Help for package gateR

Type:

Package

Title:

Flow/Mass Cytometry Gating via Spatial Kernel Density Estimation

Version:

0.1.15

Date:

2024-01-23

Maintainer:

Ian D. Buller <ian.buller@alumni.emory.edu>

Description:

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 estimated using the 'sparr' package. Details about the 'sparr' package methods can be found in the tutorial: Davies et al. (2018) <doi:10.1002/sim.7577>. Details about kernel density estimation can be found in J. F. Bithell (1990) <doi:10.1002/sim.4780090616>. More information about relative risk functions using kernel density estimation can be found in J. F. Bithell (1991) <doi:10.1002/sim.4780101112>.

License:

Apache License (≥ 2.0)

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.2.3

Depends:

R (≥ 3.5.0)

Imports:

fields, graphics, grDevices, lifecycle, rlang, sparr, SpatialPack, spatstat.geom, stats, terra, tibble

Suggests:

dplyr, R.rsp, spelling, testthat, usethis, utils

VignetteBuilder:

R.rsp

Language:

en-US

URL:

https://github.com/lance-waller-lab/gateR

BugReports:

https://github.com/lance-waller-lab/gateR/issues

NeedsCompilation:

Packaged:

2024-01-23 14:13:48 UTC; ian.buller

Author:

Ian D. Buller

[aut, cre, cph], Elena Hsieh

[ctb], Debashis Ghosh

[ctb], Lance A. Waller

[ctb], NCI [cph]

Repository:

CRAN

Date/Publication:

2024-01-23 14:30:04 UTC

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

Description

Estimates statistically significant fluorescent 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 fluorescent markers to examine features of cells that may be different between groups.

Details

For a two-group comparison, the 'gateR' package uses the spatial relative risk function estimated using the sparr package. Details about the sparr package methods can be found in the tutorial: Davies et al. (2018) doi:10.1002/sim.7577. Details about kernel density estimation can be found in J. F. Bithell (1990) doi:10.1002/sim.4780090616. More information about relative risk functions using kernel density estimation can be found in J. F. Bithell (1991) doi:10.1002/sim.4780101112.

This package provides a function to perform a gating strategy for flow cytometry data. The 'gateR' package also provides basic visualization for each gate.

Key content of the 'gateR' package include:

Gating Strategy

gating Extracts cells within statistically significant combinations of fluorescent markers, successively, for a set of markers. Statistically significant combinations are identified using two-tailed p-values of a relative risk surface assuming asymptotic normality. This function is currently available for two-level comparisons of a single condition (e.g., case/control) or two conditions (e.g., case/control at time 1 and time 2). Provides functionality for basic visualization and multiple testing correction.

rrs Estimates a relative risk surface and computes the asymptotic p-value surface for a single gate with a single condition, including features for basic visualization. This function is used internally within the gating function to extract the points within the significant areas. This function can also be used as a standalone function.

lotrrs Estimates a ratio of relative risk surfaces and computes the asymptotic p-value surface for a single gate with two conditions, including features for basic visualization. This function is used internally within the gating function to extract the points within the significant areas. This function can also be used as a standalone function.

Flow Cytometry Data

randCyto A sample dataset containing information about flow cytometry data with two binary categorical variables. The data are a random subset of the 'extdata' data in the 'flowWorkspaceData' package found on Bioconductor https://bioconductor.org/packages/release/data/experiment/html/flowWorkspaceData.html and formatted for 'gateR' input.

Dependencies

The 'gateR' package relies heavily upon sparr, spatstat.geom, and terra. For a two-level comparison, the spatial relative risk function uses the risk function. The calculation of a Bonferroni correction for multiple testing accounting for the spatial correlation of the estimated surface uses the modified.ttest function. Basic visualizations rely on the image.plot function.

Author(s)

Ian D. Buller
Social & Scientific Systems, Inc., a division of DLH Corporation, Silver Spring, Maryland, USA (current); Occupational and Environmental Epidemiology Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health, Rockville, Maryland, USA (former); Environmental Health Sciences, James T. Laney School of Graduate Studies, Emory University, Atlanta, Georgia, USA. (original)

Maintainer: I.D.B. ian.buller@alumni.emory.edu

Gating strategy for mass cytometry data using spatial relative risk functions

Description

Extracts cells within statistically significant combinations of fluorescent markers, successively, for a set of markers. Statistically significant combinations are identified using two-tailed p-values of a relative risk surface assuming asymptotic normality. This function is currently available for two-level comparisons of a single condition (e.g., case/control) or two conditions (e.g., case/control at time 1 and time 2). Provides functionality for basic visualization and multiple testing correction.

