gateR: Flow/Mass Cytometry Gating via Spatial Kernel Density Estimation

Ian D. Buller, Ph.D., M.A. (Github: @idblr)

2020-12-04

The gateR package is a suite of R functions to identify significant spatial clustering of mass and flow cytometry data used in immunological investigations. The gateR package can be used for a panel of all surface markers, or a mixture of surface markers and functional read outs. The gateR package performs a gating technique that estimates statistically significant marker combination values within which one immunologically distinctive group (i.e., disease case) is more associated than another group (i.e., healthy control), successively, using various combinations (i.e., “gates”) of markers to examine features of cells that may be different between groups. For a two-group comparison, the gateR package uses the spatial relative risk function that is estimated using the sparr package. The gates are conducted in two-dimensional space comprised of two markers.

Examples of a single condition with two groups:

  1. Disease case v. healthy control
  2. Time 2 v. Time 1 (baseline)

For a two-group comparison of two conditions we estimate two relative risk surfaces for one condition and then a ratio of the relative risks. For example:

  1. Estimate a relative risk surface for:
    1. Condition 2B v. Condition 2A
    2. Condition 1B v. Condition 1A
  2. Estimate relative risk surface for the ratio:

\[\frac{(\frac{Condition2B}{Condition2A})}{(\frac{Condition1B}{Condition1A})}\]

Within areas where the relative risk exceeds an asymptotic normal assumption, the gateR package has functionality to examine the features of these cells.

This vignette provides an implementation of the gateR package using a randomly generated data set. Please see the README.md file within the gateR GitHub repository for an example using publicly available flow cytometry data from the flowWorkspaceData package available via Bioconductor. Here, we generate data with two conditions, four markers, and two additional features.

We start with the necessary packages and seed for the vignette.

  loadedPackages <- c("gateR", "graphics", "maptools", "raster", "sp", "sparr", "spatstat", "stats", "tibble", "utils")
  invisible(lapply(loadedPackages, library, character.only = TRUE))
  set.seed(1234) # for reproducibility

Generate random toy data using the spatstat package

Unique function to randomly generate data multivariate normal (MVN) around a central point. Parameters include the centroid coordinates (centre), number of observations to generate (ncell), and the standard deviation of the normal distribution (scalar).

  rand_mvn <- function(centre, ncell, scalar) {
    x0 <- centre[1]  
    y0 <- centre[2]
    x1 <- rep(x0, ncell)
    y1 <- rep(y0, ncell)
    x2 <- x1 + stats::rnorm(ncell, 0, scalar) 
    y2 <- y1 + stats::rnorm(ncell, 0, scalar) 
    x <- cbind(x2, y2)
  }

Gate 1: Marker 1 and Marker 2

At Condition 1, we generate 100,000 cases and 100,000 controls (ncell = 100000) randomly MVN with a case centroid at (0.55, 0.55) and a control centroid at (0.40, 0.40) within a unit square window (0, 1), and cases have a more focal cluster (scalar = 0.05) than controls (scalar = 0.15).

# Initial parameters
  ncell <- 100000 # number of observations per group per condition
  c1_cas_center <- c(0.55, 0.55)
  c1_con_center <- c(0.40, 0.40)
# V1 and V2 at Condition 1
  c1_cas <- rand_mvn(centre = c1_cas_center, ncell = ncell, scalar = 0.05)
  c1_con <- rand_mvn(centre = c1_con_center, ncell = ncell, scalar = 0.15)
  graphics::par(pty = "s")
  graphics::plot(c1_con,
                 col = "blue",
                 xlim = c(0, 1),
                 ylim = c(0, 1),
                 main = "Gate 1, Condition 1",
                 xlab = "V1",
                 ylab = "V2")
  graphics::points(c1_cas, col = "orangered4")

At Condition 2, we generate 100,000 cases and 100,000 controls (ncell = 100000) randomly MVN with a case centroid at (0.45, 0.45) and a control centroid at (0.40, 0.40) within a unit square window (0, 1), and cases have a more focal cluster (scalar = 0.05) than controls (scalar = 0.10).

