Description Usage Arguments Details Value Author(s) References See Also Examples
Fits a collection of treatment and response models using the Bayesian Additive Regression Trees (BART) algorithm, producing estimates of treatment effects.
1 2 3 4 5 6 7 8 9 10 11 12  bartc(response, treatment, confounders, data, subset, weights,
method.rsp = c("bart", "tmle", "p.weight"),
method.trt = c("bart", "glm", "none"),
estimand = c("ate", "att", "atc"),
group.by = NULL,
commonSup.rule = c("none", "sd", "chisq"),
commonSup.cut = c(NA_real_, 1, 0.05),
args.rsp = list(), args.trt = list(),
p.scoreAsCovariate = TRUE, use.ranef = TRUE, group.effects = FALSE,
crossvalidate = FALSE,
keepCall = TRUE, verbose = TRUE,
...)

response 
A vector of the outcome variable, or a reference to such in the 
treatment 
A vector of the binary treatment variable, or a reference to 
confounders 
A matrix or data frame of covariates to be used in estimating the treatment
and response model. Can also be the righthandside of a formula (e.g.

data 
An optional data frame or named list containing the 
subset 
An optional vector using to subset the data. Can refer to 
weights 
An optional vector of population weights used in model fitting and
estimating the treatment effect. Can refer to 
method.rsp 
A character string specifying which method to use when fitting the response
surface and estimating the treatment effect. Options are: 
method.trt 
A character string specifying which method to use when fitting the treatment
assignment mechanism, or a vector/matrix of propensity scores. Character
string options are: 
estimand 
A character string specifying which causal effect to target. Options are

group.by 
An optional factor that, when present, causes the treatment effect estimate to be calculated within each group. 
commonSup.rule 
Rule for exclusion of observations lacking in common support. Options are

commonSup.cut 
Cutoffs for 
p.scoreAsCovariate 
A logical such that when 
use.ranef 
Logical specifying if 
group.effects 
Logical specifying if effects should be calculated within groups if the

keepCall 
A logical such that when 
crossvalidate 
One of 
verbose 
A logical that when 
args.rsp, args.trt, ... 
Further arguments to the treatment and response model fitting algorithms.
Arguments passed to the main function as ... will be used in both models.

bartc
represents a collection of methods that primarily use the
Bayesian Additive Regression Trees (BART) algorithm to estimate causal
treatment effects with binary treatment variables and continuous
outcomes. This requires models to be fit to the response surface (distribution
of the response as a function of treatment and confounders,
p(Y(1), Y(0)  X) and optionally for treatment assignment mechanism
(probability of receiving treatment, i.e. propensity score,
Pr(Z = 1  X)). The response surface model is used to impute
counterfactuals, which may then be adjusted together with the propensity score
to produce estimates of effects.
Similar to lm
, models can be specified symbolically. When the
data
term is present, it will be added to the search path for the
response
, treatment
, and confounders
variables. The
confounders must be specified devoid of any "left hand side", as they appear
in both of the models.
Response Surface
The response surface methods included are:
"bart"
 use BART to fit the response surface and produce
individual estimates Y(1)^hat_i and
Y(0)^hat_i. Treatment effect estimates are
obtained by averaging the difference of these across the population of
interest.
"p.weight"
 individual effects are estimated as in
"bart"
, but treatment effect estimates are obtained by using a
propensity score weighted average. For the average treatment effect on
the treated, these weights are p(z_i  x_i) / (∑ z / n). For
ATC, replace z with 1  z. For ATE, "p.weight"
is
equal to "bart"
.
"tmle"
 individual effects are estimated as in "bart"
and a weighted average is taken as in "p.weight"
, however the
response surface estimates and propensity scores are corrected by
using the Targeted Minimum Loss based Estimation method.
Treatment Assignment
The treatment assignment models are:
"bart"
 fit a binary BART directly to the treatment using all
the confounders.
"none"
 no modeling is done. Only applies when using response
method "bart"
and p.scoreAsCovariate
is FALSE
.
"glm"
 fit a binomial generalized linear model with logistic
link and confounders included as linear terms.
Finally, a vector or matrix of propensity scores can be supplied. Propensity score matrices should have a number of rows equal to the number of observations in the data and a number of columns equal to the number of posterior samples.
Generics
For a fitted model, the easiest way to analyze the resulting fit is to use the
generics fitted
, extract
, and
predict
to analyze specific quantities and
summary
to aggregate those values into
targets (e.g. ATE, ATT, or ATC).
Common Support Rules
Common support, or that the probability of receiving all treatment conditions
is nonzero within every area of the covariate space
(P(Z = 1  X = x) > 0 for all x in the inferential sample), can be
enforced by excluding observations with high posterior uncertainty.
bartc
supports two common support rules through commonSup.rule
argument:
"sd"
 observations are cut from the inferential sample if:
s_i^f(1z) > m_z + a * sd(s_j^f(z)),
where s_i^f(1z) is the posteriors standard
deviation of the predicted counterfactual for observation i,
s_j^f(z) is the posterior standard deviation of the prediction
for the observed treatment condition of observation j,
sd(s_j^f(z)) is the empirical standard deviation
of those quantities, and
m_z = max_j s_j^f(z) for all j
in the same treatment group, i.e. Z_j = z. a is a constant
to be passed in using commonSup.cut
and its default is 1.
"chisq"
 observations are cut from the inferential sample if:
s_i^f(1z) / s_i^f(z))^2 > q_α,
where s_i are as above and q_α, is the upper
α percentile of a χ^2 distribution with one degree
of freedom, corresponding to a null hypothesis of equal variance. The
default for α is 0.05, and it is specified using the
commonSup.cut
parameter.
Special Arguments
Some default arguments are unconventional or are passed in a unique fashion.
If n.chains
is missing, unlike in bart2
a default
of 10 is used.
For method.rsp == "tmle"
, a special arg.trt
of
posteriorOfTMLE
determines if the TMLE correction should be
applied to each posterior sample (TRUE
), or just the posterior
mean (FALSE
).
Missing Data
Missingness is allowed only in the response. If some response values are
NA
, the BART models will be trained just for where data are available
and those values will be used to make predictions for the missing
observations. Missing observations are not used when calculating statistics
for assessing common support, although they may still be excluded on those
grounds. Further, missing observations may not be compatible with response
method "tmle"
.
bartc
returns an object of class bartcFit
. Information about the
object can be derived by using methods summary
,
plot_sigma
, plot_est
, plot_indiv
,
and plot_support
. Numerical quantities are recovered with the
fitted
and
extract
generics. Predictions for new
observations are obtained with predict
.
Objects of class bartcFit
are lists containing items:

