Package 'causalBatch' reference manual

Title:	Causal Batch Effects
Description:	Software which provides numerous functionalities for detecting and removing group-level effects from high-dimensional scientific data which, when combined with additional assumptions, allow for causal conclusions, as-described in our manuscripts Bridgeford et al. (2024) <doi:10.1101/2021.09.03.458920> and Bridgeford et al. (2023) <doi:10.48550/arXiv.2307.13868>. Also provides a number of useful utilities for generating simulations and balancing covariates across multiple groups/batches of data via matching and propensity trimming for more than two groups.
Authors:	Eric W. Bridgeford [aut, cre], Michael Powell [ctb], Brian Caffo [ctb], Joshua T. Vogelstein [ctb]
Maintainer:	Eric W. Bridgeford <[email protected]>
License:	GPL-3
Version:	1.4.0
Built:	2025-03-20 20:42:41 UTC
Source:	https://github.com/neurodata/causal_batch

K-Way matching

Description

A function for performing k-way matching using the matchIt package. Looks for samples which have corresponding matches across all other treatment levels.

Usage

cb.align.kway_match(
  Ts,
  Xs,
  match.form,
  reference = NULL,
  match.args = list(method = "nearest", exact = NULL, replace = FALSE, caliper = 0.1),
  retain.ratio = 0.05
)
cb.align.kway_match(
  Ts,
  Xs,
  match.form,
  reference = NULL,
  match.args = list(method = "nearest", exact = NULL, replace = FALSE, caliper = 0.1),
  retain.ratio = 0.05
)

Arguments

`Ts`	`[n]` the labels of the samples, with `K < n` levels, as a factor variable.
`Xs`	`[n, r]` the `r` covariates/confounding variables, for each of the `n` samples, as a data frame with named columns.
`match.form`	A formula of columns from `Xs`, to be passed directly to `matchit` for subsequent matching. See `formula` argument from `matchit` for details.
`reference`	the name of the reference/control batch, against which to match. Defaults to `NULL`, which treats the reference batch as the smallest batch.
`match.args`	A named list arguments for the `matchit` function, to be used to specify specific matching strategies, where the list names are arguments and the corresponding values the value to be passed to `matchit`. Defaults to inexact nearest-neighbor caliper (width 0.1) matching without replacement.
`retain.ratio`	If the number of samples retained is less than `retain.ratio*n`, throws a warning. Defaults to `0.05`.

Value

a list, containing the following:

Retained.Ids [m] vector consisting of the sample ids of the n original samples that were retained after matching.
Reference the reference batch.

Details

For more details see the help vignette: vignette("causal_balancing", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Imaging Neuroscience (2025).

Daniel E. Ho, et al. "MatchIt: Nonparametric Preprocessing for Parametric Causal Inference" JSS (2011).

Examples

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=1.5)
cb.align.kway_match(sim$Ts, data.frame(Covar=sim$Xs), "Covar")
library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=1.5)
cb.align.kway_match(sim$Ts, data.frame(Covar=sim$Xs), "Covar")

A function for implementing the vector matching procedure, a pre-processing step for causal conditional distance correlation. Uses propensity scores to strategically include/exclude samples from subsequent inference, based on whether (or not) there are samples with similar propensity scores across all treatment levels (conceptually, a k-way "propensity trimming"). It is imperative that this function is used in conjunction with domain expertise to ensure that the covariates are not colliders, and that the system satisfies the strong ignorability condiiton to derive causal conclusions.

Usage

cb.align.vm_trim(
  Ts,
  Xs,
  prop.form = NULL,
  retain.ratio = 0.05,
  ddx = FALSE,
  reference = NULL
)
cb.align.vm_trim(
  Ts,
  Xs,
  prop.form = NULL,
  retain.ratio = 0.05,
  ddx = FALSE,
  reference = NULL
)

Arguments

`Ts`	`[n]` the labels of the samples, with `K < n` levels, as a factor variable.
`Xs`	`[n, r]` the `r` covariates/confounding variables, for each of the `n` samples.
`prop.form`	a formula specifying a propensity scoring model. Defaults o `NULL`, which uses all of the covariates as exposure predictors.
`retain.ratio`	If the number of samples retained is less than `retain.ratio*n`, throws a warning. Defaults to `0.05`.
`ddx`	whether to show additional diagnosis messages. Defaults to `FALSE`. Can help with debugging if unexpected results are obtained.
`reference`	the name of a reference label, against which to align other labels. Defaults to `NULL`, which identifies a shared region of covariate overlap across all labels..

Value

a [m] vector containing the indices of samples retained after vector matching.

Details

For more details see the help vignette: vignette("causal_balancing", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Michael J. Lopez, et al. "Estimation of Causal Effects with Multiple Treatments" Statistical Science (2017). ran

Examples

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=3)
cb.align.vm_trim(sim$Ts, sim$Xs)

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=3)
cb.align.vm_trim(sim$Ts, sim$Xs)

Augmented Inverse Probability Weighting Conditional ComBat

Description

A function for implementing the AIPW conditional ComBat (AIPW cComBat) algorithm. This algorithm allows users to remove batch effects (in each dimension), while adjusting for known confounding variables. It is imperative that this function is used in conjunction with domain expertise (e.g., to ensure that the covariates are not colliders, and that the system could be argued to satisfy the ignorability condition) to derive causal conclusions. See citation for more details as to the conditions under which conclusions derived are causal.