# Initial parameters
  c2_cas_center <- c(0.45, 0.45)
  c2_con_center <- c(0.40, 0.40)
# V1 and V2 at Condition 2
  c2_cas <- rand_mvn(centre = c2_cas_center, ncell = ncell, scalar = 0.05)
  c2_con <- rand_mvn(centre = c2_con_center, ncell = ncell, scalar = 0.10)
  graphics::par(pty = "s")
  graphics::plot(c2_con,
                 col = "cornflowerblue",
                 xlim = c(0, 1),
                 ylim = c(0, 1),
                 main = "Gate 1, Condition 2",
                 xlab = "V1",
                 ylab = "V2")
  graphics::points(c2_cas, col = "orangered1")

# compile data
  df_full <- tibble::tibble("id" = seq(1, ncell * 2 * 2, 1),
                            "group" = factor(c(rep("case", ncell * 2),
                                               rep("control", ncell * 2))),
                            "condition" = factor(c(rep("2", ncell), rep("1", ncell),
                                              rep("2", ncell), rep("1", ncell))),
                            "V1" = c(c2_cas[ , 1], c1_cas[ , 1], c2_con[ , 1], c1_con[ , 1]),
                            "V2" = c(c2_cas[ , 2], c1_cas[ , 2], c2_con[ , 2], c1_con[ , 2]))

  rm(c2_cas, c1_cas, c2_con, c1_con) # conserve memory

Gate 2: Marker 3 and Marker 4

At Condition 1, we generate 100,000 cases and 100,000 controls (ncell = 100000) randomly MVN with a case centroid at (0.55, 0.55) and a control centroid at (0.50, 0.50) within a unit square window (0, 05), but both have the same amount of spread (scalar = 0.10).

# Initial parameters
  c1_cas_center <- c(0.55, 0.55)
  c1_con_center <- c(0.50, 0.50)
# V3 and V4 at Condition 1
  c1_cas <- rand_mvn(centre = c1_cas_center, ncell = ncell, scalar = 0.05)
  c1_con <- rand_mvn(centre = c1_con_center, ncell = ncell, scalar = 0.10)
  graphics::par(pty = "s")
  graphics::plot(c1_con,
                 col = "blue",
                 xlim = c(0, 1),
                 ylim = c(0, 1),
                 main = "Gate 2, Condition 1",
                 xlab = "V3",
                 ylab = "V4")
  graphics::points(c1_cas, col = "orangered4")

At Condition 2, we generate 100,000 cases and 100,000 controls (ncell = 100000) randomly with a case centroid at (0.65, 0.65) and control a centroid at (0.50, 0.50) within a unit square window (0, 1), and cases have a more focal cluster (scalar = 0.05) than controls (scalar = 0.10).

# Initial parameters
  c2_cas_center <- c(0.65, 0.65)
  c2_con_center <- c(0.50, 0.50)
# V3 and V4 at Condition 2
  c2_cas <- rand_mvn(centre = c2_cas_center, ncell = ncell, scalar = 0.05)
  c2_con <- rand_mvn(centre = c2_con_center, ncell = ncell, scalar = 0.10)
  graphics::par(pty = "s")
  graphics::plot(c2_con,
                 col = "cornflowerblue",
                 xlim = c(0, 1),
                 ylim = c(0, 1),
                 main = "Gate 2, Condition 2",
                 xlab = "V3",
                 ylab = "V4")
  graphics::points(c2_cas, col = "orangered1")

Compile the toy data into a data frame

  df_full$V3 <-  c(c2_cas[ , 1], c1_cas[ , 1], c2_con[ , 1], c1_con[ , 1])
  df_full$V4 <-  c(c2_cas[ , 2], c1_cas[ , 2], c2_con[ , 2], c1_con[ , 2])
  
  rm(c2_cas, c1_cas, c2_con, c1_con) # conserve memory

Generate random values for two example cytokines and append to the data frame.

# Two Cytokines
  Z1 <- stats::rchisq(ncell * 4, df = 5) # Random Chi-square distribution
  Z2 <- stats::rnorm(ncell * 4, 0, 1) # Random Gaussian distribution
# Append to data.frame
  df_full$Z1 <- Z1
  df_full$Z2 <- Z2
  rm(Z1, Z2) # conserve memory
# Visualize histograms by the two group conditions
  graphics::par(mfrow = c(2, 2), pty = "s")
  graphics::plot(stats::density(df_full$Z1[df_full$group == "case" 
                                           & df_full$condition == "1"]),
                 main = "Cytokine 1 of Cases at Condition 1")
  graphics::plot(stats::density(df_full$Z1[df_full$group == "case" 
                                           & df_full$condition == "2"]),
                 main = "Cytokine 1 of Cases at Condition 2")
  graphics::plot(stats::density(df_full$Z1[df_full$group == "control"
                                           & df_full$condition == "1"]),
                 main = "Cytokine 1 of Controls at Condition 1")
  graphics::plot(stats::density(df_full$Z1[df_full$group == "control"
                                           & df_full$condition == "2"]),
                 main = "Cytokine 1 of Controls at Condition 2")
  graphics::plot(stats::density(df_full$Z2[df_full$group == "case"
                                           & df_full$condition == "1"]),
                 main = "Cytokine 2 of Cases at Condition 1")
  graphics::plot(stats::density(df_full$Z2[df_full$group == "case" 
                                           & df_full$condition == "2"]),
                 main = "Cytokine 2 of Cases at Condition 2")
  graphics::plot(stats::density(df_full$Z2[df_full$group == "control" 
                                           & df_full$condition == "1"]),
                 main = "Cytokine 2 of Controls at Condition 1")
  graphics::plot(stats::density(df_full$Z2[df_full$group == "control" 
                                           & df_full$condition == "2"]),
                 main = "Cytokine 2 of Controls at Condition 2")