Usage

gating(
  dat,
  vars,
  n_condition = c(1, 2),
  numerator = TRUE,
  bandw = NULL,
  alpha = 0.05,
  p_correct = "none",
  nbc = NULL,
  plot_gate = FALSE,
  save_gate = FALSE,
  name_gate = NULL,
  path_gate = NULL,
  rcols = c("#FF0000", "#CCCCCC", "#0000FF"),
  lower_lrr = NULL,
  upper_lrr = NULL,
  c1n = NULL,
  c2n = NULL,
  win = NULL,
  ...,
  doplot = lifecycle::deprecated(),
  verbose = lifecycle::deprecated()
)

Arguments

dat

Input data frame flow cytometry data with the following features (columns): 1) ID, 2) Condition A ID, 3) Condition B ID (optional), and a set of markers.

vars

A vector of characters with the name of features (columns) within dat to use as markers for each gate. See details below.

n_condition

A numeric value of either 1 or 2 designating if the gating is performed with one condition or two conditions.

numerator

Logical. If TRUE (the default), cells will be extracted within all statistically significant numerator (i.e., case) clusters. If FALSE, cells will be extracted within all statistically significant denominator (i.e., control) clusters.

bandw

Optional, numeric. Fixed bandwidth for the kernel density estimation. Default is based on the internal [sparr]{OS} function.

alpha

Numeric. The two-tailed alpha level for significance threshold (default is 0.05).

p_correct

Optional. Character string specifying whether to apply a correction for multiple comparisons including a False Discovery Rate p_correct = "FDR", a spatially dependent Sidak correction p_correct = "correlated Sidak", a spatially dependent Bonferroni correction p_correct = "correlated Bonferroni", an independent Sidak correction p_correct = "uncorrelated Sidak", an independent Bonferroni correction p_correct = "uncorrelated Bonferroni", and a correction based on Random Field Theory using an equation by Adler and Hasofer p_correct = "Adler and Hasofer" or an equation by Friston et al. p_correct = "Friston". If p_correct = "none" (the default), then no correction is applied.

nbc

Optional. An integer for the number of bins when p_correct = "correlated". Similar to nbclass argument in modified.ttest. The default is 30.

plot_gate

Logical. If TRUE, the output includes basic data visualizations.

save_gate

Logical. If TRUE, the output saves each visualization as a separate PNG file.

name_gate

Optional, character. The filename of the visualization(s). The default is "gate_k" where "k" is the gate number.

path_gate

Optional, character. The path of the visualization(s). The default is the current working directory.

rcols

Character string of length three (3) specifying the colors for: 1) group A (numerator), 2) neither, and 3) group B (denominator) designations. The defaults are c("#FF0000", "#cccccc", "#0000FF") or c("red", "grey80", "blue").

lower_lrr

Optional, numeric. Lower cut-off value for the log relative risk value in the color key (typically a negative value). The default is no limit, and the color key will include the minimum value of the log relative risk surface.

upper_lrr

Optional, numeric. Upper cut-off value for the log relative risk value in the color key (typically a positive value). The default is no limit, and the color key will include the maximum value of the log relative risk surface.

c1n

Optional, character. The name of the level for the numerator of condition A. The default is NULL, and the first level is treated as the numerator.

c2n

Optional, character. The name of the level for the numerator of condition B. The default is NULL, and the first level is treated as the numerator.

win

Optional. Object of class owin for a custom two-dimensional window within which to estimate the surfaces. The default is NULL and calculates a convex hull around the data.

...

Arguments passed to risk to select resolution.

doplot

doplot is no longer supported and has been renamed plot_gate.

verbose

verbose is no longer supported; this function will not display verbose output from internal risk function.

Details

This function performs a sequential gating strategy for mass cytometry data comparing two levels with one or two conditions. Gates are typically two-dimensional space comprised of two fluorescent markers. The two-level comparison allows for the estimation of a spatial relative risk function and the computation of p-value based on an assumption of asymptotic normality. Cells within statistically significant areas are extracted and used in the next gate. This function relies heavily upon the risk function. Basic visualization is available if plot_gate = TRUE.