Usage

cb.correct.aipw_cComBat(
  Ys,
  Ts,
  Xs,
  aipw.form,
  covar.out.form = NULL,
  retain.ratio = 0.05
)
cb.correct.aipw_cComBat(
  Ys,
  Ts,
  Xs,
  aipw.form,
  covar.out.form = NULL,
  retain.ratio = 0.05
)

Arguments

`Ys`	an `[n, d]` matrix, for the outcome variables with `n` samples in `d` dimensions.
`Ts`	`[n]` the labels of the samples, with at most two unique batches.
`Xs`	`[n, r]` the `r` covariates/confounding variables, for each of the `n` samples, as a data frame with named columns.
`aipw.form`	A covariate model, given as a formula. Applies for the estimation of propensities for the AIPW step.
`covar.out.form`	A covariate model, given as a formula. Applies for the outcome regression step of the `ComBat` algorithm. Defaults to `NULL`, which re-uses `aipw.form` for the covariate/outcome model.
`retain.ratio`	If the number of samples retained is less than `retain.ratio*n`, throws a warning. Defaults to `0.05`.

Details

Note: This function is experimental, and has not been tested on real data. It has only been tested with simulated data with binary (0 or 1) exposures.

Value

a list, containing the following:

Ys.corrected an [m, d] matrix, for the m retained samples in d dimensions, after correction.
Ts [m] the labels of the m retained samples, with K < n levels.
Xs the r covariates/confounding variables for each of the m retained samples.
Model the fit batch effect correction model.
Corrected.Ids the ids to which batch effect correction was applied.

Details

For more details see the help vignette: vignette("causal_ccombat", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Imaging Neuroscience (2025).

W Evan Johnson, et al. "Adjusting batch effects in microarray expression data using empirical Bayes methods" Biostatistics (2007).

Examples

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=2)
cb.correct.aipw_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), "Covar")

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=2)
cb.correct.aipw_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), "Covar")

Fit AIPW ComBat model for batch effect correction

Description

This function applies an Augmented Inverse Probability Weighting (AIPW) ComBat model for batch effect correction to new data.

Usage

cb.correct.apply_aipw_cComBat(Ys, Ts, Xs, Model)
cb.correct.apply_aipw_cComBat(Ys, Ts, Xs, Model)

Arguments

`Ys`	an `[n, d]` matrix, for the outcome variables with `n` samples in `d` dimensions.
`Ts`	`[n]` the labels of the samples, with `K < n` levels, as a factor variable.
`Xs`	`[n, r]` the `r` covariates/confounding variables, for each of the `n` samples, as a data frame with named columns.
`Model`	a list containing the following parameters: `Prop_model` Fitted propensity model `Putcome_models` List of fitted outcome models for each feature and treatment level `Levels` Levels of the treatment factor `Treatment_effects` Estimated treatment effects `AIPW_est` AIPW estimator results `covar.out.form` Formula used for the outcome model This model is output after fitting with `cb.correct.aipw_cComBat`.

Details

Note: This function is experimental, and has not been tested on real data. It has only been tested with simulated data with binary (0 or 1) exposures.

Value

an [n, d] matrix, the batch-effect corrected data.

Examples

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=200, err=1/8, unbalancedness=3)
# fit batch effect correction for first 100 samples
cb.fit <- cb.correct.matching_cComBat(sim$Ys[1:100,,drop=FALSE], sim$Ts[1:100], 
                                  data.frame(Covar=sim$Xs[1:100,,drop=FALSE]), "Covar")
# apply to all samples
cor.dat <- cb.correct.apply_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), cb.fit$Model)

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=200, err=1/8, unbalancedness=3)
# fit batch effect correction for first 100 samples
cb.fit <- cb.correct.matching_cComBat(sim$Ys[1:100,,drop=FALSE], sim$Ts[1:100], 
                                  data.frame(Covar=sim$Xs[1:100,,drop=FALSE]), "Covar")
# apply to all samples
cor.dat <- cb.correct.apply_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), cb.fit$Model)

Adjust for batch effects using an empirical Bayes framework

Description

ComBat allows users to adjust for batch effects in datasets where the batch covariate is known, using methodology described in Johnson et al. 2007. It uses either parametric or non-parametric empirical Bayes frameworks for adjusting data for batch effects. Users are returned an expression matrix that has been corrected for batch effects. The input data are assumed to be cleaned and normalized before batch effect removal.

Usage

cb.correct.apply_cComBat(Ys, Ts, Xs, Model)
cb.correct.apply_cComBat(Ys, Ts, Xs, Model)

Arguments

`Ys`	an `[n, d]` matrix, for the outcome variables with `n` samples in `d` dimensions.
`Ts`	`[n]` the labels of the samples, with `K < n` levels, as a factor variable.
`Xs`	`[n, r]` the `r` covariates/confounding variables, for each of the `n` samples, as a data frame with named columns.
`Model`	a list containing the following parameters: `Var` the pooled variance `Grand.mean` the overall mean of the data `B.hat` the fit regression coefficients `Gamma` additive batch effects `Delta` multiplicative batch effects `Levels` the order of levels for each batch `Covar.Mod` the covariate model for adjustment This model is output after fitting with `cb.correct.matching_cComBat`.

Details

Note: this code is adapted directly from the ComBat algorithm featured in the 'sva' package.

Value

an [n, d] matrix, the batch-effect corrected data.

Examples

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=200, err=1/8, unbalancedness=3)
# fit batch effect correction for first 100 samples
cb.fit <- cb.correct.matching_cComBat(sim$Ys[1:100,,drop=FALSE], sim$Ts[1:100], 
                                  data.frame(Covar=sim$Xs[1:100,,drop=FALSE]), "Covar")
# apply to all samples
cor.dat <- cb.correct.apply_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), cb.fit$Model)

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=200, err=1/8, unbalancedness=3)
# fit batch effect correction for first 100 samples
cb.fit <- cb.correct.matching_cComBat(sim$Ys[1:100,,drop=FALSE], sim$Ts[1:100], 
                                  data.frame(Covar=sim$Xs[1:100,,drop=FALSE]), "Covar")
# apply to all samples
cor.dat <- cb.correct.apply_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), cb.fit$Model)

Matching Conditional ComBat

Description

A function for implementing the matching conditional ComBat (matching cComBat) algorithm. This algorithm allows users to remove batch effects (in each dimension), while adjusting for known confounding variables. It is imperative that this function is used in conjunction with domain expertise (e.g., to ensure that the covariates are not colliders, and that the system could be argued to satisfy the ignorability condition) to derive causal conclusions. See citation for more details as to the conditions under which conclusions derived are causal.

