R/bi_ripleys_k_WSI.R
In FridleyLab/spatialTIME: Spatial Analysis of Vectra Immunoflourescent Data
Defines functions
bi_ripleys_k_WSI
Documented in
bi_ripleys_k_WSI
#' Bivariate Ripley's K for Whole Slide Images
#'
#' @param mif mIF object with spatial data frames, clinical, and per-sample summary information
#' @param mnames vector of column names for phenotypes or data frame of marker combinations
#' @param r_range vector range of radii to calculate co-localization *K*
#' @param edge_correction character edge_correction method, one of "translation", or none"
#' @param num_permutations integer number of permutations to estimate CSR
#' @param permute whether or not to use permutations to estimate CSR (TRUE) or to calculate exact CSR (FALSE)
#' @param keep_permutation_distribution boolean as to whether to summarise permutations to mean
#' @param overwrite boolean as to whether to replace existing bivariate_Count if exists
#' @param workers integer number of CPU workers to use
#' @param big integer used as the threshold for subsetting large samples, default is 1000 either *i* or *j*
#' @param nlarge number of cells in either *i* or *j* to flip to no edge correction - at small (relative to whole spatial region) *r* values differences in results between correction methods is negligible so running a few samples is recommended. Perhaps compute outweighs small differences in correction methods.
#' @param xloc the x and y positions that correspond to cells. If left as NULL, XMin, XMax, YMin, and YMax must be present in the spatial files
#' @param yloc the x and y positions that correspond to cells. If left as NULL, XMin, XMax, YMin, and YMax must be present in the spatial files
#'
#' @return mif object with bivariate Ripley's K calculated
#'
#' @description
#' Bivariate Ripley's K function within spatialTIME, `bi_ripleys_k` is a function that takes in a `mIF` object, along with
#' some parameters like marker names of interest and range of radii in which to assess bivariate clustering or colocalization.
#' In 1.3.3.3 we have introduced the ability to forsgo the need for permutations with the implementation of the exact CSR estimate.
#' This is both faster and being the exact CSR, produces an exact degree of clustering in the spatial files.
#'
#' Due to the availability of whole slide images (WSI), there's a possibility users will be running bivariate Ripley's K on samples
#' that have millions of cells. When doing this, keep in mind that a nearest neighbor matrix with *n* cell is *n* by *n* in size and
#' therefore easily consumers high performance compute levels of RAM. To combat this, we have implemented a tiling method that performs
#' counts for small chunks of the distance matrix at a time before finally calculating the bivariate Ripley's K value on the total counts.
#' When doing this there are now 2 import parameters to keep in mind. The `big` parameter is the size of the tile to use. We have found
#' 1000 to be a good number that allows for high number of cores while maintaining low RAM usage. The other important parameter when
#' working with WSI is nlarge which is the fall over for switching to no edge correction. The spatstat.explore::Kest univariate
#' Ripley's K uses a default of 3000 but we have defaulted to 1000 to keep compute minimized as edge correction uses large amounts
#' of RAM over 'none'.
#'
#' @export
#'
#' @examples
#' x <- spatialTIME::create_mif(clinical_data = spatialTIME::example_clinical %>%
#' dplyr::mutate(deidentified_id = as.character(deidentified_id)),
#' sample_data = spatialTIME::example_summary %>%
#' dplyr::mutate(deidentified_id = as.character(deidentified_id)),
#' spatial_list = spatialTIME::example_spatial,
#' patient_id = "deidentified_id",
#' sample_id = "deidentified_sample")
#' 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.")
