Spatial Mixed-Effects Modelling with spicy
10 July 2020
Package
spicyR 1.0.1
Contents
# load required packages
library(spicyR)
library(ggplot2)1 Installation
if (!require("BiocManager"))
install.packages("BiocManager")
BiocManager::install("spicyR")2 Overview
This guide will provide a step-by-step guide on how mixed effects models can be applied to multiple segmented and labelled images to identify how the localisation of different cell types can change across different conditions. Here, the subject is modelled as a random effect, and the different conditions are modelled as a fixed effect.
3 Example data
Here, we use a melanoma image dataset with two conditions: Responders and Non-Responders. With this data set, we want to see if there are differences in how cell types are localised with respect to each other.
cells is a SegmentedCells object containing single-cell data of 135 images
from 27 subjects, with 5 images per subjects. There are 9 Non-Responder subjects
and 18 Responder subjects.
cellSummary() returns a DataFrame object providing the location (x and y)
and cell type (cellType) of each cell and the image it belongs to (imageID).
imagePheno() returns a DataFrame object providing the corresponding subject
(subject) and condition (condition) for each image.
data("melanomaResponders")
melanomaResponders
cellSummary(melanomaResponders)
#> DataFrame with 296523 rows and 6 columns
#> imageID cellID imageCellID x y cellType
#> <factor> <character> <character> <numeric> <numeric> <factor>
#> 1 1 cell_1 cell_1 49.5 1.25 CD8-PD1-PDL1-
#> 2 1 cell_2 cell_2 85.0 1.00 CD8-PD1-PDL1-
#> 3 1 cell_3 cell_3 169.0 1.25 SOX10+
#> 4 1 cell_4 cell_4 245.0 1.00 CD8-PD1-PDL1-
#> 5 1 cell_5 cell_5 291.0 1.00 SOX10+
#> ... ... ... ... ... ... ...
#> 296519 525 cell_351307 cell_351307 4.75 248.75 CD8-PD1-PDL1-
#> 296520 525 cell_351308 cell_351308 80.50 249.00 SOX10+
#> 296521 525 cell_351309 cell_351309 255.75 249.00 CD8-PD1-PDL1-
#> 296522 525 cell_351310 cell_351310 291.50 248.75 SOX10+
#> 296523 525 cell_351311 cell_351311 310.25 248.75 SOX10+
imagePheno(melanomaResponders)
#> DataFrame with 135 rows and 3 columns
#> imageID condition subject
#> <factor> <factor> <factor>
#> 1 1 Non-Responders SP12-18569
#> 2 2 Non-Responders SP12-18569
#> 3 3 Non-Responders SP12-18569
#> 4 4 Non-Responders SP12-18569
#> 5 5 Non-Responders SP12-18569
#> ... ... ... ...
#> 131 521 Responders SW14-18104
#> 132 522 Responders SW14-18104
#> 133 523 Responders SW14-18104
#> 134 524 Responders SW14-18104
#> 135 525 Responders SW14-18104In this data set, cellType can be some combination of the expression of CD8,
PD1 or PDL1, or is SOX10+.
4 Mixed Effects Modelling
To investigate changes in colocalisation between two different cell types, we
measure the level of colocalisation between two cell types by modelling with the
Lcross() function in the spatstat package. Specifically, the mean difference
between the obtained function and the theoretical function is used as a measure
for the level of colocalisation. Differences of this statistic between two
conditions is modelled using a weighted mixed effects model, with condition as
the fixed effect and subject as the random effect.
4.1 Testing for change in colocalisation for a specific pair of cells
Firstly, we can see whether one cell type tends to be around another cell type
in one condition compared to the other. This can be done using the spicy()
function, where we include condition, and subject. In this example, we want
to see whether or not CD8-PD1+PDL1+ cells (to) thend to be found around
CD8+PD1+PDL1- cells (from).
spicyTestPair <- spicy(melanomaResponders,
condition = "condition",
subject = "subject",
from = "CD8+PD1+PDL1-",
to = "CD8-PD1+PDL1+")
#> Calculating pairwise spatial associations
#> Testing for spatial differences across conditions accounting for multiple images per subject
spicyTestPair
#>
#> Number of cell type pairs: 1
#> Number of differentially localised cell type pairs:
#> [1] 0
topPairs(spicyTestPair)
#> intercept coefficient p.value adj.pvalue
#> CD8+PD1+PDL1-_CD8-PD1+PDL1+ 12.30061 -6.676495 0.07270545 0.07270545
#> from to
#> CD8+PD1+PDL1-_CD8-PD1+PDL1+ CD8+PD1+PDL1- CD8-PD1+PDL1+We obtain a spicy object which details the results of the mixed effects
modelling performed. As the coefficient in spicyTest is negative, we find
that CD8-PD1+PDL1+ cells are more likely to be found around CD8+PD1+PDL1- cells
in Non-Responders.