Usage

cb.correct.matching_cComBat(
  Ys,
  Ts,
  Xs,
  match.form,
  covar.out.form = NULL,
  prop.form = NULL,
  reference = NULL,
  match.args = list(method = "nearest", exact = NULL, replace = FALSE, caliper = 0.1),
  retain.ratio = 0.05,
  apply.oos = FALSE
)
cb.correct.matching_cComBat(
  Ys,
  Ts,
  Xs,
  match.form,
  covar.out.form = NULL,
  prop.form = NULL,
  reference = NULL,
  match.args = list(method = "nearest", exact = NULL, replace = FALSE, caliper = 0.1),
  retain.ratio = 0.05,
  apply.oos = FALSE
)

Arguments

`Ys`	an `[n, d]` matrix, for the outcome variables with `n` samples in `d` dimensions.
`Ts`	`[n]` the labels of the samples, with `K < n` levels, as a factor variable.
`Xs`	`[n, r]` the `r` covariates/confounding variables, for each of the `n` samples, as a data frame with named columns.
`match.form`	A formula of columns from `Xs`, to be passed directly to `matchit` for subsequent matching. See `formula` argument from `matchit` for details.
`covar.out.form`	A covariate model, given as a formula. Applies for the outcome regression step of the `ComBat` algorithm. Defaults to `NULL`, which re-uses `match.form` for the covariate/outcome model.
`prop.form`	A propensity model, given as a formula. Applies for the estimation of propensities for the propensity trimming step. Defaults to `NULL`, which re-uses `match.form` for the covariate/outcome model.
`reference`	the name of the reference/control batch, against which to match. Defaults to `NULL`, which treats the reference batch as the smallest batch.
`match.args`	A named list arguments for the `matchit` function, to be used to specify specific matching strategies, where the list names are arguments and the corresponding values the value to be passed to `matchit`. Defaults to inexact nearest-neighbor caliper (width 0.1) matching without replacement.
`retain.ratio`	If the number of samples retained is less than `retain.ratio*n`, throws a warning. Defaults to `0.05`.
`apply.oos`	A boolean that indicates whether or not to apply the learned batch effect correction to non-matched samples that are still within a region of covariate support. Defaults to `FALSE`.

Value

a list, containing the following:

Ys.corrected an [m, d] matrix, for the m retained samples in d dimensions, after correction.
Ts [m] the labels of the m retained samples, with K < n levels.
Xs the r covariates/confounding variables for each of the m retained samples.
Model the fit batch effect correction model. See ComBat for details.
InSample.Ids the ids which were used to fit the batch effect correction model.
Corrected.Ids the ids to which batch effect correction was applied. Differs from InSample.Ids if apply.oos is TRUE.

Details

For more details see the help vignette: vignette("causal_ccombat", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Imaging Neuroscience (2025).

Daniel E. Ho, et al. "MatchIt: Nonparametric Preprocessing for Parametric Causal Inference" JSS (2011).

W Evan Johnson, et al. "Adjusting batch effects in microarray expression data using empirical Bayes methods" Biostatistics (2007).

Leek JT, Johnson WE, Parker HS, Fertig EJ, Jaffe AE, Zhang Y, Storey JD, Torres LC (2024). sva: Surrogate Variable Analysis. R package version 3.52.0.

Examples

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=2)
cb.correct.matching_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), "Covar")

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=2)
cb.correct.matching_cComBat(sim$Ys, sim$Ts, data.frame(Covar=sim$Xs), "Covar")

Causal Conditional Distance Correlation

Description

A function for implementing the causal conditional distance correlation (causal cDCorr) algorithm. This algorithm allows users to identify whether a treatment causes changes in an outcome, given assorted covariates/confounding variables. It is imperative that this function is used in conjunction with domain expertise (e.g., to ensure that the covariates are not colliders, and that the system satisfies the strong ignorability condiiton) to derive causal conclusions. See citation for more details as to the conditions under which conclusions derived are causal.

Usage

cb.detect.caus_cdcorr(
  Ys,
  Ts,
  Xs,
  prop.form = NULL,
  R = 1000,
  dist.method = "euclidean",
  distance = FALSE,
  width = "scott",
  seed = 1,
  num.threads = 1,
  retain.ratio = 0.05,
  ddx = FALSE,
  normalize = TRUE
)
cb.detect.caus_cdcorr(
  Ys,
  Ts,
  Xs,
  prop.form = NULL,
  R = 1000,
  dist.method = "euclidean",
  distance = FALSE,
  width = "scott",
  seed = 1,
  num.threads = 1,
  retain.ratio = 0.05,
  ddx = FALSE,
  normalize = TRUE
)