#' x2 = bi_ripleys_k_WSI(mif = x, mnames = mnames_good[1:2],
#' r_range = 0:100, edge_correction = "none", permute = FALSE,
#' num_permutations = 50, keep_permutation_distribution = FALSE,
#' workers = 1, big = 1000)
bi_ripleys_k_WSI = function(mif,
mnames,
r_range = 0:100,
edge_correction = "translation",
num_permutations = 50,
permute = FALSE, #redo for permutation or estimate
keep_permutation_distribution = FALSE,
overwrite = TRUE,
workers = 6,
big = 1000,
nlarge = 1000,
xloc = NULL,
yloc = NULL){
Label = Anchor = Counted = `Exact CSR` = NULL
#check whether the object assigned to mif is of class mif
if(!inherits(mif, "mif")){
stop("Please use a mIF object for mif")
}
#check whether mnames is either a character vector a data frame
if(!inherits(mnames, "character") & !inherits(mnames, "data.frame")){
stop("Please use either a character vector or data frame of marker combinations for mnames")
}
#r_range has to have 0 for use with AUC (0,0)
if(!(0 %in% r_range)){
r_range = c(0, r_range)
}
if(!(edge_correction %in% c("trans", "none", "translation")))
stop("provide either translation or none for border correction")
#split mif into jobs for spatial files
#split mif into jobs for spatial files
out = parallel::mclapply(names(mif$spatial), function(spatial_name){
#prepare spatial data with x and y location (cell centers)
spat = mif$spatial[[spatial_name]]
if(is.null(xloc) & is.null(yloc)){
spat = spat %>%
dplyr::mutate(xloc = (XMin + XMax)/2,
yloc = (YMin + YMax)/2)
} else {
spat = spat %>%
dplyr::rename('xloc' := xloc,
'yloc' := yloc)
}
#find the window of the point process
win = spatstat.geom::convexhull.xy(spat$xloc, spat$yloc)
#calculate area of the window
area = spatstat.geom::area(win)
#matrix operations are WAY faster than data frame
#since now all numeric, easy enough to use matrix
spat = as.matrix(spat[,c("xloc", "yloc", as.character(unique(unlist(mnames))))])
#get the combinations data frame
if(inherits(mnames, "data.frame")){
m_combos = mnames
}
if(inherits(mnames, "character")){
m_combos = expand.grid(anchor = mnames,
counted = mnames) %>%
dplyr::filter(anchor != counted)
}
#calculating exact K works now!
if(!permute){
#calculate exact K
exact_K = spatstat.explore::Kest(spatstat.geom::ppp(x = spat[,'xloc'],
y = spat[,'yloc'],
window = win),
r = r_range,
correction = edge_correction) %>%
data.frame() %>%
dplyr::pull(3)
}
#for the combinations of markers, do bivark and permutations
res = parallel::mclapply(1:nrow(m_combos), function(combo){
#pull anchor and counted marker from combos data frame
anchor = m_combos[combo, ] %>% dplyr::pull(anchor) %>% as.character()
counted = m_combos[combo, ] %>% dplyr::pull(counted) %>% as.character()
cat(spatial_name, "\t", combo, "\t", anchor, "\t", counted, "\n")
#remove rows that are positive for both counted and anchor
spat_tmp = spat[!(spat[,anchor] == 1 & spat[,counted] == 1),c("xloc", "yloc", anchor, counted)]
#get data for both anchor and counted
i_dat = spat_tmp[spat_tmp[,3] == 1,]
j_dat = spat_tmp[spat_tmp[,4] == 1,]
#if the number of positive cells for either counted or anchor is less than 2, return empty K
if(sum(spat_tmp[,3]) < 2 | sum(spat_tmp[,4]) < 2){
final = data.frame(Label = spatial_name,
r = r_range,
Anchor = anchor,
Counted = counted,
`Theoretical CSR` = pi*r_range^2,
`Observed K` = NA,
`Permuted CSR` = NA,
`Exact CSR` = NA,
check.names=FALSE)
if(permute){
final = final %>%
dplyr::full_join(expand.grid(r = r_range,
iter = seq(num_permutations)),
by = "r")
} else {
final$iter = 1
}
return(final)
}
#make empty data frame to begin the final K table
K_obs = data.frame(r = r_range,
`Theoretical CSR` = pi * r_range^2,
check.names = FALSE)
#get observed K
K_obs$`Observed K` = calculateK(i_dat = i_dat,
j_dat = j_dat,
anchor = anchor,
counted = counted,
area = area, win = win, big = big,
r_range = r_range,
edge_correction = edge_correction,
cores = 1)
#set the anchor and counted in final table
K_obs$Anchor = anchor
K_obs$Counted = counted
if(permute){
#randomly sample the rows of possible cell locations for permuting
perm_rows = lapply(seq(num_permutations), function(x){
sample(1:nrow(spat), sum(nrow(i_dat), nrow(j_dat)), replace = FALSE)
})
#assign("perm_rows", perm_rows, envir = .GlobalEnv)
#calculate BiK for each permutation of cells
kpermed = parallel::mclapply(seq(perm_rows), function(perm_n){
cat(perm_n)
#extract vector of rows for permutation run
perm = perm_rows[[perm_n]]
#subset the x and y coords for those to use for permutation
dat = spat[perm,1:2]
#create label vector of anchor and counted cells of length anchor + counted
label = c(rep(anchor, nrow(i_dat)), rep(counted, nrow(j_dat)))
#subset permute rows for anchor and counted
i_dat = dat[label == anchor,]
j_dat = dat[label == counted,]
#prep permtued K table
permed = data.frame(r = r_range,
`Theoretical CSR` = pi * r_range^2,
iter = perm_n,
check.names = FALSE)
permed$`Permuted CSR` = calculateK(i_dat = i_dat,
j_dat = j_dat,
anchor = anchor,
counted = counted,
area = area, win = win, big = big,
r_range = r_range,
edge_correction = edge_correction,
cores = 1)
return(permed)
}, mc.preschedule = FALSE, mc.allow.recursive = TRUE) %>%
do.call(dplyr::bind_rows, .)