4.2 Test for change in colocalisation for all pairwise cell combinations
Here, we can perform what we did above for all pairwise combinations of cell
types by excluding the from and to parameters from spicy().
spicyTest <- spicy(melanomaResponders,
condition = "condition",
subject = "subject")
spicyTest
#>
#> Number of cell type pairs: 81
#> Number of differentially localised cell type pairs:
#> conditionResponders
#> 0
topPairs(spicyTest)
#> intercept coefficient p.value adj.pvalue
#> CD8-PD1+PDL1+_CD8+PD1+PDL1- 21.403625 -14.143257 0.006696371 0.3184453
#> CD8+PD1+PDL1-_CD8-PD1+PDL1+ 21.300751 -13.854313 0.007862848 0.3184453
#> CD8-PD1+PDL1-_CD8+PD1-PDL1+ 6.348714 -7.144476 0.076475111 0.9174987
#> CD8-PD1+PDL1-_CD8-PD1+PDL1+ 12.485009 -7.625312 0.081119183 0.9174987
#> CD8+PD1-PDL1-_CD8+PD1-PDL1- 20.934811 -11.403936 0.093658867 0.9174987
#> CD8-PD1+PDL1+_CD8-PD1+PDL1- 11.621590 -6.942920 0.112733933 0.9174987
#> CD8+PD1-PDL1+_CD8-PD1+PDL1- 4.821599 -6.028484 0.119793885 0.9174987
#> CD8+PD1-PDL1-_CD8+PD1+PDL1- 11.049319 7.124038 0.123391930 0.9174987
#> CD8-PD1-PDL1-_CD8+PD1-PDL1- 9.067690 -2.765159 0.141393584 0.9174987
#> CD8+PD1+PDL1-_CD8+PD1-PDL1- 11.041912 6.860201 0.143290192 0.9174987
#> from to
#> CD8-PD1+PDL1+_CD8+PD1+PDL1- CD8-PD1+PDL1+ CD8+PD1+PDL1-
#> CD8+PD1+PDL1-_CD8-PD1+PDL1+ CD8+PD1+PDL1- CD8-PD1+PDL1+
#> CD8-PD1+PDL1-_CD8+PD1-PDL1+ CD8-PD1+PDL1- CD8+PD1-PDL1+
#> CD8-PD1+PDL1-_CD8-PD1+PDL1+ CD8-PD1+PDL1- CD8-PD1+PDL1+
#> CD8+PD1-PDL1-_CD8+PD1-PDL1- CD8+PD1-PDL1- CD8+PD1-PDL1-
#> CD8-PD1+PDL1+_CD8-PD1+PDL1- CD8-PD1+PDL1+ CD8-PD1+PDL1-
#> CD8+PD1-PDL1+_CD8-PD1+PDL1- CD8+PD1-PDL1+ CD8-PD1+PDL1-
#> CD8+PD1-PDL1-_CD8+PD1+PDL1- CD8+PD1-PDL1- CD8+PD1+PDL1-
#> CD8-PD1-PDL1-_CD8+PD1-PDL1- CD8-PD1-PDL1- CD8+PD1-PDL1-
#> CD8+PD1+PDL1-_CD8+PD1-PDL1- CD8+PD1+PDL1- CD8+PD1-PDL1-Again, we obtain a spicy object which outlines the result of the mixed effects
models performed for each pairwise combination if cell types.
We can represent this as a heatmap using the spatialMEMMultiPlot() function by
providing it the spicy object obtained.
signifPlot(spicyTest, breaks=c(-3, 3, 0.5))
4.3 Bootstrapping with spicy
There are multiple ways for calculating p-values for mixed effects models. We
have also implemented a bootstrapping approach. All that is needed is a choice
for the number of resamples used in the bootstrap which can be set with the
nsim parameter in spicy().