Arguments

`Ys`	Either: `[n, d]` matrix the outcome variables with `n` samples in `d` dimensions. In this case, `distance` should be `FALSE`. `[n, n]` `dist` object a distance object for the `n` samples. In this case, `distance` should be `TRUE`.
`Ts`	`[n]` the labels of the samples, with `K < n` levels, as a factor variable.
`Xs`	`[n, r]` the `r` covariates/confounding variables, for each of the `n` samples. Ensure that all covariates are encoded properly as continuous or factors (categorical or ordinal) for the bandwidth selection step for kernel width selection.
`prop.form`	a formula specifying a propensity scoring model. Defaults o `NULL`, which uses all of the covariates as exposure predictors.
`R`	the number of repetitions for permutation testing. Defaults to `1000`.
`dist.method`	the method used for computing distance matrices. Defaults to `"euclidean"`. Other options can be identified by seeing the appropriate documention for the `method` argument for the `dist` function.
`distance`	a boolean for whether (or not) `Ys` are already distance matrices. Defaults to `FALSE`, which will use `dist.method` parameter to compute an `[n, n]` pairwise distance matrix for `Ys`.
`width`	Either: "scott"Specifies to use Scott's rule for bandwidth computation. "xv"Computes bandwidths using cross validation via the `npudensbw` function. `r` vectorA vector specifying the bandwidths for each dimension of `Xs`. Defaults to `"scott"`.
`seed`	a random seed to set. Defaults to `1`.
`num.threads`	The number of threads for parallel processing (if desired). Defaults to `1`.
`retain.ratio`	If the number of samples retained is less than `retain.ratio*n`, throws a warning. Defaults to `0.05`.
`ddx`	whether to show additional diagnosis messages. Defaults to `FALSE`. Can help with debugging if unexpected results are obtained.
`normalize`	whether or not to compute the distance correlation (`TRUE`) or distance covariance (`FALSE`). Skips unnecessary computation if the test outcome is the only item of interest. Defaults to `TRUE`.

Value

a list, containing the following:

Test The outcome of the statistical test, from cdcov.test.
Retained.Ids The sample indices retained after vertex matching, which correspond to the samples for which statistical inference is performed.

Details

For more details see the help vignette: vignette("causal_cdcorr", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Imaging Neuroscience (2025).

Eric W. Bridgeford, et al. "Learning sources of variability from high-dimensional observational studies" arXiv (2023).

Xueqin Wang, et al. "Conditional Distance Correlation" American Statistical Association (2015).

Examples

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=3)
cb.detect.caus_cdcorr(sim$Ys, sim$Ts, sim$Xs)

library(causalBatch)
sim <- cb.sims.sim_linear(a=-1, n=100, err=1/8, unbalancedness=3)
cb.detect.caus_cdcorr(sim$Ys, sim$Ts, sim$Xs)

Simulate Data with Heteroskedastic Conditional Average Treatment Effects

Description

Simulate Data with Heteroskedastic Conditional Average Treatment Effects

Usage

cb.sims.cate.heteroskedastic_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  covar_eff_sz = 3,
  alpha = 2,
  beta = 8,
  common = 10,
  a = 2,
  b = 8,
  err = 0.5,
  nbreaks = 200,
  rotate = TRUE
)
cb.sims.cate.heteroskedastic_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  covar_eff_sz = 3,
  alpha = 2,
  beta = 8,
  common = 10,
  a = 2,
  b = 8,
  err = 0.5,
  nbreaks = 200,
  rotate = TRUE
)

Arguments

`n`	number of samples to generate
`p`	number of dimensions for the response variable
`pi`	probability of assignment to treatment group 1
`balance`	a parameter that governs the similarity between the covariate distributions
`eff_sz`	effect size parameter controlling the heteroskedasticity between groups
`covar_eff_sz`	effect size parameter for the covariate influence
`alpha`	the alpha parameter for beta distribution of control group
`beta`	the beta parameter for beta distribution of control group
`common`	parameter governing the shape of the common sampling distribution
`a`	scaling factor for response variable generation
`b`	scaling factor for sigmoid transformation
`err`	standard deviation for the error term
`nbreaks`	number of points to use for generating the true signal
`rotate`	whether to apply a random rotation to the outcomes. Defaults to `TRUE`.

Value

A list containing:

`Ys`	response matrix of size [n, p]
`Ts`	treatment assignment vector of size [n]
`Xs`	covariate vector of size [n]
`Eps`	error matrix of size [n, p]
`Ytrue`	true response matrix for evaluation
`Ttrue`	true treatment vector for evaluation
`Xtrue`	true covariate vector for evaluation
`Group.Effect`	the effect size parameter
`Covar.Effect`	the covariate effect size parameter
`R`	Optional argument returned if a rotation is requested for the rotation matrix applied.

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "Learning Sources of Variability from High-Dimensional Observational Studies" arXiv (2025).

Examples


library(causalBatch)
sim = cb.sims.cate.heteroskedastic_sim()

library(causalBatch)
sim = cb.sims.cate.heteroskedastic_sim()

K-class Sigmoidal CATE Simulation

Description

K-class Sigmoidal CATE Simulation

Usage

cb.sims.cate.kclass_sigmoidal_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  covar_eff_sz = 5,
  alpha = 2,
  beta = 8,
  common = 10,
  a = 2,
  b = 8,
  err = 1,
  nbreaks = 200,
  K = 3,
  rotate = TRUE
)
cb.sims.cate.kclass_sigmoidal_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  covar_eff_sz = 5,
  alpha = 2,
  beta = 8,
  common = 10,
  a = 2,
  b = 8,
  err = 1,
  nbreaks = 200,
  K = 3,
  rotate = TRUE
)

Arguments

`n`	the number of samples. Defaults to `100`.
`p`	the number of dimensions. Defaults to `10`.
`pi`	the fraction of points which are sampled from a common distribution. Should be a number between `0` and `1`.
`balance`	a parameter governing the covariate similarity between the two groups. Defaults to `1`, which is the same covariate distributions for both groups.
`eff_sz`	the conditional treatment effect size between the different groups, which governs the rotation in radians between the first and second group. Defaults to `1`.
`covar_eff_sz`	A parameter which governs the covariate effect size with respect to the outcome. Defaults to `5`..
`alpha`	the alpha for sampling the `0` group, and the beta for sampling the other `K - 1` groups.
`beta`	the beta for sampling the `0` group, and the alpha for sampling the other `K - 1` groups.
`common`	a parameter which governs the shape of the common sampling distribution.
`a`	the first parameter for the covariate/outcome relationship. Defaults to `2`.
`b`	the second parameter for the covariate/outcome relationship. Defaults to `8`.
`err`	the level of noise for the simulation. Defaults to `1`.
`nbreaks`	the number of breakpoints for computing the expected outcome at a given covariate level for each batch. Defaults to `200`.
`K`	the number of classes. Defaults to `3`.
`rotate`	whether to apply a random rotation to the outcomes. Defaults to `TRUE`.