The vars argument must be a vector with an even-numbered length where the odd-numbered elements are the markers used on the x-axis of a gate, and the even-numbered elements are the markers used on the y-axis of a gate. For example, if vars = c("V1", "V2", "V3", and "V4") then the first gate is "V1" on the x-axis and "V2" on the y-axis and then the second gate is V3" on the x-axis and "V4" on the y-axis. Makers can be repeated in successive gates.

The n_condition argument specifies if the gating strategy is performed for one condition or two conditions. If n_condition = 1, then the function performs a one condition gating strategy using the internal rrs function, which computes the statistically significant areas (clusters) of a relative risk surface at each gate and selects the cells within the clusters specified by the numerator argument. If n_condition = 2, then the function performs a two conditions gating strategy using the internal lotrrs function, which computes the statistically significant areas (clusters) of a ratio of relative risk surfaces at each gate and selects the cells within the clusters specified by the numerator argument. The condition variable(s) within dat must be of class 'factor' with two levels. The first level is considered the numerator (i.e., "case") value, and the second level is considered the denominator (i.e., "control") value. The levels can also be specified using the c1n and c2n parameters. See the documentation for the internal rrs and lotrrs functions for more details.

The p-value surface of the ratio of relative risk surfaces is estimated assuming asymptotic normality of the ratio value at each gridded knot. The bandwidth is fixed across all layers.

Provides functionality for a correction for multiple testing. If p_correct = "FDR", calculates a False Discovery Rate by Benjamini and Hochberg. If p_correct = "uncorrelated Sidak", calculates an independent Sidak correction. If p_correct = "uncorrelated Bonferroni", calculates an independent Bonferroni correction. If p_correct = "correlated Sidak" or if p_correct = "correlated Bonferroni", then the corrections take into account the into account the spatial correlation of the surface. (NOTE: If p_correct = "correlated Sidak" or if p_correct = "correlated Bonferroni", it may take a considerable amount of computation resources and time to calculate). If p_correct = "Adler and Hasofer" or if p_correct = "Friston", then calculates a correction based on Random Field Theory. If p_correct = "none" (the default), then the function does not account for multiple testing and uses the uncorrected alpha level. See the internal pval_correct function documentation for more details.

Value

An object of class list. This is a named list with the following components:

obs: An object of class 'tibble' of the same features as dat that includes the information for the cells extracted with significant clusters in the final gate.
n: An object of class 'list' of the sample size of cells at each gate. The length is equal to the number of successful gates plus the final result.
gate: An object of class 'list' of 'rrs' objects from each gate. The length is equal to the number of successful gates.
note: An object of class 'character' of the gating diagnostic message.

The objects of class 'rrs' is similar to the output of the risk function with two additional components:

rr: An object of class 'im' with the relative risk surface.
f: An object of class 'im' with the spatial density of the numerator.
g: An object of class 'im' with the spatial density of the denominator.
P: An object of class 'im' with the asymptotic p-value surface.
lrr: An object of class 'im' with the log relative risk surface.
alpha: A numeric value for the alpha level used within the gate.

Examples

if (interactive()) {
## Single condition, no multiple testing correction
  test_gate <- gating(dat = randCyto,
                      vars = c("arcsinh_CD4", "arcsinh_CD38",
                               "arcsinh_CD8", "arcsinh_CD3"),
                      n_condition = 1)
}

A single gate for two conditions

Description

Estimates a ratio of relative risk surfaces and computes the asymptotic p-value surface for a single gate with two conditions. Includes features for basic visualization. This function is used internally within the gating function to extract the points within the significant areas. This function can also be used as a standalone function.

