bart function

Fit BART models to select confounders and estimate treatment effect

Fit Bayesian Regression Additive Trees (BART) models to select relevant confounders among a large set of potential confounders and to estimate average treatment effect $E[Y(1) - Y(0)]$.

separate_bart(
  Y, trt, X,
  trt_treated     = 1,
  trt_control     = 0,
  num_tree        = 50,
  num_chain       = 4,
  num_burn_in     = 100,
  num_thin        = 1,
  num_post_sample = 100,
  step_prob       = c(0.28, 0.28, 0.44),
  alpha           = 0.95,
  beta            = 2,
  nu              = 3,
  q               = 0.95,
  dir_alpha       = 5,
  parallel        = FALSE,
  verbose         = TRUE
)

single_bart(
  Y, trt, X,
  trt_treated     = 1,
  trt_control     = 0,
  num_tree        = 50,
  num_chain       = 4,
  num_burn_in     = 100,
  num_thin        = 1,
  num_post_sample = 100,
  step_prob       = c(0.28, 0.28, 0.44),
  alpha           = 0.95,
  beta            = 2,
  nu              = 3,
  q               = 0.95,
  dir_alpha       = 5,
  parallel        = FALSE,
  verbose         = TRUE
)

Arguments

• Y: A vector of outcome values.

• trt: A vector of treatment values. Binary treatment works for both model and continuous treatment works for single_bart(). For binary treatment, use 1 to indicate the treated group and 0 for the control group.

• X: A matrix of potential confounders.

• trt_treated: Value of trt for the treated group. The default value is set to 1.

• trt_control: Value of trt for the control group. The default value is set to 0.

• num_tree: Number of trees in BART model. The default value is set to 100.

• num_chain: Number of MCMC chains. Need to set num_chain > 1 for the Gelman-Rubin diagnostic. The default value is set to 4.

• num_burn_in: Number of MCMC samples to be discarded per chain as initial burn-in periods. The default value is set to 100.

• num_thin: Number of thinning per chain. One in every num_thin samples are selected. The default value is set to 1.

• num_post_sample: Final number of posterior samples per chain. Number of MCMC iterations per chain is burn_in + num_thin * num_post_sample. The default value is set to 100.

• step_prob: A vector of tree alteration probabilities (GROW, PRUNE, CHANGE). Each alteration is proposed to change the tree structure.

  The default setting is (0.28, 0.28, 0.44).

• alpha, beta: Hyperparameters for tree regularization prior. A terminal node of depth d will split with probability of alpha * (1 + d)^(-beta).

  The default setting is (alpha, beta) = (0.95, 2) from Chipman et al. (2010).

• nu, q: Values to calibrate hyperparameter of sigma prior.

  The default setting is (nu, q) = (3, 0.95) from Chipman et al. (2010).

• dir_alpha: Hyperparameter of Dirichlet prior for selection probabilities. The default value is 5.

• parallel: If TRUE, model fitting will be parallelized with respect to N = nrow(X). Parallelization is recommended for very high n only. The default setting is FALSE.

• verbose: If TRUE, message will be printed during training. If FALSE, message will be suppressed.

Returns

A bartcs object. A list object contains the following components.

• mcmc_list: A mcmc.list object from coda package. mcmc_list contains the following items.

• ATE Posterior sample of average treatment effect $E[Y(1) - Y(0)]$.
• Y1 Posterior sample of potential outcome $E[Y(1)]$.
• Y0 Posterior sample of potential outcome $E[Y(0)]$.
• dir_alpha Posterior sample of dir_alpha.
• sigma2_out Posterior sample of sigma2 in the outcome model.

• var_prob: Aggregated posterior inclusion probability of each variable.

• var_count: Number of selection of each variable in each MCMC iteration. Its dimension is num_post_sample * ncol(X).

• chains: A list of results from each MCMC chain.

• model: separate or single.

• label: Column names of X.

• params: Parameters used in the model.

Details

separate_bart() and single_bart() fit an exposure model and outcome model(s) for estimating treatment effect with adjustment of confounders in the presence of a large set of potential confounders (Kim et al. 2023).

The exposure model $E[A|X]$ and the outcome model(s) $E[Y|A,X]$ are linked together with a common Dirichlet prior that accrues posterior selection probabilities to the corresponding confounders ($X$) on the basis of association with both the exposure ($A$) and the outcome ($Y$).

There is a distinction between fitting separate outcome models for the treated and control groups and fitting a single outcome model for both groups.

• separate_bart() specifies two "separate" outcome models for two binary treatment levels. Thus, it fits three models: one exposure model and two separate outcome models for $A = 0, 1$.
• single_bart() specifies one "single" outcome model. Thus, it fits two models: one exposure model and one outcome model for the entire sample.

All inferences are made with outcome model(s).

Examples

data(ihdp, package = "bartcs")
single_bart(
  Y               = ihdp$y_factual,
  trt             = ihdp$treatment,
  X               = ihdp[, 6:30],
  num_tree        = 10,
  num_chain       = 2,
  num_post_sample = 20,
  num_burn_in     = 10,
  verbose         = FALSE
)
separate_bart(
  Y               = ihdp$y_factual,
  trt             = ihdp$treatment,
  X               = ihdp[, 6:30],
  num_tree        = 10,
  num_chain       = 2,
  num_post_sample = 20,
  num_burn_in     = 10,
  verbose         = FALSE
)

References

Chipman, H. A., George, E. I., & McCulloch, R. E. (2010). BART: Bayesian additive regression trees. The Annals of Applied Statistics, 4(1), 266-298. tools:::Rd_expr_doi("10.1214/09-AOAS285")

Kim, C., Tec, M., & Zigler, C. M. (2023). Bayesian Nonparametric Adjustment of Confounding, Biometrics

tools:::Rd_expr_doi("10.1111/biom.13833")