Package 'CERFIT'

Fits a Random Forest of Interactions Trees

Description

Estimates an observations individualized treatment effect for RCT and observational data. Treatment can be an binary, categorical, ordered, or continuous variable. Currently if response is binary useRes must be set equal to TRUE.

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,
  a = 50,
  sampleMethod = c("bootstrap", "subsample", "subsampleByID", "allData"),
  useRes = TRUE,
  scale.y = FALSE
)

Arguments

formula	Formula to build CERFIT. Categorical predictors must be listed as a factor. e.g., Y ~ x1 + x2 | treatment
data	Data to grow a tree.
ntrees	Number of Trees to grow
subset	A logical vector that controls what observations are used to grow the forest. The default value will use the entire dataframe
search	Method to search through candidate splits
method	For observational study data, method="observational";for randomized study data, method="RCT".
PropForm	Method to estimate propensity score
split	Impurity measure splitting statistic
mtry	Number of variables to consider at each split
nsplit	Number of cut points selected
nsplit.random	Logical: indicates if process to select cut points are random
minsplit	Number of observations required to continue growing tree
minbucket	Number of observations required in each child node
maxdepth	Maximum depth of tree
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	Logical indicator if you want to fit the CERFIT model to the residuals from a linear model
scale.y	Logical, standardize y when creating splits (For "sss" to increase stability)

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 maximized 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 gives us unbiased estimates of treatment effect in observational studies 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 CERIT 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 for continuous treatment and estimates the general propensity score. Some of these options only work for certain treatment types. Full list below

• binary: GBM, CBPS, randomForest

• categorical: GBM, CBPS

• ordered: GBM, CBPS

• continuous: CBPS, HI

Value

Returns a fitted CERFIT object which is a list with 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. Cant 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 also contains the 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)

---

Observational Educational Dataset

Description

A simulated dataset containing the grades and other attributes of 1000 simulated students

Usage

educational

Format

A data frame with 1000 rows and 7 variables:

SAT_MATH

SAT Math Score

HSGPA

High School GPA

AGE

Age of Student

GENDER

Gender of Student

URM

Under Represented Minority

A

Treatment Variable

Y

Students Final Grade

Source

Wilke, Morten C., et al. “Estimating the Optimal Treatment Regime for Student Success Programs.” Behaviormetrika, vol. 48, no. 2, 2021, pp. 309–343., https://doi.org/10.1007/s41237-021-00140-0.

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Calculate Variable Importance

Description

Calculates the average minimal depth of each predictor used to fit a CERFIT object. It calculates Variables importance by using a Variables average minimal depth. variable's with a lower average minimal depth are more important.

Usage

MinDepth(cerfit)

Arguments

cerfit

A fitted CERFIT object

Details

The depth of the root node is zero and if a variable does not appear at any split in a tree it is assigned maxdepth + 1 for that tree.

Value

Returns a named vector with the name of each predictor used to fit the CERFIT object and its corresponding average minimal depth across all trees

Examples

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

---

Get predictions from a CERFIT object

Description

Get predictions from a CERFIT object

Usage

## S3 method for class 'CERFIT'
predict(
  object,
  newdata = NULL,
  gridval = NULL,
  prediction = c("overall", "by iter"),
  type = c("response", "ITE", "node", "opT"),
  alpha = 0.5,
  ...
)

Arguments

object	A fitted CERFIT object
newdata	New data to make predictions from. IF not provided will make predictions on training data
gridval	For continuous treatment. Controls for what values of treatment to predict
prediction	Return prediction using all trees ("overall") or using first i trees ("by iter")
type	Choose what value you wish to predict. Response will predict the response. ITE will predict the Individualized treatment effect. Node will predict the node. And opT will predict the optimal treatment for each observation.
alpha	For continuous treatment it is the mixing parameter for the elastic net regularization in each node. When equal to 0 it is ridge regression and when equal to 1 it is lasso regression.
...	Additional Arguments

Value

The return value depends of the type argument. If type is response the function will return a matrix with n rows and the number of columns equal to the level of treatment. If type is ITE then it returns a matrix with n rows and a number of columns equal to one minus the levels of treatment. And if type is opT then it returns a matrix with n rows and two columns. With the first column denoting the optimal treatment and the second column denoting the optimal response.

Examples

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

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Randomized Controlled Trial Warts Dataset

Description

A dataset comparing immunotherapy to cryotherapy treatments and their effeteness of removing warts

Usage

warts

Format

A data frame with 180 rows and 8 variables:

sex

Patients Sex

age

Patients Age

Time

Time Elapsed Before Treatment

Number_of_Warts

Number of Warts

Type

Type of Wart

Area

Wart Surface Area

Result_of_Treatment

Treatment Outcome

treatment

0 for immunotherapy and 1 for cryotherapy

Source

Khozeimeh, Fahime, et al. “An Expert System for Selecting Wart Treatment Method.” Computers in Biology and Medicine, vol. 81, 2017, pp. 167–175., https://doi.org/10.1016/j.compbiomed.2017.01.001.

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