations of Ripley’s K
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   /
   𝐾 𝑟 =
   |𝐴|
   𝑛(𝑛 − 1)
   4
   %
   &
   4
   %'(
   𝐼 𝑑 𝑐%, 𝑐) ≤ 𝑟 𝑒%)
   L- function
   - 𝐿 𝑟 = * +
   ,
   Marcon’s M
   - * +
   ,+!
   

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10. Can interpret as probability of a neighboring cell occurring within radius r
    • 𝑑!
    = 𝑚𝑖𝑛"#!
    ||𝑥"
    − 𝑥_𝑖|| finds the nearest neighbor
    • 𝐺 𝑟 = ℙ 𝑑 𝑢, 𝑿\u ≤ 𝑟|𝑿 ℎ𝑎𝑠 𝑎 𝑝𝑜𝑖𝑛𝑡 𝑢 for any location u
    Nearest Neighbor G-function
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11. • Mark correlation function
    • Derivative of K function
    • Moran’s I
    • Can be used to quantify continuous marks
    • Local and global versions
    • Univariate and bivariate
    Other spatial summary statistics
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12. • Rare cell types: spatially summary metrics cannot be computed for
    images with no or few cells of a certain subtype
    • Makes it challenging to compare across images
    • Multiple images per subject
    • Needs to be accounted for in analysis
    • Violation of homogeneity assumptions bias estimation of K, G functions
    • Inhomogeneity can give appearance of spatial clustering
    Issues that arise in multiplex imaging data
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13. Homogenous vs. Inhomogeneous Poisson processes
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14. Ovarian tumor samples have inhomogeneity due to poor
    tissue quality
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15. • Cells are missing, resulting appearance of inhomogeneity of 𝜆 when
    underlying unobserved process may have been homogeneous
    • Violates homogeneity assumption of K-function!
    • Can no longer compare to theoretical K under CSR of 𝜋𝑟-
    • Wilson et. al, 2022 resolve this using a permutation approach
    • Calculates empirical estimate of K-function under CSR by randomly
    permuting cell labels
    • Then compare empirical K to permuted K rather than theoretical K
    • Effectively separates clustering from “patchy” effects
    Permutation solution to TMA inhomogeneity
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16. Permutation solution to TMA inhomogeneity
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17. Fridley Lab
    Moffitt Cancer Center
    spatialTIME package
    

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18. • Visualize samples
    • Calculate spatial summary
    statistics across samples
    • Correct for spatial
    inhomogeneity using
    permutation approach
    • iTIME: Shiny interface
    What can we do with spatialTIME?
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