Value

a list, containing the following:

`Y`	an `[n, p]` matrix, containing the outcomes for each sample.
`Ts`	an `[n, 1]` matrix, containing the group labels for each sample.
`Xs`	an `[n, 1]` matrix, containing the covariate values for each sample.
`Eps`	an `[n, 1]` matrix, containing the error for each sample.
`Ytrue`	an `[nbreaks*2, 2]` matrix, containing the expected outcomes at a covariate level indicated by `Xtrue`.
`Ttrue`	an `[nbreaks*2,1]` matrix, indicating the group/batch the expected outcomes and covariate breakpoints correspond to.
`Xtrue`	an `[nbreaks*2, 1]` matrix, indicating the values of the covariate breakpoints for the theoretical expected outcome in `Ytrue`.
`Group.Effect`	The group effect magnitude.
`Covar.Effect`	The covariate effect magnitude.
`K`	The total number of classes.
`R`	Optional argument returned if a rotation is requested for the rotation matrix applied.

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "Learning Sources of Variability from High-Dimensional Observational Studies" arXiv (2025).

Examples


library(causalBatch)
sim = cb.sims.cate.kclass_rotation_sim()

library(causalBatch)
sim = cb.sims.cate.kclass_rotation_sim()

Non-monotone CATE Simulation

Description

Non-monotone CATE Simulation

Usage

cb.sims.cate.nonmonotone_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  alpha = 2,
  beta = 8,
  common = 10,
  err = 1,
  nbreaks = 200,
  rotate = TRUE
)
cb.sims.cate.nonmonotone_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  alpha = 2,
  beta = 8,
  common = 10,
  err = 1,
  nbreaks = 200,
  rotate = TRUE
)

Arguments

`n`	the number of samples. Defaults to `100`.
`p`	the number of dimensions. Defaults to `10`.
`pi`	the fraction of points which are sampled from a common distribution. Should be a number between `0` and `1`.
`balance`	a parameter governing the covariate similarity between the two groups. Defaults to `1`, which is the same covariate distributions for both groups.
`eff_sz`	the conditional treatment effect size between the different groups, which governs the rotation in radians between the first and second group. Defaults to `1`.
`alpha`	the alpha for sampling the `0` group, and the beta for sampling the other `K - 1` groups.
`beta`	the beta for sampling the `0` group, and the alpha for sampling the other `K - 1` groups.
`common`	a parameter which governs the shape of the common sampling distribution.
`err`	the level of noise for the simulation. Defaults to `1`.
`nbreaks`	the number of breakpoints for computing the expected outcome at a given covariate level for each batch. Defaults to `200`.
`rotate`	whether to apply a random rotation to the outcomes. Defaults to `TRUE`.
`covar_eff_sz`	A parameter which governs the covariate effect size with respect to the outcome. Defaults to `5`..

Value

a list, containing the following:

`Y`	an `[n, p]` matrix, containing the outcomes for each sample.
`Ts`	an `[n, 1]` matrix, containing the group labels for each sample.
`Xs`	an `[n, 1]` matrix, containing the covariate values for each sample.
`Eps`	an `[n, 1]` matrix, containing the error for each sample.
`Ytrue`	an `[nbreaks*2, 2]` matrix, containing the expected outcomes at a covariate level indicated by `Xtrue`.
`Ttrue`	an `[nbreaks*2,1]` matrix, indicating the group/batch the expected outcomes and covariate breakpoints correspond to.
`Xtrue`	an `[nbreaks*2, 1]` matrix, indicating the values of the covariate breakpoints for the theoretical expected outcome in `Ytrue`.
`Group.Effect`	The group effect magnitude.
`R`	Optional argument returned if a rotation is requested for the rotation matrix applied.

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "Learning Sources of Variability from High-Dimensional Observational Studies" arXiv (2025).

Examples


library(causalBatch)
sim = cb.sims.cate.nonmonotone_sim()

library(causalBatch)
sim = cb.sims.cate.nonmonotone_sim()

Sigmoidal CATE Simulation

Description

Sigmoidal CATE Simulation

Usage

cb.sims.cate.sigmoidal_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  covar_eff_sz = 5,
  alpha = 2,
  beta = 8,
  common = 10,
  a = 2,
  b = 8,
  err = 1,
  nbreaks = 200,
  rotate = TRUE
)
cb.sims.cate.sigmoidal_sim(
  n = 100,
  p = 10,
  pi = 0.5,
  balance = 1,
  eff_sz = 1,
  covar_eff_sz = 5,
  alpha = 2,
  beta = 8,
  common = 10,
  a = 2,
  b = 8,
  err = 1,
  nbreaks = 200,
  rotate = TRUE
)

Arguments

`n`	the number of samples. Defaults to `100`.
`p`	the number of dimensions. Defaults to `10`.
`pi`	the fraction of points which are sampled from a common distribution. Should be a number between `0` and `1`.
`balance`	a parameter governing the covariate similarity between the two groups. Defaults to `1`, which is the same covariate distributions for both groups.
`eff_sz`	the conditional treatment effect size between the different groups, which governs the rotation in radians between the first and second group. Defaults to `1`.
`covar_eff_sz`	A parameter which governs the covariate effect size with respect to the outcome. Defaults to `5`..
`alpha`	the alpha for sampling the `0` group, and the beta for sampling the other `K - 1` groups.
`beta`	the beta for sampling the `0` group, and the alpha for sampling the other `K - 1` groups.
`common`	a parameter which governs the shape of the common sampling distribution.
`a`	the first parameter for the covariate/outcome relationship. Defaults to `2`.
`b`	the second parameter for the covariate/outcome relationship. Defaults to `8`.
`err`	the level of noise for the simulation. Defaults to `1`.
`nbreaks`	the number of breakpoints for computing the expected outcome at a given covariate level for each batch. Defaults to `200`.