character string specifying the method used to fit the response surface 

character string specifying the method used to fit the treatment assignment mechanism 

character string specifying the targeted causal effect 

object containing the fitted response model 



object containing the fitted treatment model 

optional factor vector containing the groups in which treatment effects are estimated 

matrix or array of posterior samples of the treatment effect estimate 

the vector of propensity scores used as a covariate in the response model, when applicable 

matrix or array of posterior samples of the propensity score, when applicable 

samples from the posterior of the expected value for individual responses under the observed treatment regime 

samples from the posterior of the expected value for individual responses under the counterfactual treatment 

character string giving the name of the treatment
variable in the data of 

vector of treatment assignments 

how 

number of independent posterior sampler chains in response model 

common support rule used for suppressing observations 

common support parameter used to set cutoff when suppressing observations 

vector of standard deviations of individual posterior predictors for observed treatment conditions 

vector of standard deviations of individual posterior predictors for counterfactuals 

logical vector expressing which observations are used when estimating treatment effects 

logical for whether ranef models were used; only added when true 

logical for whether grouplevel estimates are made; only added when true 

a random seed for use when drawing from the posterior predictive distribution 
Vincent Dorie: vdorie@gmail.com.
Chipman, H., George, E. and McCulloch R. (2010) BART: Bayesian additive regression trees. The Annals of Applied Statistics 4(1), 266–298. The Institute of Mathematical Statistics. https://doi.org/10.1214/09AOAS285.
Hill, J. L. (2011) Bayesian Nonparametric Modeling for Causal Inference. Journal of Computational and Graphical Statistics 20(1), 217–240. Taylor & Francis. https://doi.org/10.1198/jcgs.2010.08162.
Hill, J. L. and Su Y. S. (2013) Assessing Lack of Common Support in Causal Inference Using Bayesian Nonparametrics: Implications for Evaluating the Effect of Breastfeeding on Children's Cognitive Outcomes The Annals of Applied Statistics 7(3), 1386–1420. The Institute of Mathematical Statistics. https://doi.org/10.1214/13AOAS630.
Carnegie, N. B. (2019) Comment: Contributions of Model Features to BART Causal Inference Performance Using ACIC 2016 Competition Data Statistical Science 34(1), 90–93. The Institute of Mathematical Statistics. https://doi.org/10.1214/18STS682
Hahn, P. R., Murray, J. S., and Carvalho, C. M. (2020) Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion). Bayesian Analysis 15(3), 965–1056. International Society for Bayesian Analysis. https://doi.org/10.1214/19BA1195.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  ## fit a simple linear model
n < 100L
beta.z < c(.75, 0.5, 0.25)
beta.y < c(.5, 1.0, 1.5)
sigma < 2
set.seed(725)
x < matrix(rnorm(3 * n), n, 3)
tau < rgamma(1L, 0.25 * 16 * rgamma(1L, 1 * 32, 32), 16)
p.score < pnorm(x %*% beta.z)
z < rbinom(n, 1, p.score)
mu.0 < x %*% beta.y
mu.1 < x %*% beta.y + tau
y < mu.0 * (1  z) + mu.1 * z + rnorm(n, 0, sigma)
# low parameters only for example
fit < bartc(y, z, x, n.samples = 100L, n.burn = 15L, n.chains = 2L)
summary(fit)
## example to show refitting under the common support rule
fit2 < refit(fit, commonSup.rule = "sd")
fit3 < bartc(y, z, x, subset = fit2$commonSup.sub,
n.samples = 100L, n.burn = 15L, n.chains = 2L)

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