The toy data frame has nine columns (id, groups, markers, and cytokines).

  utils::head(df_full)
## # A tibble: 6 x 9
##      id group condition    V1    V2    V3    V4    Z1      Z2
##   <dbl> <fct> <fct>     <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl>
## 1     1 case  2         0.491 0.402 0.677 0.586  4.35 -0.488 
## 2     2 case  2         0.407 0.493 0.714 0.698  8.61  0.279 
## 3     3 case  2         0.508 0.409 0.547 0.644  6.79 -0.786 
## 4     4 case  2         0.423 0.480 0.657 0.656  1.04 -0.552 
## 5     5 case  2         0.367 0.420 0.635 0.637  4.10  0.239 
## 6     6 case  2         0.499 0.405 0.547 0.656  6.99  0.0472

For two conditions

# Initial parameters
  alpha <- 0.05
  vars <- c("V1", "V2", "V3", "V4")
  p_correct <- "uncorrelated"
  set.seed(1234) # for reproducibility
  df_full <- as.data.frame(df_full)

# Gates 1 and 2
  start_time <- Sys.time() # record start time
  out_gate <- gateR::gating(dat = df_full,
                            vars = vars,
                            n_condition = 2,
                            plot_gate = TRUE,
                            alpha = alpha,
                            p_correct = p_correct,
                            c1n = "case", # level "case" as the numerator of first condition
                            c2n = "2") # level "2" as the numerator of second condition
  end_time <- Sys.time() # record end time
  total_time <- end_time - start_time # calculate duration of gating() example

The gating process took about 10.9 seconds on a Macbook Pro (4 variables, 2 gates, 2 cytokines, 400,000 observations). The corrected significance level in the first gate was . The histograms for the two cytokines are the same as above.

# Plot of Cytokine 1
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(out_gate$obs$Z1[out_gate$obs$group == "case"
                                                & out_gate$obs$condition == "2"]),
                 col = "red", main = "Cytokine 1 of cases\npost-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
  graphics::plot(stats::density(out_gate$obs$Z1[out_gate$obs$group == "control" 
                                                & out_gate$obs$condition == "2"]),
                 col = "blue",
                 main = "Cytokine 1 of controls\npost-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
# Plot of Cytokine 2
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(out_gate$obs$Z2[out_gate$obs$group == "case"
                                                & out_gate$obs$condition == "2"]),
                 col = "red",
                 main = "Cytokine 2 of cases\npost-gating",
                 xlim = c(-5, 5),
                 ylim = c(0, 0.5))
  graphics::plot(stats::density(out_gate$obs$Z2[out_gate$obs$group == "control" 
                                                & out_gate$obs$condition == "2"]),
                 col = "blue",
                 main = "Cytokine 2 of controls\npost-gating",
                 xlim = c(-5, 5),
                 ylim = c(0, 0.5))

Compare histograms before and after gating. Gating reduced the overall sample size of observations from 400,000 (cases & controls and Condition 1 & Condition 2) to 63,463 observations (cases & controls and Condition 1 & Condition 2).

