Package 'cdgd' reference manual

Title:	Causal Decomposition of Group Disparities
Description:	The framework of causal decomposition of group disparities developed by Yu and Elwert (2023) <doi:10.48550/arXiv.2306.16591>. This package implements the decomposition estimators that are based on efficient influence functions. For the nuisance functions of the estimators, both parametric and nonparametric options are provided, as well as manual options in case the default models are not satisfying.
Authors:	Ang Yu [aut, cre, cph] (<https://ang-yu.github.io/>, <https://orcid.org/0000-0002-1828-0165>)
Maintainer:	Ang Yu <[email protected]>
License:	MIT + file LICENSE
Version:	0.3.5
Built:	2024-10-31 03:04:02 UTC
Source:	https://github.com/ang-yu/cdgd

Perform unconditional decomposition with nuisance functions estimated beforehand

Description

This function gives the user full control over the estimation of the nuisance functions. For the unconditional decomposition, three nuisance functions (YgivenGX.Pred_D0, YgivenGX.Pred_D1, and DgivenGX.Pred) need to be estimated. The nuisance functions should be estimated using cross-fitting if Donsker class is not assumed.

Usage

cdgd0_manual(
  Y,
  D,
  G,
  YgivenGX.Pred_D1,
  YgivenGX.Pred_D0,
  DgivenGX.Pred,
  data,
  alpha = 0.05
)
cdgd0_manual(
  Y,
  D,
  G,
  YgivenGX.Pred_D1,
  YgivenGX.Pred_D0,
  DgivenGX.Pred,
  data,
  alpha = 0.05
)

Arguments

`Y`	Outcome. The name of a numeric variable.
`D`	Treatment status. The name of a binary numeric variable taking values of 0 and 1.
`G`	Advantaged group membership. The name of a binary numeric variable taking values of 0 and 1.
`YgivenGX.Pred_D1`	A numeric vector of predicted Y values given X, G, and D=1. Vector length=nrow(data).
`YgivenGX.Pred_D0`	A numeric vector of predicted Y values given X, G, and D=0. Vector length=nrow(data).
`DgivenGX.Pred`	A numeric vector of predicted D values given X and G. Vector length=nrow(data).
`data`	A data frame.
`alpha`	1-alpha confidence interval.

Value

A list of estimates.

Examples

# This example will take a minute to run.

data(exp_data)

Y="outcome"
D="treatment"
G="group_a"
X=c("Q","confounder")
data=exp_data

set.seed(1)

### estimate the nuisance functions with cross-fitting
sample1 <- sample(nrow(data), floor(nrow(data)/2), replace=FALSE)
sample2 <- setdiff(1:nrow(data), sample1)

### outcome regression model

message <- utils::capture.output( YgivenDGX.Model.sample1 <-
    caret::train(stats::as.formula(paste(Y, paste(D,G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample1,], method="ranger", trControl=caret::trainControl(method="cv"),
             tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )
message <- utils::capture.output( YgivenDGX.Model.sample2 <-
    caret::train(stats::as.formula(paste(Y, paste(D,G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample2,], method="ranger", trControl=caret::trainControl(method="cv"),
             tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )

### propensity score model
data[,D] <- as.factor(data[,D])
levels(data[,D]) <- c("D0","D1")  # necessary for caret implementation of ranger

message <- utils::capture.output( DgivenGX.Model.sample1 <-
    caret::train(stats::as.formula(paste(D, paste(G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample1,], method="ranger",
             trControl=caret::trainControl(method="cv", classProbs=TRUE),
             tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )
message <- utils::capture.output( DgivenGX.Model.sample2 <-
    caret::train(stats::as.formula(paste(D, paste(G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample2,], method="ranger",
             trControl=caret::trainControl(method="cv", classProbs=TRUE),
             tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )

data[,D] <- as.numeric(data[,D])-1

### cross-fitted predictions
YgivenGX.Pred_D0 <- YgivenGX.Pred_D1 <- DgivenGX.Pred <- rep(NA, nrow(data))

pred_data <- data
pred_data[,D] <- 0
YgivenGX.Pred_D0[sample2] <- stats::predict(YgivenDGX.Model.sample1, newdata = pred_data[sample2,])
YgivenGX.Pred_D0[sample1] <- stats::predict(YgivenDGX.Model.sample2, newdata = pred_data[sample1,])

pred_data <- data
pred_data[,D] <- 1
YgivenGX.Pred_D1[sample2] <- stats::predict(YgivenDGX.Model.sample1, newdata = pred_data[sample2,])
YgivenGX.Pred_D1[sample1] <- stats::predict(YgivenDGX.Model.sample2, newdata = pred_data[sample1,])

pred_data <- data
DgivenGX.Pred[sample2] <- stats::predict(DgivenGX.Model.sample1,
    newdata = pred_data[sample2,], type="prob")[,2]
DgivenGX.Pred[sample1] <- stats::predict(DgivenGX.Model.sample2,
    newdata = pred_data[sample1,], type="prob")[,2]

results <- cdgd0_manual(Y=Y,D=D,G=G,
                       YgivenGX.Pred_D0=YgivenGX.Pred_D0,
                       YgivenGX.Pred_D1=YgivenGX.Pred_D1,
                       DgivenGX.Pred=DgivenGX.Pred,
                       data=data)

results
# This example will take a minute to run.

data(exp_data)

Y="outcome"
D="treatment"
G="group_a"
X=c("Q","confounder")
data=exp_data

set.seed(1)

### estimate the nuisance functions with cross-fitting
sample1 <- sample(nrow(data), floor(nrow(data)/2), replace=FALSE)
sample2 <- setdiff(1:nrow(data), sample1)

