CERFIT: Fits a Random Forest of Interaction Trees

In CERFIT: Causal Effect Random Forest of Interaction Trees

Fits a Random Forest of Interaction Trees

Description

Estimates individualized treatment effects (ITEs) using Random Forest of Interaction Trees. Works with randomized controlled trials (RCTs) and observational data. Treatment variables may be binary, categorical, ordered, or continuous. For binary and survival outcomes, useRes = TRUE must be specified.

Usage

CERFIT(
  formula,
  data,
  ntrees,
  subset = NULL,
  search = c("exhaustive", "sss"),
  method = c("RCT", "observational"),
  PropForm = c("randomForest", "CBPS", "GBM", "HI"),
  split = c("t.test"),
  mtry = NULL,
  nsplit = NULL,
  nsplit.random = FALSE,
  minsplit = 20,
  minbucket = round(minsplit/3),
  maxdepth = 30,
  oob = FALSE,
  a = 50,
  sampleMethod = c("bootstrap", "subsample", "subsampleByID", "allData"),
  useRes = TRUE,
  scale.y = FALSE,
  response = c("auto", "continuous", "binary", "survival"),
  surv_resid = c("deviance", "martingale"),
  surv_id = NULL
)

Arguments

formula	Formula to build CERFIT. Categorical predictors must be listed as a factor. e.g., Y ~ x1 + x2 | treatment. For survival outcomes, the response may be specified as Surv(time, event) or Surv(start, stop, event).
data	Data to grow a tree.
ntrees	Number of trees to grow. This value should not be too small, as observations may not be well represented and averaging is insufficient, leading to unstable results. A value of 1000 is often recommended, but it can be reduced for smaller datasets or to speed up computation.
subset	A logical vector that controls what observations are used to grow the forest. The default value will use the entire data frame.
search	Split search strategy. Options: “exhaustive” (evaluate all cut points) or “sss” (sigmoid approximation, experimental).
method	Study type. "RCT" for randomized data, "observational" for observational data.
PropForm	Method for estimating propensity scores (if method = "observational"). Options: "randomForest", "CBPS", "GBM", "HI". Not all options are compatible with all treatment types. See details.
split	Impurity measure splitting statistic. Currently supports "t.test".
mtry	Number of variables to consider at each split
nsplit	Number of candidate cut points. If NULL, all possible cut points are considered. If an integer is provided, that many cut points are randomly selected from the set of possible cut points.
nsplit.random	Default is FALSE. If TRUE, candidate cut points are chosen randomly.
minsplit	Number of observations required to continue growing tree.
minbucket	Number of observations required in each child node.
maxdepth	Maximum depth of tree.
oob	Logical, whether or not to use out-of-bag sample for predictions. Default is FALSE.
a	Sigmoid approximation variable (for "sss" which is still under development).
sampleMethod	Method to sample learning sample. Default is bootstrap. Subsample takes a subsample of the original data. SubsamplebyID samples by an ID column and uses all observations that have that ID. allData uses the entire data set for every tree.
useRes	Default is TRUE. If TRUE, fits the model using residuals from a regression of the response on covariates (excluding treatment). Improves stability and accuracy. Linear regression is used for continuous responses, logistic regression for binary responses, Cox proportional hazards model are used for survival responses. If response is binary or survival, useRes must be set equal to TRUE.
scale.y	Logical, standardize y when creating splits (For "sss" to increase stability).
response	Response type. Options are "auto", "continuous", "binary", and "survival". When response = auto, the function automatically detects a survival response if the formula uses Surv(...), detects a binary response if the outcome is stored as a factor with exactly two levels, and otherwise treats the response as continuous. Thus, numeric continuous outcomes are recognized automatically, but binary outcomes coded numerically (for example, 0/1) are not automatically identified as binary and should be specified with response = binary if that behavior is desired.
surv_resid	Residual type used for survival responses. Options are "deviance" and "martingale".
surv_id	Optional subject ID column name for survival models with time-dependent covariates in counting-process format, e.g. Surv(start, stop, event). Required for that format.

Details

This function implements Random Forest of Interaction Trees proposed in Su (2018), which is a modification of the Random Forest algorithm where instead of a split being chosen to maximize prediction accuracy; each split is chosen to maximize subgroup treatment heterogeneity. It chooses the best split by maximizing the test statistic for H_0: \beta_3=0 in the following linear model:

Y_i = \beta_0 + \beta_1I(X_{ij} < c) + \beta_2I(Z = 1) + \beta_3I(X_{ij} < c)I(Z = 1) + \varepsilon_i

Where X_{ij} represents the splitting variable and Z = 1 represents treatment. So, by maximizing the test statistic for \beta_3 we are maximizing the treatment difference between the nodes.

The above equation only works when the data comes from a randomized controlled trial, but we can modify it to give us unbiased estimates of treatment effect in observational studies, as shown by Li et al. (2022). To do that we add propensity score into the linear model.

Y_i = \beta_0 + \beta_1I(X_{ij} < c) + \beta_2I(Z = 1) + \beta_3I(X_{ij} < c)I(Z = 1) + \beta_4e_i + \varepsilon_i

Where e_i represents the propensity score. The CERFIT function will estimate propensity score automatically when the method argument is set to observational.

To control how this function estimates propensity score, you can use the PropForm argument. Which can take four possible values randomForest, CBPS, GBM and HI. randomForest uses the randomForest package to use a random forest to estimate propensity score, CBPS uses Covariate Balancing Propensity Score to estimate propensity score, GBM uses generalized boosted regression models to estimate propensity score, and HI is the Hirano–Imbens generalized propensity score weighting for continuous treatments. Some of these options only work for certain treatment types. See the full list below.

• binary: GBM, CBPS, randomForest

• categorical: GBM, CBPS

• ordered: GBM, CBPS

• continuous: CBPS, HI

Note: CBPS option supports up to four categories/levels of treatment, if there are more than four use GBM.

Value

Returns a fitted CERFIT object which is a list containing the following elements:

• randFor: The Random Forest of Interaction Trees.

• trt.type: A string containing the treatment type of the data used to fit the model. Can be binary, multiple, ordered, or continuous.

• response.type: A string representing the response type of the data. Can be binary or continuous.

• useRes: A logical indicator that is TRUE if the model was fit on the residuals of a linear model.

• data: The data used to fit the model and includes the estimated propensity score if method was set to observational.

References

• Li, Luo, et al. Causal Effect Random Forest of Interaction Trees for Learning Individualized Treatment Regimes with Multiple Treatments in Observational Studies. Stat, 2022, https://doi.org/10.1002/sta4.457.

• Su, X., Peña, A., Liu, L., & Levine, R. (2018). Random forests of interaction trees for estimating individualized treatment effects in randomized trials. Statistics in Medicine, 37(17), 2547- 2560.

• G. W. Imbens, The role of the propensity score in estimating dose-response functions., Biometrika, 87 (2000), pp. 706–710.

• G. Ridgeway, D. McCarey, and A. Morral, The twang package: Toolkit for weighting and analysis of nonequivalent groups, (2006).

• A. Liaw and M. Wiener, Classification and regression by randomforest, R News, 2 (2002), pp. 18–22

Examples

fit <- CERFIT(Result_of_Treatment ~ sex + age + Number_of_Warts + Area + Time + Type | treatment,
data = warts,
ntrees = 30,
method = "RCT",
mtry = 2)

CERFIT documentation built on May 7, 2026, 5:09 p.m.