# Plot of Cytokine 1
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(df_full$Z1[df_full$group == "case"
                                 & df_full$condition == "2"]),
                 col = "black",
                 lty = 1,
                 main = "Cytokine 1 of cases\npre-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
  graphics::plot(stats::density(out_gate$obs$Z1[out_gate$obs$group == "case"
                                      & out_gate$obs$condition == "2"]),
                 col = "black",
                 lty = 1,
                 main = "Cytokine 1 of cases\npost-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
# Plot of Cytokine 2
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(df_full$Z2[df_full$group == "case" 
                                           & df_full$condition == "2"]),
                 col = "black",
                 lty = 1,
                 main = "Cytokine 2 of cases\npre-gating",
                 xlim = c(-5, 5),
                 ylim = c(0, 0.5))
  graphics::plot(stats::density(out_gate$obs$Z2[out_gate$obs$group == "case" 
                                                & out_gate$obs$condition == "2"]),
                 col = "black",
                 lty = 1, 
                 main = "Cytokine 2 of cases\npost-gating",
                 xlim = c(-5 ,5),
                 ylim = c(0, 0.5))

For a one condition (using only Condition 1)

# Data subset, only c1
  df_sub <- df_full[df_full$condition == 1, ] # For only condition condition = 1

# Initial parameters
  alpha <- 0.05
  vars <- c("V1", "V2", "V3", "V4")
  p_correct <- "uncorrelated"
  set.seed(1234) # for reproducibility
  
# Gates 1 and 2
  start_time <- Sys.time() # record start time
  out_gate <- gateR::gating(dat = df_sub,
                            vars = vars,
                            plot_gate = TRUE,
                            n_condition = 1,
                            alpha = alpha,
                            p_correct = p_correct,
                            c1n = "case") # level "case" as the numerator of first condition
  end_time <- Sys.time() # record end time
  total_time <- end_time - start_time # calculate duration of gating() example

The gating process took about 6.1 seconds on a Macbook Pro (4 variables, 2 gates, 2 cytokines, 200,000 observations). The corrected significance level in the first gate was . The histograms for the two cytokines are the same as above.

# Plot of Cytokine 1
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(out_gate$obs$Z1[out_gate$obs$group == "case"]),
                 col = "red",
                 main = "Cytokine 1 of cases\npost-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
  graphics::plot(stats::density(out_gate$obs$Z1[out_gate$obs$group == "control"]),
                 col = "blue",
                 main = "Cytokine 1 of controls\npost-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
# Plot of Cytokine 2
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(out_gate$obs$Z2[out_gate$obs$group == "case"]),
                 col = "red",
                 main = "Cytokine 2 of cases\npost-gating",
                 xlim = c(-5, 5),
                 ylim = c(0, 0.5))
  graphics::plot(stats::density(out_gate$obs$Z2[out_gate$obs$group == "control"]),
                 col = "blue",
                 main = "Cytokine 2 of controls\npost-gating",
                 xlim = c(-5, 5),
                 ylim = c(0, 0.5))

Compare histograms before and after gating. Gating reduced the overall sample size of observations from 200,000 (cases & controls) to 85,729 observations (cases & controls).

# Plot of Cytokine 1
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(df_full$Z1[df_full$group == "case"]),
                 col = "black",
                 lty = 1,
                 main = "Cytokine 1 of cases\npre-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
  graphics::plot(stats::density(out_gate$obs$Z1[out_gate$obs$group == "case"]),
                 col = "black",
                 lty = 1,
                 main = "Cytokine 1 of cases\npost-gating",
                 xlim = c(-5, 30),
                 ylim = c(0, 0.2))
# Plot of Cytokine 2
  graphics::par(mfrow = c(1, 2), pty = "s")
  graphics::plot(stats::density(df_full$Z2[df_full$group == "case"]),
                 col = "black",
                 lty = 1,
                 main = "Cytokine 2 of cases\npre-gating",
                 xlim = c(-5, 5),
                 ylim = c(0, 0.5))
  graphics::plot(stats::density(out_gate$obs$Z2[out_gate$obs$group == "case"]),
                 col = "black",
                 lty = 1,
                 main = "Cytokine 2 of cases\npost-gating",
                 xlim = c(-5 ,5),
                 ylim = c(0, 0.5))

Current limitations

  1. Extracts observations at all significant clusters (either case or controls) and there is currently no functionality to select cells within a specific (set of) cluster(s) for the next gate.
  2. Only two dimensions (i.e., markers) per gate because the spatial relative risk function is a two-dimensional spatial statistic.
  3. Only two-group comparisons (e.g., case v. control) per gate because the spatial relative risk function is a ratio by nature.
  4. Only comparisons of one condition or comparisons of two conditions are possible.
  5. Large computational expense (i.e., run-time) to calculate the correlated Bonferroni correction.
  6. A large sample size of observations (i.e., cells) may overload the gateR process. We are evaluating this potential limitation and developing a possible solution (e.g., randomly subsetting the data to estimate the clusters at each gate).