spicyTestBootstrap <- spicy(melanomaResponders,
condition = "condition",
subject = "subject",
nsim = 199)spicyTestBootstrap
#>
#> Number of cell type pairs: 81
#> Number of differentially localised cell type pairs:
#> conditionResponders
#> 18
topPairs(spicyTestBootstrap)
#> intercept coefficient p.value adj.pvalue
#> CD8+PD1+PDL1+_SOX10+ -1.849790 -2.277733 0 0
#> CD8+PD1-PDL1-_CD8+PD1+PDL1- 11.049319 7.124038 0 0
#> CD8-PD1+PDL1+_CD8+PD1+PDL1- 21.403625 -14.143257 0 0
#> CD8+PD1+PDL1+_CD8-PD1+PDL1- 6.579050 -2.957959 0 0
#> CD8-PD1+PDL1+_CD8-PD1+PDL1- 11.621590 -6.942920 0 0
#> CD8+PD1-PDL1+_CD8-PD1+PDL1- 4.821599 -6.028484 0 0
#> CD8-PD1-PDL1+_CD8-PD1+PDL1- 4.438305 -2.245794 0 0
#> CD8-PD1-PDL1-_CD8+PD1-PDL1- 9.067690 -2.765159 0 0
#> CD8+PD1+PDL1-_CD8+PD1-PDL1- 11.041912 6.860201 0 0
#> CD8+PD1-PDL1-_CD8+PD1-PDL1- 20.934811 -11.403936 0 0
#> from to
#> CD8+PD1+PDL1+_SOX10+ CD8+PD1+PDL1+ SOX10+
#> CD8+PD1-PDL1-_CD8+PD1+PDL1- CD8+PD1-PDL1- CD8+PD1+PDL1-
#> CD8-PD1+PDL1+_CD8+PD1+PDL1- CD8-PD1+PDL1+ CD8+PD1+PDL1-
#> CD8+PD1+PDL1+_CD8-PD1+PDL1- CD8+PD1+PDL1+ CD8-PD1+PDL1-
#> CD8-PD1+PDL1+_CD8-PD1+PDL1- CD8-PD1+PDL1+ CD8-PD1+PDL1-
#> CD8+PD1-PDL1+_CD8-PD1+PDL1- CD8+PD1-PDL1+ CD8-PD1+PDL1-
#> CD8-PD1-PDL1+_CD8-PD1+PDL1- CD8-PD1-PDL1+ CD8-PD1+PDL1-
#> CD8-PD1-PDL1-_CD8+PD1-PDL1- CD8-PD1-PDL1- CD8+PD1-PDL1-
#> CD8+PD1+PDL1-_CD8+PD1-PDL1- CD8+PD1+PDL1- CD8+PD1-PDL1-
#> CD8+PD1-PDL1-_CD8+PD1-PDL1- CD8+PD1-PDL1- CD8+PD1-PDL1-
signifPlot(spicyTestBootstrap, breaks=c(-3, 3, 0.5))
Indeed, we get improved statistical power compared to the previous method.
5 sessionInfo()
sessionInfo()
#> R version 4.0.2 (2020-06-22)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 18.04.4 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.11-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.11-bioc/R/lib/libRlapack.so
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] parallel stats4 stats graphics grDevices utils datasets
#> [8] methods base
#>
#> other attached packages:
#> [1] S4Vectors_0.26.1 BiocGenerics_0.34.0 ggplot2_3.3.2
#> [4] spicyR_1.0.1 BiocStyle_2.16.0
#>
#> loaded via a namespace (and not attached):
#> [1] Rcpp_1.0.5 lattice_0.20-41 deldir_0.1-25
#> [4] class_7.3-17 digest_0.6.25 V8_3.2.0
#> [7] R6_2.4.1 evaluate_0.14 tensor_1.5
#> [10] pillar_1.4.6 rlang_0.4.7 curl_4.3
#> [13] minqa_1.2.4 nloptr_1.2.2.2 magick_2.4.0
#> [16] rpart_4.1-15 Matrix_1.2-18 goftest_1.2-2
#> [19] rmarkdown_2.3 labeling_0.3 splines_4.0.2
#> [22] lme4_1.1-23 BiocParallel_1.22.0 statmod_1.4.34
#> [25] stringr_1.4.0 pheatmap_1.0.12 polyclip_1.10-0
#> [28] munsell_0.5.0 spatstat.data_1.4-3 compiler_4.0.2
#> [31] numDeriv_2016.8-1.1 xfun_0.15 pkgconfig_2.0.3
#> [34] lmerTest_3.1-2 mgcv_1.8-31 htmltools_0.5.0
#> [37] tidyselect_1.1.0 tibble_3.0.3 bookdown_0.20
#> [40] IRanges_2.22.2 crayon_1.3.4 dplyr_1.0.0
#> [43] withr_2.2.0 MASS_7.3-51.6 grid_4.0.2
#> [46] jsonlite_1.7.0 nlme_3.1-148 gtable_0.3.0
#> [49] lifecycle_0.2.0 magrittr_1.5 concaveman_1.1.0
#> [52] scales_1.1.1 stringi_1.4.6 farver_2.0.3
#> [55] spatstat_1.64-1 ellipsis_0.3.1 spatstat.utils_1.17-0
#> [58] generics_0.0.2 vctrs_0.3.1 boot_1.3-25
#> [61] RColorBrewer_1.1-2 tools_4.0.2 glue_1.4.1
#> [64] purrr_0.3.4 abind_1.4-5 yaml_2.2.1
#> [67] colorspace_1.4-1 BiocManager_1.30.10 knitr_1.29