CRE

Interpretable Discovery and Inference of Heterogeneous Treatment Effects

In health and social sciences, it is critically important to identify subgroups of the study population where a treatment has notable heterogeneity in the causal effects with respect to the average treatment effect (ATE). The bulk of heterogeneous treatment effect (HTE) literature focuses on two major tasks: (i) estimating HTEs by examining the conditional average treatment effect (CATE); (ii) discovering subgroups of a population characterized by HTE.

Several methodologies have been proposed for both tasks, but providing interpretability in the results is still an open challenge. Bargagli-Stoffi et al. (2023) proposed Causal Rule Ensemble, a new method for HTE characterization in terms of decision rules, via an extensive exploration of heterogeneity patterns by an ensemble-of-trees approach, enforcing stability in the discovery. CRE is an R Package providing a flexible implementation of the Causal Rule Ensemble algorithm.

Installation

Installing from CRAN.

install.packages("CRE")

Installing the latest developing version.

library(devtools)
install_github("NSAPH-Software/CRE", ref="develop")

Import.

library("CRE")

The full list of required dependencies can be found in project in the DESCRIPTION file.

Arguments

Data (required)
y The observed response/outcome vector (binary or continuous).

z The treatment/exposure/policy vector (binary).

X The covariate matrix (binary or continuous).

Parameters (not required)
method_parameters The list of parameters to define the models used, including:

• ratio_dis The ratio of data delegated to the discovery sub-sample (default: 0.5).
• ite_method The method to estimate the individual treatment effect (ITE) pseudo-outcome estimation (default: "aipw") [1].
• learner_ps The SuperLearner model for the propensity score estimation (default: "SL.xgboost", used only for "aipw","bart","cf" ITE estimators).
• learner_y The SuperLearner model for the outcome estimation (default: "SL.xgboost", used only for "aipw","slearner","tlearner" and "xlearner" ITE estimators).

hyper_params The list of hyper parameters to finetune the method, including:

• intervention_vars Array with intervention-able covariates names used for Rules Generation. Empty or null array means that all the covariates are considered as intervention-able (default: NULL).
• ntrees The number of decision trees for random forest (default: 20).
• node_size Minimum size of the trees' terminal nodes (default: 20).
• max_rules Maximum number of generated candidates rules (default: 50).
• max_depth Maximum rules length (default: 3).
• t_decay The decay threshold for rules pruning (default: 0.025).
• t_ext The threshold to define too generic or too specific (extreme) rules (default: 0.01).
• t_corr The threshold to define correlated rules (default: 1).
• stability_selection Method for stability selection for selecting the rules. "vanilla" for stability selection, "error_control" for stability selection with error control and "no" for no stability selection (default: "vanilla").
• B Number of bootstrap samples for stability selection in rules selection and uncertainty quantification in estimation (default: 20).
• subsample Bootstrap ratio subsample and stability selection in rules selection, and uncertainty quantification in estimation (default: 0.5).
• offset Name of the covariate to use as offset (i.e. "x1") for T-Poisson ITE Estimation. NULL if not used (default: NULL).
• cutoff Threshold defining the minimum cutoff value for the stability scores in Stability Selection (default: 0.9).
• pfer Upper bound for the per-family error rate (tolerated amount of falsely selected rules) in Error Control Stability Selection (default: 1).

Additional Estimates (not required)
ite The estimated ITE vector. If given, both the ITE estimation steps in Discovery and Inference are skipped (default: NULL).

Notes

[1] Options for the ITE estimation are as follows:

• S-Learner (slearner)
• T-Learner (tlearner)
• T-Poisson (tpoisson)
• X-Learner (xlearner)
• Augmented Inverse Probability Weighting (aipw)
• Causal Forests (cf)
• Causal Bayesian Additive Regression Trees (bart)

If other estimates of the ITE are provided in ite additional argument, both the ITE estimations in discovery and inference are skipped and those values estimates are used instead. The ITE estimator requires also an outcome learner and/or a propensity score learner from the SuperLearner package (i.e., "SL.lm", "SL.svm"). Both these models are simple classifiers/regressors. By default XGBoost algorithm is used for both these steps.

Examples

Example 1 (default parameters)

set.seed(2023)
dataset <- generate_cre_dataset(n = 2000, 
                                rho = 0, 
                                n_rules = 2, 
                                p = 10,
                                effect_size = 5, 
                                binary_covariates = TRUE,
                                binary_outcome = FALSE,
                                confounding = "no")
y <- dataset[["y"]]
z <- dataset[["z"]]
X <- dataset[["X"]]

cre_results <- cre(y, z, X)
summary(cre_results)
plot(cre_results)
ite_pred <- predict(cre_results, X) 

Example 2 (personalized ite estimation)

set.seed(2023)
dataset <- generate_cre_dataset(n = 2000, 
                                rho = 0, 
                                n_rules = 2, 
                                p = 10,
                                effect_size = 5, 
                                binary_covariates = TRUE,
                                binary_outcome = FALSE,
                                confounding = "no")
  y <- dataset[["y"]]
  z <- dataset[["z"]]
  X <- dataset[["X"]]

# personalized ITE estimation (S-Learner with Linear Regression)
model <- lm(y ~., data = data.frame(y = y, X = X, z = z))
ite_pred <- predict(model, newdata = data.frame(X = X, z = z))

cre_results <- cre(y, z, X, ite = ite_pred)
summary(cre_results)
plot(cre_results)
ite_pred <- predict(cre_results, X)

Example 3 (setting parameters)

  set.seed(2023)
  dataset <- generate_cre_dataset(n = 2000, 
                                  rho = 0, 
                                  n_rules = 2, 
                                  p = 10,
                                  effect_size = 2, 
                                  binary_covariates = TRUE,
                                  binary_outcome = FALSE,
                                  confounding = "no")
  y <- dataset[["y"]]
  z <- dataset[["z"]]
  X <- dataset[["X"]]

  method_params = list(ratio_dis = 0.5,
                       ite_method ="aipw",
                       learner_ps = "SL.xgboost",
                       learner_y = "SL.xgboost")

 hyper_params = list(intervention_vars = c("x1","x2","x3","x4","x5","x6"),
                     offset = NULL,
                     ntrees = 20,
                     node_size = 20,
                     max_rules = 50,
                     max_depth = 2,
                     t_decay = 0.025,
                     t_ext = 0.025,
                     t_corr = 1,
                     stability_selection = "vanilla",
                     cutoff = 0.8,
                     pfer = 0.1,
                     B = 50,
                     subsample = 0.1)

cre_results <- cre(y, z, X, method_params, hyper_params)
summary(cre_results)
plot(cre_results)
ite_pred <- predict(cre_results, X)

More synthetic data sets can be generated using generate_cre_dataset().

Simulations

Reproduce simulation experiments in Section 4 in @bargagli2023causal, evaluating Causal Rule Ensemble Discovery and Estimation performances, comparing with different benchmarks.

Discovery: Evaluate performance of Causal Rule Ensemble algorithm (varying the pseudo-outcome estimator) in rules and effect modifier discovery.

CRE/functional_tests/experiments/discovery.R

Estimation: Evaluate performance of Causal Rule Ensemble algorithm (varying the pseudo-outcome estimator) in treatment effect estimation and comparing it with the corresponding stand-alone ITE estimators.

CRE/functional_tests/experiments/estimation.R

More exhaustive simulation studies and real world experiment of CRE package can be found at https://github.com/NSAPH-Projects/cre_applications.

Code of Conduct

Please note that the CRE project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms. More information about the opening issues and contributing (i.e., git branching model) can be found on CRE website.