kpermed$`Exact CSR` = NA
} else {
kpermed = data.frame(r = r_range,
`Theoretical CSR` = pi * r_range^2,
iter = 1,
check.names = FALSE)
kpermed$`Permuted CSR` = NA
kpermed$`Exact CSR` = exact_K
}
#join the emperical K and the permuted CSR estimate
final = dplyr::full_join(K_obs,
kpermed, by = c("r", "Theoretical CSR")) %>%
#add the image label to the data frame
dplyr::mutate(Label = spatial_name, .before = 1)
return(final)
}) %>% #, mc.cores = cores, mc.preschedule = F,mc.allow.recursive = T
do.call(dplyr::bind_rows, .)
#reorder columns to make more sense
res = res[,c(1,2,7,5,6,3,4,8,9)]
return(res)
}, mc.cores = workers, mc.preschedule = FALSE,mc.allow.recursive = TRUE) %>%
do.call(dplyr::bind_rows, .)%>% #collapse all samples to single data frame
dplyr::rename(!!mif$sample_id := Label)
#if user doesn't want the permutation distribution, get average of the permutation estimate
if(!keep_permutation_distribution & permute){
out = out %>%
#remove iter since this is the permutation number
dplyr::select(-iter) %>%
#group by those used for permuting
dplyr::group_by(dplyr::across(mif$sample_id), r, Anchor, Counted) %>%
#take mean of theoretical, permuted, observed
dplyr::summarise_all(~mean(., na.rm=TRUE)) %>%
#calculate the degree of clustering from both the theoretical and permuted
dplyr::mutate(`Degree of Clustering Permutation` = `Observed K` - `Permuted CSR`,
`Degree of Clustering Theoretical` = `Observed K` - `Theoretical CSR`,
`Exact CSR` = NA) %>%
dplyr::mutate(iter = num_permutations, .before = Anchor)
}
#if overwrite is true, replace the bivariate count in the derived slot
if(overwrite){
mif$derived$bivariate_Count = out %>%
#calculate the degree of clustering from both the theoretical and permuted
dplyr::mutate(`Degree of Clustering Theoretical` = `Observed K` - `Theoretical CSR`,
`Degree of Clustering Permutation` = `Observed K` - `Permuted CSR`,
`Degree of Clustering Exact` = `Observed K` - `Exact CSR`) %>%
#add run number to differentiate between bivariate compute runs
dplyr::mutate(Run = 1)
}
#if don't overwrite
if(!overwrite){
#bind old and new bivar runs together, incrementing Run
mif$derived$bivariate_Count = mif$derived$bivariate_Count%>%
dplyr::bind_rows(out %>%
#calculate the degree of clustering from both the theoretical and permuted
dplyr::mutate(`Degree of Clustering Theoretical` = `Observed K` - `Theoretical CSR`,
`Degree of Clustering Permutation` = `Observed K` - `Permuted CSR`,
`Degree of Clustering Exact` = `Observed K` - `Exact CSR`) %>%
dplyr::mutate(Run = ifelse(exists("bivariate_Count", mif$derived),
max(mif$derived$bivariate_Count$Run) + 1,
1)))
}
#return the final mif object
return(mif)
}
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Defines functions bi_ripleys_k_WSI
Documented in bi_ripleys_k_WSI
#' Bivariate Ripley's K for Whole Slide Images
#'
#' @param mif mIF object with spatial data frames, clinical, and per-sample summary information
#' @param mnames vector of column names for phenotypes or data frame of marker combinations
#' @param r_range vector range of radii to calculate co-localization *K*
#' @param edge_correction character edge_correction method, one of "translation", or none"
#' @param num_permutations integer number of permutations to estimate CSR
#' @param permute whether or not to use permutations to estimate CSR (TRUE) or to calculate exact CSR (FALSE)
#' @param keep_permutation_distribution boolean as to whether to summarise permutations to mean
#' @param overwrite boolean as to whether to replace existing bivariate_Count if exists
#' @param workers integer number of CPU workers to use
#' @param big integer used as the threshold for subsetting large samples, default is 1000 either *i* or *j*
#' @param nlarge number of cells in either *i* or *j* to flip to no edge correction - at small (relative to whole spatial region) *r* values differences in results between correction methods is negligible so running a few samples is recommended. Perhaps compute outweighs small differences in correction methods.