Usage

lotrrs(
  dat,
  bandw = NULL,
  alpha = 0.05,
  p_correct = "none",
  nbc = NULL,
  plot_gate = FALSE,
  save_gate = FALSE,
  name_gate = NULL,
  path_gate = NULL,
  rcols = c("#FF0000", "#CCCCCC", "#0000FF"),
  lower_lrr = NULL,
  upper_lrr = NULL,
  c1n = NULL,
  c2n = NULL,
  win = NULL,
  ...,
  doplot = lifecycle::deprecated(),
  verbose = lifecycle::deprecated()
)

Arguments

dat

Input data frame flow cytometry data with five (5) features (columns): 1) ID, 2) Condition A ID, 3) Condition B ID, 4) Marker A as x-coordinate, 5) Marker B as y-coordinate.

bandw

Optional, numeric. Fixed bandwidth for the kernel density estimation. Default is based on the internal [sparr]{OS} function.

alpha

Numeric. The two-tailed alpha level for significance threshold (default is 0.05).

p_correct

nbc

Optional. An integer for the number of bins when p_correct = "correlated". Similar to nbclass argument in modified.ttest. The default is 30.

plot_gate

Logical. If TRUE, the output includes basic data visualization.

save_gate

Logical. If TRUE, the output saves the visualization as a separate PNG file.

name_gate

Optional, character. The filename of the visualization. The default is "gate".

path_gate

Optional, character. The path of the visualization. The default is the current working directory.

rcols

lower_lrr

upper_lrr

c1n

Optional, character. The name of the level for the numerator of condition A. The default is NULL, and the first level is treated as the numerator.

c2n

Optional, character. The name of the level for the numerator of condition B. The default is NULL, and the first level is treated as the numerator.

win

Optional. Object of class owin for a custom two-dimensional window within which to estimate the surfaces. The default is NULL and calculates a convex hull around the data.

...

Arguments passed to risk to select resolution.

doplot

doplot is no longer supported and has been renamed plot_gate.

verbose

verbose is no longer supported; this function will not display verbose output from internal risk function.

Details

This function estimates a ratio of relative risk surfaces and computes the asymptotic p-value surface for a single gate with two conditions using three successive risk functions. A relative risk surface is estimated for Condition A at each level of Condition B, and then a ratio of the two relative risk surfaces is computed.

RR_{Condition B1} = \frac{Condition A2 of B1}{Condition A1 of B1}

RR_{Condition B2} = \frac{Condition A2 of B2}{Condition A1 of B2}

ln(rRR) = ln\left (\frac{RR_{Condition B2}}{CRR_{Condition B2}}\right )

The p-value surface of the ratio of relative risk surfaces is estimated assuming asymptotic normality of the ratio value at each gridded knot. The bandwidth is fixed across all layers. Basic visualization is available if plot_gate = TRUE.

The two condition variables (Condition A and Condition B) within dat must be of class 'factor' with two levels. The first level in each variable is considered the numerator (i.e., "case") value, and the second level is considered the denominator (i.e., "control") value. The levels can also be specified using the c1n and c2n parameters.

Value

An object of class 'list' where each element is a object of class 'rrs' created by the risk function with two additional components:

rr: An object of class 'im' with the relative risk surface.
f: An object of class 'im' with the spatial density of the numerator.
g: An object of class 'im' with the spatial density of the denominator.
P: An object of class 'im' with the asymptotic p-value surface.
lrr: An object of class 'im' with the log relative risk surface.
alpha: A numeric value for the alpha level used within the gate.

Examples

test_lotrrs <- lotrrs(dat = randCyto)

Prepare log relative risk values for plotting with a diverging color palette

Description

Internal function to convert an object of class 'im' to values readable by image.plot function within the rrs and lotrrs functions.

Usage

lrr_plot(
  input,
  cols,
  midpoint = 0,
  lower_lrr = NULL,
  upper_lrr = NULL,
  digits = 1
)

Arguments

input

An object of class 'rrs' from the rrs or lotrrs function.

cols

Character string of length three (3) specifying the colors for plotting: 1) numerator, 2) insignificant, and 3) denominator from the rrs or lotrrs function.

midpoint

Numeric. The value to center the diverging color palette.

lower_lrr

Numeric. The lower value to concatenate the color key. The default (NULL) uses the minimum value from input.

upper_lrr

Numeric. The upper value to concatenate the color key. The default (NULL) uses the maximum value from input.

digits

Integer. The number of significant digits for the labels using the round function (default is 1).

Value

An object of class 'list'. This is a named list with the following components:

v: An object of class 'SpatRaster' for the estimated gating surface.
cols: An object of class 'vector', returns diverging color palette values.
breaks: An object of class 'vector', returns diverging color palette breaks.
at: An object of class 'vector', returns legend breaks.
labels: An object of class 'vector', returns legend labels.

