Univariate

Need for Permutations

An underlying assumption used for many spatial clustering metrics is that the cells are randomly distributed across the region, no evidence of clustering or repulsion, and that the cell intensity is constant across the entire region. This assumption is the so-called complete spatial randomness (CSR). Damage can occur to TMAs, due to how they are collect. This damage can lead to rips and tears in the TMA which results in regions where it appears that cells cannot be locations, which is not actually the case. Due to these violations of the CSR assumption, the theoretical estimate for CSR may not be accurate, to address this the cell positivity can be permuted across all observed locations and the permutation distribution of \(K\), \(L\), \(M\), and \(G\) is a TMA specific measure of CSR.

Univariate Count-Based Methods

The ripleys_k_v2 function reports a permuted and theoretical estimate of CSR, the observed value for \(K\) (method = 'K'), \(L\) (method = L), or Marcon \(M\) (method = 'M'), and the full permutation distribution of \(K\), \(L\), and \(M\) of keep_perm_dis = TRUE.

Currently, the number of permutations is 10, but this should be increased to at least 100 for a more reliable estimate of the mean.

x <- spatialTIME::ripleys_k(mif = x, mnames = mnames_good, num_permutations = 10,
               edge_correction = 'translation', r = seq(0,100,10),
               keep_perm_dis = FALSE, workers = 1)
#> Registered S3 method overwritten by 'spatstat.geom':
#>   method     from
#>   print.boxx cli
# This will keeps the colors in every plot for the remainder of the vignette compatable 
values = viridis::turbo(length(unique(x$derived$univariate_Count$deidentified_sample)))
names(values) = unique(x$derived$univariate_Count$deidentified_sample)

x$derived$univariate_Count  %>%
  dplyr::filter(Marker != 'PDL1..Opal.540..Positive') %>%
  ggplot2::ggplot(ggplot2::aes(x = r, y = `Degree of Clustering Permutation`)) +
  ggplot2::geom_line(ggplot2::aes(color = deidentified_sample), show.legend = FALSE) +
  ggplot2::facet_wrap(Marker~., scales = 'free') + ggplot2::theme_bw() + 
  ggplot2::scale_color_manual(values = values)

Positive values of degree of cluster when using method = 'K' and method = 'L' indicates evidence of spatial clustering, while neagtive valueas correspond to spatial regularity. On the other hand, if using `method = ‘M’ then values larger than 1 correspond to clustering and values less than one correspond to regularity. Also, these values can be interpreted as the the percent difference from spatial clustering, for example if \(M=0.5\) that means there is 50% less spatial clustering than expected under CSR.

Bivariate Count-Based Methods

In the univariate case, we consider each cell of a single cell type and center circles around each cell (reference cell). In the bivariate case, we are interested in how many cells of Type 1 (Counted) are clustered in proximity to Type 2 (Anchor). Here the circles are centered around cell of Type 2 and then the cells of Type 1 are counted.

x <- spatialTIME::bi_ripleys_k(mif = x, mnames = c("CD3..CD8.", "CD3..FOXP3."), num_permutations = 10,
               edge_correction = 'translation', r = seq(0,100,10),
               keep_perm_dis = FALSE, workers = 1, exhaustive = TRUE)

x$derived$bivariate_Count  %>%
  dplyr::filter(anchor == 'CD3..FOXP3.') %>%
  ggplot2::ggplot(ggplot2::aes(x = r, y = `Degree of Clustering Permutation`)) +
  ggplot2::geom_line(ggplot2::aes(color = deidentified_sample), show.legend = FALSE) +
  ggplot2::theme_bw() + ggplot2::scale_color_manual(values = values)

The interpretation of the degree of clustering is the same here. The green line shows evidence that Tregs tend to cluster around Cytotoxic T cells for all values of \(r\), while the red line indicates spatial repulsion of Tregs by Cytotoxic T cells for \(25\le r\le50\).

Univariate Nearest-Neighbor Methods

The NN_G function reports a permuted and theoretical estimate of CSR, the observed value for \(G\), and the full permutation distribution of \(G\) of keep_perm_dis = TRUE. The degree of clustering is computed by taking the ratio of the observed \(G\) and either the permutation or theoretical estimate of CSR.

Currently, the number of permutations is 10, but this should be increased to at least 100 for a more reliable estimate of the mean.

x <- spatialTIME::NN_G(mif = x, mnames = mnames_good, num_permutations = 10,
                edge_correction = 'rs', r = seq(0,100,10),
                keep_perm_dis = FALSE, workers = 1)

x$derived$univariate_NN  %>%
  dplyr::filter(Marker != 'PDL1..Opal.540..Positive') %>%
  ggplot2::ggplot(ggplot2::aes(x = r, y = `Degree of Clustering Permutation`)) +
  ggplot2::geom_line(ggplot2::aes(color = deidentified_sample)) +
  ggplot2::facet_wrap(Marker~., scales = 'free') + ggplot2::theme_bw() + 
  ggplot2::scale_color_manual(values = values)

The interpretation of the degree of clustering for \(G\) that values greater than 0 indicate spatial clustering of the cell types of interest, while values less than 0 indicate dispersion of these cells. For example in core [3,B], FOXP3..Opal.620..Positive shows spatial dispersion from \(0\le r \le50\) (less than zero), while CD3..Opal.570..Positive for core [3,B] shows spatial clustering \(0\le r\le75\) (greater than zero).

Bivariate Nearest-Neighbor Methods

The interpretation of the bivariate nearest neighbor distribution is similar to bivariate Ripley’s K, in that we are measuring the degree of clustering of one cell type with respect to another. THe actual value of degree of clustering is interpreted in the same manner at the univariate nearest neighbor distribution.

x <- spatialTIME::bi_NN_G(mif = x, mnames = c("CD3..CD8.", "CD3..FOXP3."), num_permutations = 10,
               edge_correction = 'rs', r = seq(0,100,10),
               keep_perm_dis = FALSE, workers = 1)

x$derived$bivariate_NN  %>%
  dplyr::filter(anchor == 'CD3..FOXP3.') %>%
  ggplot2::ggplot(ggplot2::aes(x = r, y = `Degree of Clustering Permutation`)) +
  ggplot2::geom_line(ggplot2::aes(color = deidentified_sample), show.legend = FALSE) +
  ggplot2::theme_bw() +  ggplot2::scale_color_manual(values = values)
#> Warning: Removed 27 row(s) containing missing values (geom_path).