#' @param xloc the x and y positions that correspond to cells. If left as NULL, XMin, XMax, YMin, and YMax must be present in the spatial files
#' @param yloc the x and y positions that correspond to cells. If left as NULL, XMin, XMax, YMin, and YMax must be present in the spatial files
#'
#' @return mif object with bivariate Ripley's K calculated
#'
#' @description
#' Bivariate Ripley's K function within spatialTIME, `bi_ripleys_k` is a function that takes in a `mIF` object, along with
#' some parameters like marker names of interest and range of radii in which to assess bivariate clustering or colocalization.
#' In 1.3.3.3 we have introduced the ability to forsgo the need for permutations with the implementation of the exact CSR estimate.
#' This is both faster and being the exact CSR, produces an exact degree of clustering in the spatial files.
#'
#' Due to the availability of whole slide images (WSI), there's a possibility users will be running bivariate Ripley's K on samples
#' that have millions of cells. When doing this, keep in mind that a nearest neighbor matrix with *n* cell is *n* by *n* in size and
#' therefore easily consumers high performance compute levels of RAM. To combat this, we have implemented a tiling method that performs
#' counts for small chunks of the distance matrix at a time before finally calculating the bivariate Ripley's K value on the total counts.
#' When doing this there are now 2 import parameters to keep in mind. The `big` parameter is the size of the tile to use. We have found
#' 1000 to be a good number that allows for high number of cores while maintaining low RAM usage. The other important parameter when
#' working with WSI is nlarge which is the fall over for switching to no edge correction. The spatstat.explore::Kest univariate
#' Ripley's K uses a default of 3000 but we have defaulted to 1000 to keep compute minimized as edge correction uses large amounts
#' of RAM over 'none'.
#'
#' @export
#'
#' @examples
#' x <- spatialTIME::create_mif(clinical_data = spatialTIME::example_clinical %>%
#' dplyr::mutate(deidentified_id = as.character(deidentified_id)),
#' sample_data = spatialTIME::example_summary %>%
#' dplyr::mutate(deidentified_id = as.character(deidentified_id)),
#' spatial_list = spatialTIME::example_spatial,
#' patient_id = "deidentified_id",
#' sample_id = "deidentified_sample")
#' 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.")
