Plotting Cores
An individual plot for each core (each sample) is created. Plots can
be assigned to an R object, such as within the empty
derived slot and printed to a PDF if a file name is
provided.
When studying phenotype and individual markers, note that it is important to have the individual before the phenotype markers. This will ensure that the phenotype that are derived by multiple markers are not plotted over by the individual marker. For instance, below the the first plot appears to have no cytotoxic T cells (CD3+ and CD8+), but then the order is changed we see the cytotoxic T cells. Moral of the story: Put the marker combinations before the single markers.
mnames_bad <- c("CD3..CD8.","CD3..FOXP3.","CD3..Opal.570..Positive",
"CD8..Opal.520..Positive","FOXP3..Opal.620..Positive",
"PDL1..Opal.540..Positive", "PD1..Opal.650..Positive")
# Used to make the legends in both plots below be in same order and use the
# same coloring scheme for the purpose making a common legend
values = RColorBrewer::brewer.pal(length(mnames_bad), "Accent")
names(values) = mnames_bad
#add an element in the `derived` object position
x<- plot_immunoflo(x, plot_title = "deidentified_sample", mnames = mnames_bad,
cell_type = "Classifier.Label")
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
bad_names <- x[["derived"]][["spatial_plots"]][[4]] +
theme(legend.position = 'bottom') +
scale_color_manual(breaks = mnames_bad,
values = values,
labels = mnames_bad %>%
gsub("..Opal.*", "+", .) %>%
gsub("\\.\\.", "+", .) %>%
gsub("\\.", "+", .))
#> Scale for colour is already present.
#> Adding another scale for colour, which will replace the existing scale.
mnames_good <- c("CD3..Opal.570..Positive","CD8..Opal.520..Positive",
"FOXP3..Opal.620..Positive","PDL1..Opal.540..Positive",
"PD1..Opal.650..Positive","CD3..CD8.","CD3..FOXP3.")
x <- plot_immunoflo(x, plot_title = "deidentified_sample", mnames = mnames_good,
cell_type = "Classifier.Label")
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.
good_names <- x[["derived"]][["spatial_plots"]][[4]] +
theme(legend.position = 'bottom') +
scale_color_manual(breaks = mnames_good,
values = values[match(mnames_good, names(values))],
labels = mnames_good %>%
gsub("..Opal.*", "+", .) %>%
gsub("\\.\\.", "+", .) %>%
gsub("\\.", "+", .))
#> Scale for colour is already present.
#> Adding another scale for colour, which will replace the existing scale.
x$sample %>% filter(deidentified_sample == 'TMA3_[9,K].tif') %>% select(c(2, 4:15)) %>%
pivot_longer(cols = 2:13, names_to = 'Marker', values_to = 'Count')
#> # A tibble: 12 × 3
#> deidentified_sample Marker Count
#> <chr> <chr> <dbl>
#> 1 TMA3_[9,K].tif FOXP3 (Opal 620) Positive Cells 34
#> 2 TMA3_[9,K].tif CD3 (Opal 570) Positive Cells 536
#> 3 TMA3_[9,K].tif CD8 (Opal 520) Positive Cells 83
#> 4 TMA3_[9,K].tif PD1 (Opal 650) Positive Cells 5
#> 5 TMA3_[9,K].tif PDL1 (Opal 540) Positive Cells 1
#> 6 TMA3_[9,K].tif CD3+ FOXP3+ Cells 34
#> 7 TMA3_[9,K].tif CD3+ CD8+ Cells 68
#> 8 TMA3_[9,K].tif CD3+ CD8+ FOXP3+ Cells 4
#> 9 TMA3_[9,K].tif CD3+ PD1+ Cells 5
#> 10 TMA3_[9,K].tif CD3+ PD-L1+ Cells 1
#> 11 TMA3_[9,K].tif CD8+ PD1+ Cells 0
#> 12 TMA3_[9,K].tif CD3+ CD8+ PD-L1+ Cells 0
# Estimating the degree of spatial clustering with Count Based
Methods
Univariate
Count Based Methods
Ripley’s \(K\) measures the average number of neighboring cells across each cell. That is, the average (over all cells) number of cells within a specified radius of a cell. Ripley’s \(K\) is computed as follows:
\[\hat{K}(r) = \frac{1}{n(n-1)}\sum_{i=1}^{n}\sum_{j\neq i}w_{ij}{\bf 1}{(d(x_i,x_j)\le r)},\]
where \(r\) is the specified radius, \(d(x_i,x_j)\) is the distance between the \(i^{th}\) and \(j^{th}\) cell, \({\bf 1}_A\) is indicator function of event \(A\), and \(w_{ij}\) is the weights that are assigned for border corrections. The expected value of \(\hat{K}(r)\) is \(\pi r^2\), thus \(\hat{K}\) is expected to grow as a quadratic function of \(r\).
There are several edge corrections. Our studies have included a small number of cells and we recommend using the ‘isotropic’ or ‘translational’ edge correction, as opposed to the ‘border’ edge correction. The main goal of the edge correction is to account for the fact that there are unobserved points outside of the region, and the assumption is that the location of these cells has the same distribution as the study region. An excellent description of these corrections are provided here.
Distance Based Measures
The distribution of the nearest neighbor distances, \(\hat{G}(r)\), can be studied and is computed by
\[\hat{G}(r) = \frac{1}{n}\sum_{i=1}^{n}{\bf 1}(\min_{j}(\{d(x_i,x_j)\}\le r),\]
which is interpreted as the proportion of cells whose distance to its
nearest neighbor is less than \(r\).
Notice that there is not a weighting factor for each pair of points as
we saw above. The edge correction in these methods, reduced sample
(rs) and Hanisch (han), simply have different
cell inclusion conditions. The reduced sample correction is similar to
the border correction for count based methods, where the middle chunk of
the area of interest is studied. The Hanisch border correction leaves
out points whose \(k^{th}\) neighbor
can not be in the area of interest. For more information about these
border corrections, see the following article.
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 tissue cores due to how they are collected. This damage can lead to rips and tears in the cores which results in regions where it appears that cells are not located and 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 core specific measure of CSR than theoretical. Also, with the permutations of CSR we are able to determine whether the observed clustering is significant by lying above or below a 95% of permuted CSR estimates.
Calculating Exact CSR
The product of running all possible permutations of Ripley’s K and bivariate Ripley’s K for cells on a TMA core or an ROI spot is simply the result of running Ripley’s K or bivariate Ripley’s K on all cells ignoring their marks. This allows us to determine the exact degree of clustering that are can use for associations with survival or other clinical variables.
We can also run using the exact CSR approach which is faster and
produces a more accurate Degree of clustering.