Value

a list, containing the following:

`Y`	an `[n, p]` matrix, containing the outcomes for each sample.
`Ts`	an `[n, 1]` matrix, containing the group labels for each sample.
`Xs`	an `[n, 1]` matrix, containing the covariate values for each sample.
`Eps`	an `[n, 1]` matrix, containing the error for each sample.
`Ytrue`	an `[nbreaks*2, 2]` matrix, containing the expected outcomes at a covariate level indicated by `Xtrue`.
`Ttrue`	an `[nbreaks*2,1]` matrix, indicating the group/batch the expected outcomes and covariate breakpoints correspond to.
`Xtrue`	an `[nbreaks*2, 1]` matrix, indicating the values of the covariate breakpoints for the theoretical expected outcome in `Ytrue`.
`Group.Effect`	The group effect magnitude.
`Covar.Effect`	The covariate effect magnitude.

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "Learning Sources of Variability from High-Dimensional Observational Studies" arXiv (2025).

Examples


library(causalBatch)
sim = cb.sims.cate.sigmoidal_sim()

library(causalBatch)
sim = cb.sims.cate.sigmoidal_sim()

Impulse Simulation

Description

Impulse Simulation

Usage

cb.sims.sim_impulse(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  err = 1/2,
  null = FALSE,
  a = -0.5,
  b = 1/2,
  c = 4,
  nbreaks = 200
)
cb.sims.sim_impulse(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  err = 1/2,
  null = FALSE,
  a = -0.5,
  b = 1/2,
  c = 4,
  nbreaks = 200
)

Arguments

`n`	the number of samples. Defaults to `100`.
`pi`	the balance between the classes, where samples will be from group 1 with probability `pi`, and group 2 with probability `1 - pi`. Defaults to `0.5`.
`eff_sz`	the treatment effect between the different groups. Defaults to `1`.
`alpha`	the alpha for the covariate sampling procedure. Defaults to `2`.
`unbalancedness`	the level of covariate dissimilarity between the covariates for each of the groups. Defaults to `1`.
`err`	the level of noise for the simulation. Defaults to `1/2`.
`null`	whether to generate a null simulation. Defaults to `FALSE`. Same behavior can be achieved by setting `eff_sz = 0`.
`a`	the first parameter for the covariate/outcome relationship. Defaults to `-0.5`.
`b`	the second parameter for the covariate/outcome relationship. Defaults to `1/2`.
`c`	the third parameter for the covariate/outcome relationship. Defaults to `1`.
`nbreaks`	the number of breakpoints for computing the expected outcome at a given covariate level for each batch. Defaults to `200`.

Value

a list, containing the following:

`Ys`	an `[n, 2]` matrix, containing the outcomes for each sample. The first dimension contains the "treatment effect".
`Ts`	an `[n, 1]` matrix, containing the group/batch labels for each sample.
`Xs`	an `[n, 1]` matrix, containing the covariate values for each sample.
`Eps`	an `[n, 1]` matrix, containing the error for each sample.
`x.bounds`	the theoretical bounds for the covariate values.
`Ytrue`	an `[nbreaks*2, 2]` matrix, containing the expected outcomes at a covariate level indicated by `Xtrue`.
`Ttrue`	an `[nbreaks*2,1]` matrix, indicating the group/batch the expected outcomes and covariate breakpoints correspond to.
`Xtrue`	an `[nbreaks*2, 1]` matrix, indicating the values of the covariate breakpoints for the theoretical expected outcome in `Ytrue`.
`Effect`	The batch effect magnitude.
`Overlap`	the theoretical degree of overlap between the covariate distributions for each of the two groups/batches.
`oracle_fn`	A function for fitting outcomes given covariates.

Details

A sigmoidal relationship between the covariate and the outcome. The first dimension of the outcome is:

$Y_i = c \times \phi(X_i, \mu = a, \sigma = b) - \text{eff\_sz} \times T_i + \frac{1}{2} \epsilon_i$

where $\phi(x, \mu, \sigma)$ is the probability density function for the normal distribution with mean $\mu$ and standard deviation $\sigma$ .

where the batch/group labels are:

$T_i \overset{iid}{\sim} Bern(\pi)$

The beta coefficient for the covariate sampling is:

$\beta = \alpha \times \text{unbalancedness}$

The covariate values for the first batch are:

$X_i | T_i = 0 \overset{ind}{\sim} 2 Beta(\alpha, \beta) - 1$

and the covariate values for the second batch are:

$X_i | T_i = 1 \overset{ind}{\sim} 2 Beta(\beta, \alpha) - 1$

Note that $X_i | T_i = 0 \overset{D}{=} - X_i | T_i = 1$ , or that the covariates are symmetric about the origin in distribution.

Finally, the error terms are:

$\epsilon_i \overset{iid}{\sim} Norm(0, \text{err}^2)$

For more details see the help vignette: vignette("causal_simulations", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Biorxiv (2024).