#' x2 = bi_ripleys_k_WSI(mif = x, mnames = mnames_good[1:2],
#' r_range = 0:100, edge_correction = "none", permute = FALSE,
#' num_permutations = 50, keep_permutation_distribution = FALSE,
#' workers = 1, big = 1000)
bi_ripleys_k_WSI = function(mif,
mnames,
r_range = 0:100,
edge_correction = "translation",
num_permutations = 50,
permute = FALSE, #redo for permutation or estimate
keep_permutation_distribution = FALSE,
overwrite = TRUE,
workers = 6,
big = 1000,
nlarge = 1000,
xloc = NULL,
yloc = NULL){
Label = Anchor = Counted = `Exact CSR` = NULL
#check whether the object assigned to mif is of class mif
if(!inherits(mif, "mif")){
stop("Please use a mIF object for mif")
}
#check whether mnames is either a character vector a data frame
if(!inherits(mnames, "character") & !inherits(mnames, "data.frame")){
stop("Please use either a character vector or data frame of marker combinations for mnames")
}
#r_range has to have 0 for use with AUC (0,0)
if(!(0 %in% r_range)){
r_range = c(0, r_range)
}
if(!(edge_correction %in% c("trans", "none", "translation")))
stop("provide either translation or none for border correction")
#split mif into jobs for spatial files
#split mif into jobs for spatial files
out = parallel::mclapply(names(mif$spatial), function(spatial_name){
#prepare spatial data with x and y location (cell centers)
spat = mif$spatial[[spatial_name]]
if(is.null(xloc) & is.null(yloc)){
spat = spat %>%
dplyr::mutate(xloc = (XMin + XMax)/2,
yloc = (YMin + YMax)/2)
} else {
spat = spat %>%
dplyr::rename('xloc' := xloc,
'yloc' := yloc)
}
#find the window of the point process
win = spatstat.geom::convexhull.xy(spat$xloc, spat$yloc)
#calculate area of the window
area = spatstat.geom::area(win)
#matrix operations are WAY faster than data frame
#since now all numeric, easy enough to use matrix
spat = as.matrix(spat[,c("xloc", "yloc", as.character(unique(unlist(mnames))))])
#get the combinations data frame
if(inherits(mnames, "data.frame")){
m_combos = mnames
}
if(inherits(mnames, "character")){
m_combos = expand.grid(anchor = mnames,
counted = mnames) %>%
dplyr::filter(anchor != counted)
}
#calculating exact K works now!
if(!permute){
#calculate exact K
exact_K = spatstat.explore::Kest(spatstat.geom::ppp(x = spat[,'xloc'],
y = spat[,'yloc'],
window = win),
r = r_range,
correction = edge_correction) %>%
data.frame() %>%
dplyr::pull(3)
}
#for the combinations of markers, do bivark and permutations
res = parallel::mclapply(1:nrow(m_combos), function(combo){
#pull anchor and counted marker from combos data frame
anchor = m_combos[combo, ] %>% dplyr::pull(anchor) %>% as.character()
counted = m_combos[combo, ] %>% dplyr::pull(counted) %>% as.character()
cat(spatial_name, "\t", combo, "\t", anchor, "\t", counted, "\n")
#remove rows that are positive for both counted and anchor
spat_tmp = spat[!(spat[,anchor] == 1 & spat[,counted] == 1),c("xloc", "yloc", anchor, counted)]
#get data for both anchor and counted
i_dat = spat_tmp[spat_tmp[,3] == 1,]
j_dat = spat_tmp[spat_tmp[,4] == 1,]
#if the number of positive cells for either counted or anchor is less than 2, return empty K
if(sum(spat_tmp[,3]) < 2 | sum(spat_tmp[,4]) < 2){
final = data.frame(Label = spatial_name,
r = r_range,
Anchor = anchor,
Counted = counted,
`Theoretical CSR` = pi*r_range^2,
`Observed K` = NA,
`Permuted CSR` = NA,
`Exact CSR` = NA,
check.names=FALSE)
if(permute){
final = final %>%
dplyr::full_join(expand.grid(r = r_range,
iter = seq(num_permutations)),
by = "r")
} else {
final$iter = 1
}
return(final)
}
#make empty data frame to begin the final K table
K_obs = data.frame(r = r_range,
`Theoretical CSR` = pi * r_range^2,
check.names = FALSE)
#get observed K
K_obs$`Observed K` = calculateK(i_dat = i_dat,
j_dat = j_dat,
anchor = anchor,
counted = counted,
area = area, win = win, big = big,
r_range = r_range,
edge_correction = edge_correction,
cores = 1)
#set the anchor and counted in final table
K_obs$Anchor = anchor
K_obs$Counted = counted
if(permute){
#randomly sample the rows of possible cell locations for permuting
perm_rows = lapply(seq(num_permutations), function(x){
sample(1:nrow(spat), sum(nrow(i_dat), nrow(j_dat)), replace = FALSE)
})
#assign("perm_rows", perm_rows, envir = .GlobalEnv)
#calculate BiK for each permutation of cells
kpermed = parallel::mclapply(seq(perm_rows), function(perm_n){
cat(perm_n)
#extract vector of rows for permutation run
perm = perm_rows[[perm_n]]
#subset the x and y coords for those to use for permutation
dat = spat[perm,1:2]
#create label vector of anchor and counted cells of length anchor + counted
label = c(rep(anchor, nrow(i_dat)), rep(counted, nrow(j_dat)))
#subset permute rows for anchor and counted
i_dat = dat[label == anchor,]
j_dat = dat[label == counted,]
#prep permtued K table
permed = data.frame(r = r_range,
`Theoretical CSR` = pi * r_range^2,
iter = perm_n,
check.names = FALSE)
permed$`Permuted CSR` = calculateK(i_dat = i_dat,
j_dat = j_dat,
anchor = anchor,
counted = counted,
area = area, win = win, big = big,
r_range = r_range,
edge_correction = edge_correction,
cores = 1)
return(permed)
}, mc.preschedule = FALSE, mc.allow.recursive = TRUE) %>%
do.call(dplyr::bind_rows, .)