Calculate p-value corrections for multiple testing

Description

Internal function to calculate various p-value corrections for use within the rrs and lotrrs functions.

Usage

pval_correct(
  input,
  type = c("FDR", "correlated Sidak", "correlated Bonferroni", "uncorrelated Sidak",
    "uncorrelated Bonferroni", "Adler and Hasofer", "Friston"),
  alpha = 0.05,
  nbc = NULL
)

Arguments

input

An object of class 'rrs' from the rrs or lotrrs function.

type

Character string specifying which correction for multiple comparisons. Options include a False Discovery Rate p_correct = "FDR", a spatially dependent Sidak correction p_correct = "correlated Sidak", a spatially dependent Bonferroni correction p_correct = "correlated Bonferroni", an independent Sidak correction p_correct = "uncorrelated Sidak", an independent Bonferroni correction p_correct = "uncorrelated Bonferroni", a Adler and Hasofer equation for the maximum of a Gaussian random field p_correct = "Adler and Hasofer", and a Friston et al. equation for the maximum of a Gaussian random field p_correct = "Friston".

alpha

Numeric. The two-tailed alpha level for significance threshold (default in rrs and lotrrs functions is 0.05).

nbc

Integer. The number of bins. Similar to nbclass argument in modified.ttest function. The default is 30.

Details

This function provides functionality for multiple testing correction in five ways:

Computes a False Discovery Rate by Benjamini and Hochberg doi:10.1111/j.2517-6161.1995.tb02031.x (p_correct = "FDR") by: 1) sorting the p-values (p_i) of each knot in ascending order (p_1 <= p_2 <= ... <= p_m), 2) starting from p_m find the first p_i for which p_i <= (i/m) * alpha.
Computes an independent Sidak correction doi:10.2307/2283989 (p_correct = "uncorrelated Sidak") by 1 - (1 - alpha) ^ (1 / total number of gridded knots across the estimated surface). The default in the risk function is a resolution of 128 x 128 or n = 16,384 knots and a custom resolution can be specified using the resolution argument within the risk function.
Computes an independent Bonferroni correction (p_correct = "uncorrelated Bonferroni") by alpha / total number of gridded knots across the estimated surface. The default in the risk function is a resolution of 128 x 128 or n = 16,384 knots and a custom resolution can be specified using the resolution argument within the risk function.
Computes a spatially dependent Sidak correction (p_correct = "correlated Sidak") by taking into account the spatial correlation of the relative risk surface values (if using the rrs function for a single condition gate) or the ratio of relative risk surfaces values (if using the lotrrs function for a two condition gate). The correction uses the minimum number of knots that are not spatially correlated instead of the total number of knots. The minimum number of knots that are not spatially correlated is computed by counting the knots that are a distance apart that exceeds the minimum distance of non-significant spatial correlation based on a correlogram using the modified.ttest function.
Computes a spatially dependent Bonferroni correction (p_correct = "correlated Bonferroni") by taking into account the spatial correlation of the relative risk surface values (if using the rrs function for a single condition gate) or the ratio of relative risk surfaces values (if using the lotrrs function for a two condition gate). The correction uses the minimum number of knots that are not spatially correlated instead of the total number of knots. The minimum number of knots that are not spatially correlated is computed by counting the knots that are a distance apart that exceeds the minimum distance of non-significant spatial correlation based on a correlogram using the modified.ttest function.
Computes a critical p-value based on Random Field Theory and the Adler and Hasofer equation (p_correct = "Euler A&H") doi:10.1214/aop/1176996176 and p.111 of doi:10.1137/1.9780898718980. The correction uses the number of knots that are independent based on the bandwidth used in the kernel density estimation of the spatial relative risk function.
Computes a critical p-value based on Random Field Theory and the Friston et al. equation (p_correct = "Euler Friston") doi:10.1038/jcbfm.1991.122 which differs from Adler and Hasofer's equation by a factor of 0.79. The correction uses the number of knots that are independent based on the bandwidth used in the kernel density estimation of the spatial relative risk function.

Value

An object of class 'numeric' with the corrected alpha level.

Prepare significant p-values for plotting

Description

Internal function to convert an object of class 'im' to values readable by image.plot function within the rrs, lotrrs, and gating functions.