Examples


library(causalBatch)
sim = cb.sims.sim_impulse()

library(causalBatch)
sim = cb.sims.sim_impulse()

Impulse Simulation with Asymmetric Covariates

Description

Impulse Simulation with Asymmetric Covariates

Usage

cb.sims.sim_impulse_asycov(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  null = FALSE,
  a = -0.5,
  b = 1/2,
  c = 4,
  err = 1/2,
  nbreaks = 200
)
cb.sims.sim_impulse_asycov(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  null = FALSE,
  a = -0.5,
  b = 1/2,
  c = 4,
  err = 1/2,
  nbreaks = 200
)

Arguments

`n`	the number of samples. Defaults to `100`.
`pi`	the balance between the classes, where samples will be from group 1 with probability `pi`, and group 2 with probability `1 - pi`. Defaults to `0.5`.
`eff_sz`	the treatment effect between the different groups. Defaults to `1`.
`alpha`	the alpha for the covariate sampling procedure. Defaults to `2`.
`unbalancedness`	the level of covariate dissimilarity between the covariates for each of the groups. Defaults to `1`.
`null`	whether to generate a null simulation. Defaults to `FALSE`. Same behavior can be achieved by setting `eff_sz = 0`.
`a`	the first parameter for the covariate/outcome relationship. Defaults to `-0.5`.
`b`	the second parameter for the covariate/outcome relationship. Defaults to `1/2`.
`c`	the third parameter for the covariate/outcome relationship. Defaults to `1`.
`err`	the level of noise for the simulation. Defaults to `1/2`.
`nbreaks`	the number of breakpoints for computing the expected outcome at a given covariate level for each batch. Defaults to `200`.

Value

a list, containing the following:

`Ys`	an `[n, 2]` matrix, containing the outcomes for each sample. The first dimension contains the "treatment effect".
`Ts`	an `[n, 1]` matrix, containing the group/batch labels for each sample.
`Xs`	an `[n, 1]` matrix, containing the covariate values for each sample.
`Eps`	an `[n, 1]` matrix, containing the error for each sample.
`x.bounds`	the theoretical bounds for the covariate values.
`Ytrue`	an `[nbreaks*2, 2]` matrix, containing the expected outcomes at a covariate level indicated by `Xtrue`.
`Ttrue`	an `[nbreaks*2,1]` matrix, indicating the group/batch the expected outcomes and covariate breakpoints correspond to.
`Xtrue`	an `[nbreaks*2, 1]` matrix, indicating the values of the covariate breakpoints for the theoretical expected outcome in `Ytrue`.
`Effect`	The batch effect magnitude.
`Overlap`	the theoretical degree of overlap between the covariate distributions for each of the two groups/batches.
`oracle_fn`	A function for fitting outcomes given covariates.

Details

A sigmoidal relationship between the covariate and the outcome. The first dimension of the outcome is:

$Y_i = c \times \phi(X_i, \mu = a, \sigma = b) - \text{eff\_sz} \times T_i + \frac{1}{2} \epsilon_i$

where $\phi(x, \mu, \sigma)$ is the probability density function for the normal distribution with mean $\mu$ and standard deviation $\sigma$ .

where the batch/group labels are:

$T_i \overset{iid}{\sim} Bern(\pi)$

The beta coefficient for the covariate sampling is:

$\beta = \alpha \times \text{unbalancedness}$

The covariate values for the first batch are asymmetric, in that for the first batch:

$X_i | T_i = 0 \overset{ind}{\sim} 2 Beta(\alpha, \alpha) - 1$

and the covariate values for the second batch are:

$X_i | T_i = 1 \overset{ind}{\sim} 2 Beta(\beta, \alpha) - 1$

Finally, the error terms are:

$\epsilon_i \overset{iid}{\sim} Norm(0, \text{err}^2)$

For more details see the help vignette: vignette("causal_simulations", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Biorxiv (2024).

Examples


library(causalBatch)
sim = cb.sims.sim_impulse_asycov()

library(causalBatch)
sim = cb.sims.sim_impulse_asycov()

Linear Simulation

Description

Linear Simulation

Usage

cb.sims.sim_linear(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  err = 1/2,
  null = FALSE,
  a = -2,
  b = -1,
  nbreaks = 200
)
cb.sims.sim_linear(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  err = 1/2,
  null = FALSE,
  a = -2,
  b = -1,
  nbreaks = 200
)

Arguments

`n`	the number of samples. Defaults to `100`.
`pi`	the balance between the classes, where samples will be from group 1 with probability `pi`, and group 2 with probability `1 - pi`. Defaults to `0.5`.
`eff_sz`	the treatment effect between the different groups. Defaults to `1`.
`alpha`	the alpha for the covariate sampling procedure. Defaults to `2`.
`unbalancedness`	the level of covariate dissimilarity between the covariates for each of the groups. Defaults to `1`.
`err`	the level of noise for the simulation. Defaults to `1/2`.
`null`	whether to generate a null simulation. Defaults to `FALSE`. Same behavior can be achieved by setting `eff_sz = 0`.
`a`	the first parameter for the covariate/outcome relationship. Defaults to `-2`.
`b`	the second parameter for the covariate/outcome relationship. Defaults to `-1`.
`nbreaks`	the number of breakpoints for computing the expected outcome at a given covariate level for each batch. Defaults to `200`.

Value

a list, containing the following:

`Ys`	an `[n, 2]` matrix, containing the outcomes for each sample. The first dimension contains the "treatment effect".
`Ts`	an `[n, 1]` matrix, containing the group/batch labels for each sample.
`Xs`	an `[n, 1]` matrix, containing the covariate values for each sample.
`Eps`	an `[n, 1]` matrix, containing the error for each sample.
`x.bounds`	the theoretical bounds for the covariate values.
`Ytrue`	an `[nbreaks*2, 2]` matrix, containing the expected outcomes at a covariate level indicated by `Xtrue`.
`Ttrue`	an `[nbreaks*2,1]` matrix, indicating the group/batch the expected outcomes and covariate breakpoints correspond to.
`Xtrue`	an `[nbreaks*2, 1]` matrix, indicating the values of the covariate breakpoints for the theoretical expected outcome in `Ytrue`.
`Effect`	The batch effect magnitude.
`Overlap`	the theoretical degree of overlap between the covariate distributions for each of the two groups/batches.
`oracle_fn`	A function for fitting outcomes given covariates.