kpermed$`Exact CSR` = NA
} else {
kpermed = data.frame(r = r_range,
`Theoretical CSR` = pi * r_range^2,
iter = 1,
check.names = FALSE)
kpermed$`Permuted CSR` = NA
kpermed$`Exact CSR` = exact_K
}
#join the emperical K and the permuted CSR estimate
final = dplyr::full_join(K_obs,
kpermed, by = c("r", "Theoretical CSR")) %>%
#add the image label to the data frame
dplyr::mutate(Label = spatial_name, .before = 1)
return(final)
}) %>% #, mc.cores = cores, mc.preschedule = F,mc.allow.recursive = T
do.call(dplyr::bind_rows, .)
#reorder columns to make more sense
res = res[,c(1,2,7,5,6,3,4,8,9)]
return(res)
}, mc.cores = workers, mc.preschedule = FALSE,mc.allow.recursive = TRUE) %>%
do.call(dplyr::bind_rows, .)%>% #collapse all samples to single data frame
dplyr::rename(!!mif$sample_id := Label)
#if user doesn't want the permutation distribution, get average of the permutation estimate
if(!keep_permutation_distribution & permute){
out = out %>%
#remove iter since this is the permutation number
dplyr::select(-iter) %>%
#group by those used for permuting
dplyr::group_by(dplyr::across(mif$sample_id), r, Anchor, Counted) %>%
#take mean of theoretical, permuted, observed
dplyr::summarise_all(~mean(., na.rm=TRUE)) %>%
#calculate the degree of clustering from both the theoretical and permuted
dplyr::mutate(`Degree of Clustering Permutation` = `Observed K` - `Permuted CSR`,
`Degree of Clustering Theoretical` = `Observed K` - `Theoretical CSR`,
`Exact CSR` = NA) %>%
dplyr::mutate(iter = num_permutations, .before = Anchor)
}
#if overwrite is true, replace the bivariate count in the derived slot
if(overwrite){
mif$derived$bivariate_Count = out %>%
#calculate the degree of clustering from both the theoretical and permuted
dplyr::mutate(`Degree of Clustering Theoretical` = `Observed K` - `Theoretical CSR`,
`Degree of Clustering Permutation` = `Observed K` - `Permuted CSR`,
`Degree of Clustering Exact` = `Observed K` - `Exact CSR`) %>%
#add run number to differentiate between bivariate compute runs
dplyr::mutate(Run = 1)
}
#if don't overwrite
if(!overwrite){
#bind old and new bivar runs together, incrementing Run
mif$derived$bivariate_Count = mif$derived$bivariate_Count%>%
dplyr::bind_rows(out %>%
#calculate the degree of clustering from both the theoretical and permuted
dplyr::mutate(`Degree of Clustering Theoretical` = `Observed K` - `Theoretical CSR`,
`Degree of Clustering Permutation` = `Observed K` - `Permuted CSR`,
`Degree of Clustering Exact` = `Observed K` - `Exact CSR`) %>%
dplyr::mutate(Run = ifelse(exists("bivariate_Count", mif$derived),
max(mif$derived$bivariate_Count$Run) + 1,
1)))
}
#return the final mif object
return(mif)
}
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