Usage

pval_plot(input, alpha)

Arguments

input

An object of class 'rrs' from the rrs or lotrrs function.

alpha

Numeric. The two-tailed alpha level for significance threshold (default in rrs, lotrrs, and gating functions is 0.05).

Value

An object of class 'SpatRaster' with categorical values:

A value of 1: Significant numerator.
A value of 2: Insignificant.
A value of 3: Significant denominator.

Subset of the 'extdata' data in the 'flowWorkspaceData' package

Description

A sample dataset containing information about flow cytometry data with two binary conditions and four markers. The data are a random subset of the 'extdata' data in the 'flowWorkspaceData' package found on Bioconductor https://bioconductor.org/packages/release/data/experiment/html/flowWorkspaceData.html and formatted for 'gateR' input. The selected markers are arcsinh transformed.

Usage

randCyto

Format

A data frame with 11763 rows and 7 variables:

id: cell ID number
g1: binary condition #1
g2: binary condition #2
arcsinh_CD4: arcsinh-transformed CD4
arcsinh_CD38: arcsinh-transformed CD38
arcsinh_CD8: arcsinh-transformed CD8
arcsinh_CD3: arcsinh-transformed CD3

Source

https://github.com/lance-waller-lab/gateR/blob/master/README.md

Examples

head(randCyto)

A single gate for a single condition

Description

Estimates a relative risk surface and computes the asymptotic p-value surface for a single gate with a single condition, including features for basic visualization. This function is used internally within the gating function to extract the points within the significant areas. This function can also be used as a standalone function.

Usage

rrs(
  dat,
  bandw = NULL,
  alpha = 0.05,
  p_correct = "none",
  nbc = NULL,
  plot_gate = FALSE,
  save_gate = FALSE,
  name_gate = NULL,
  path_gate = NULL,
  rcols = c("#FF0000", "#CCCCCC", "#0000FF"),
  lower_lrr = NULL,
  upper_lrr = NULL,
  c1n = NULL,
  win = NULL,
  ...,
  doplot = lifecycle::deprecated(),
  verbose = lifecycle::deprecated()
)

Arguments

dat

Input data frame flow cytometry data with four (4) features (columns): 1) ID, 2) Condition A ID, 3) Marker A as x-coordinate, 4) Marker B as y-coordinate.

bandw

Optional, numeric. Fixed bandwidth for the kernel density estimation. Default is based on the internal [sparr]{OS} function.

alpha

Numeric. The two-tailed alpha level for significance threshold (default is 0.05).

p_correct

nbc

Optional. An integer for the number of bins when p_correct = "correlated". Similar to nbclass argument in modified.ttest. The default is 30.

plot_gate

Logical. If TRUE, the output includes basic data visualization.

save_gate

Logical. If TRUE, the output saves the visualization as a separate PNG file.

name_gate

Optional, character. The filename of the visualization. The default is "gate".

path_gate

Optional, character. The path of the visualization. The default is the current working directory.

rcols

lower_lrr

upper_lrr

c1n

Optional, character. The name of the level for the numerator of condition A. The default is NULL, and the first level is treated as the numerator.

win

Optional. Object of class owin for a custom two-dimensional window within which to estimate the surfaces. The default is NULL and calculates a convex hull around the data.

...

Arguments passed to risk to select resolution.

doplot

doplot is no longer supported and has been renamed plot_gate.

verbose

verbose is no longer supported; this function will not display verbose output from internal risk function.

Details

This function estimates a relative risk surface and computes the asymptotic p-value surface for a single gate and single condition using the risk function. Bandwidth is fixed across both layers (numerator and denominator spatial densities). Basic visualization is available if plot_gate = TRUE.

The condition variable (Condition A) within dat must be of class 'factor' with two levels. The first level is considered the numerator (i.e., "case") value, and the second level is considered the denominator (i.e., "control") value. The level can also be specified using the c1n parameter.

Value

An object of class 'list' where each element is a object of class 'rrs' created by the risk function with two additional components:

rr: An object of class 'im' with the relative risk surface.
f: An object of class 'im' with the spatial density of the numerator.
g: An object of class 'im' with the spatial density of the denominator.
P: An object of class 'im' with the asymptotic p-value surface.
lrr: An object of class 'im' with the log relative risk surface.
alpha: A numeric value for the alpha level used within the gate.

Examples

test_rrs <- rrs(dat = randCyto)