Details

A linear relationship between the covariate and the outcome. The first dimension of the outcome is:

$Y_i = a\times (X_i + b) - \text{eff\_sz} \times T_i + \frac{1}{2} \epsilon_i$

where the batch/group labels are:

$T_i \overset{iid}{\sim} Bern(\pi)$

The beta coefficient for the covariate sampling is:

$\beta = \alpha \times \text{unbalancedness}$

The covariate values for the first batch are:

$X_i | T_i = 0 \overset{ind}{\sim} 2 Beta(\alpha, \beta) - 1$

and the covariate values for the second batch are:

$X_i | T_i = 1 \overset{ind}{\sim} 2 Beta(\beta, \alpha) - 1$

Finally, the error terms are:

$\epsilon_i \overset{iid}{\sim} Norm(0, \text{err}^2)$

For more details see the help vignette: vignette("causal_simulations", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Biorxiv (2024).

Examples


library(causalBatch)
sim = cb.sims.sim_linear()

library(causalBatch)
sim = cb.sims.sim_linear()

Sigmoidal Simulation

Description

Sigmoidal Simulation

Usage

cb.sims.sim_sigmoid(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  null = FALSE,
  a = -4,
  b = 8,
  err = 1/2,
  nbreaks = 200
)
cb.sims.sim_sigmoid(
  n = 100,
  pi = 0.5,
  eff_sz = 1,
  alpha = 2,
  unbalancedness = 1,
  null = FALSE,
  a = -4,
  b = 8,
  err = 1/2,
  nbreaks = 200
)

Arguments

`n`	the number of samples. Defaults to `100`.
`pi`	the balance between the classes, where samples will be from group 1 with probability `pi`, and group 2 with probability `1 - pi`. Defaults to `0.5`.
`eff_sz`	the treatment effect between the different groups. Defaults to `1`.
`alpha`	the alpha for the covariate sampling procedure. Defaults to `2`.
`unbalancedness`	the level of covariate dissimilarity between the covariates for each of the groups. Defaults to `1`.
`null`	whether to generate a null simulation. Defaults to `FALSE`. Same behavior can be achieved by setting `eff_sz = 0`.
`a`	the first parameter for the covariate/outcome relationship. Defaults to `-4`.
`b`	the second parameter for the covariate/outcome relationship. Defaults to `8`.
`err`	the level of noise for the simulation. Defaults to `1/2`.
`nbreaks`	the number of breakpoints for computing the expected outcome at a given covariate level for each batch. Defaults to `200`.

Value

a list, containing the following:

`Y`	an `[n, 2]` matrix, containing the outcomes for each sample. The first dimension contains the "treatment effect".
`Ts`	an `[n, 1]` matrix, containing the group/batch labels for each sample.
`Xs`	an `[n, 1]` matrix, containing the covariate values for each sample.
`Eps`	an `[n, 1]` matrix, containing the error for each sample.
`x.bounds`	the theoretical bounds for the covariate values.
`Ytrue`	an `[nbreaks*2, 2]` matrix, containing the expected outcomes at a covariate level indicated by `Xtrue`.
`Ttrue`	an `[nbreaks*2,1]` matrix, indicating the group/batch the expected outcomes and covariate breakpoints correspond to.
`Xtrue`	an `[nbreaks*2, 1]` matrix, indicating the values of the covariate breakpoints for the theoretical expected outcome in `Ytrue`.
`Effect`	The batch effect magnitude.
`Overlap`	the theoretical degree of overlap between the covariate distributions for each of the two groups/batches.
`oracle_fn`	A function for fitting outcomes given covariates.

Details

A sigmoidal relationship between the covariate and the outcome. The first dimension of the outcome is:

$Y_i = a\times \text{sigmoid}(b \times X_i) - a - \text{eff\_sz} \times T_i + \frac{1}{2} \epsilon_i$

where the batch/group labels are:

$T_i \overset{iid}{\sim} Bern(\pi)$

The beta coefficient for the covariate sampling is:

$\beta = \alpha \times \text{unbalancedness}$

The covariate values for the first batch are:

$X_i | T_i = 0 \overset{ind}{\sim} 2 Beta(\alpha, \beta) - 1$

and the covariate values for the second batch are:

$X_i | T_i = 1 \overset{ind}{\sim} 2 Beta(\beta, \alpha) - 1$

Finally, the error terms are:

$\epsilon_i \overset{iid}{\sim} Norm(0, \text{err}^2)$

For more details see the help vignette: vignette("causal_simulations", package = "causalBatch")

Author(s)

Eric W. Bridgeford

References

Eric W. Bridgeford, et al. "A Causal Perspective for Batch Effects: When is no answer better than a wrong answer?" Biorxiv (2024).

Examples


library(causalBatch)
sim = cb.sims.sim_sigmoid()

library(causalBatch)
sim = cb.sims.sim_sigmoid()

Package 'causalBatch'

Help Index

K-Way matching

Description

Usage

Arguments

Value

Details

Author(s)

References

Examples

Vector Matching

Description

Usage

Arguments

Value

Details

Author(s)

References

Examples

Augmented Inverse Probability Weighting Conditional ComBat

Description

Usage

Arguments

Details

Value

Details

Author(s)

References

Examples

Fit AIPW ComBat model for batch effect correction

Description

Usage

Arguments

Details

Value

Examples

Adjust for batch effects using an empirical Bayes framework

Description

Usage

Arguments

Details

Value

Examples

Matching Conditional ComBat

Description

Usage

Arguments

Value

Details

Author(s)

References

Examples

Causal Conditional Distance Correlation

Description

Usage

Arguments

Value

Details

Author(s)

References

Examples

Simulate Data with Heteroskedastic Conditional Average Treatment Effects

Description

Usage

Arguments

Value

Author(s)

References

Examples

K-class Sigmoidal CATE Simulation

Description

Usage

Arguments

Value

Author(s)

References

Examples

Non-monotone CATE Simulation

Description