### outcome regression model

message <- utils::capture.output( YgivenDGX.Model.sample1 <-
    caret::train(stats::as.formula(paste(Y, paste(D,G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample1,], method="ranger", trControl=caret::trainControl(method="cv"),
             tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )
message <- utils::capture.output( YgivenDGX.Model.sample2 <-
    caret::train(stats::as.formula(paste(Y, paste(D,G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample2,], method="ranger", trControl=caret::trainControl(method="cv"),
             tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )

### propensity score model
data[,D] <- as.factor(data[,D])
levels(data[,D]) <- c("D0","D1")  # necessary for caret implementation of ranger

message <- utils::capture.output( DgivenGX.Model.sample1 <-
    caret::train(stats::as.formula(paste(D, paste(G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample1,], method="ranger",
             trControl=caret::trainControl(method="cv", classProbs=TRUE),
             tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )
message <- utils::capture.output( DgivenGX.Model.sample2 <-
    caret::train(stats::as.formula(paste(D, paste(G,paste(X,collapse="+"),sep="+"), sep="~")),
             data=data[sample2,], method="ranger",
             trControl=caret::trainControl(method="cv", classProbs=TRUE),
             tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )

data[,D] <- as.numeric(data[,D])-1

### cross-fitted predictions
YgivenGX.Pred_D0 <- YgivenGX.Pred_D1 <- DgivenGX.Pred <- rep(NA, nrow(data))

pred_data <- data
pred_data[,D] <- 0
YgivenGX.Pred_D0[sample2] <- stats::predict(YgivenDGX.Model.sample1, newdata = pred_data[sample2,])
YgivenGX.Pred_D0[sample1] <- stats::predict(YgivenDGX.Model.sample2, newdata = pred_data[sample1,])

pred_data <- data
pred_data[,D] <- 1
YgivenGX.Pred_D1[sample2] <- stats::predict(YgivenDGX.Model.sample1, newdata = pred_data[sample2,])
YgivenGX.Pred_D1[sample1] <- stats::predict(YgivenDGX.Model.sample2, newdata = pred_data[sample1,])

pred_data <- data
DgivenGX.Pred[sample2] <- stats::predict(DgivenGX.Model.sample1,
    newdata = pred_data[sample2,], type="prob")[,2]
DgivenGX.Pred[sample1] <- stats::predict(DgivenGX.Model.sample2,
    newdata = pred_data[sample1,], type="prob")[,2]

results <- cdgd0_manual(Y=Y,D=D,G=G,
                       YgivenGX.Pred_D0=YgivenGX.Pred_D0,
                       YgivenGX.Pred_D1=YgivenGX.Pred_D1,
                       DgivenGX.Pred=DgivenGX.Pred,
                       data=data)

results

Perform unconditional decomposition via machine learning

Description

Perform unconditional decomposition via machine learning

Usage

cdgd0_ml(Y, D, G, X, data, algorithm, alpha = 0.05, trim = 0)
cdgd0_ml(Y, D, G, X, data, algorithm, alpha = 0.05, trim = 0)

Arguments

`Y`	Outcome. The name of a numeric variable (can be binary and take values of 0 and 1).
`D`	Treatment status. The name of a binary numeric variable taking values of 0 and 1.
`G`	Advantaged group membership. The name of a binary numeric variable taking values of 0 and 1.
`X`	Confounders. A vector of variables names.
`data`	A data frame.
`algorithm`	The ML algorithm for modelling. "nnet" for neural network, "ranger" for random forests, "gbm" for generalized boosted models.
`alpha`	1-alpha confidence interval.
`trim`	Threshold for trimming the propensity score. When trim=a, individuals with propensity scores lower than a or higher than 1-a will be dropped.

Value

A list of estimates.

Examples

# This example will take a minute to run.

data(exp_data)

set.seed(1)

results <- cdgd0_ml(
Y="outcome",
D="treatment",
G="group_a",
X=c("Q","confounder"),
data=exp_data,
algorithm="gbm")

results[[1]]
# This example will take a minute to run.

data(exp_data)

set.seed(1)

results <- cdgd0_ml(
Y="outcome",
D="treatment",
G="group_a",
X=c("Q","confounder"),
data=exp_data,
algorithm="gbm")

results[[1]]

Perform unconditional decomposition via parametric models

Description

Perform unconditional decomposition via parametric models

Usage

cdgd0_pa(Y, D, G, X, data, alpha = 0.05, trim = 0)
cdgd0_pa(Y, D, G, X, data, alpha = 0.05, trim = 0)

Arguments

`Y`	Outcome. The name of a numeric variable (can be binary and take values of 0 and 1).
`D`	Treatment status. The name of a binary numeric variable taking values of 0 and 1.
`G`	Advantaged group membership. The name of a binary numeric variable taking values of 0 and 1.
`X`	Confounders. A vector of variable names.
`data`	A data frame.
`alpha`	1-alpha confidence interval.
`trim`	Threshold for trimming the propensity score. When trim=a, individuals with propensity scores lower than a or higher than 1-a will be dropped.

Value

A list of estimates.

Examples

data(exp_data)

results <- cdgd0_pa(
Y="outcome",
D="treatment",
G="group_a",
X=c("Q","confounder"),
data=exp_data)

results[[1]]
data(exp_data)

results <- cdgd0_pa(
Y="outcome",
D="treatment",
G="group_a",
X=c("Q","confounder"),
data=exp_data)

results[[1]]

Perform conditional decomposition with nuisance functions estimated beforehand

Description

This function gives user full control over the estimation of the nuisance functions. For the unconditional decomposition, ten nuisance functions need to be estimated. The nuisance functions should be estimated using cross-fitting if Donsker class is not assumed.

Usage

cdgd1_manual(
  Y,
  D,
  G,
  YgivenGXQ.Pred_D0,
  YgivenGXQ.Pred_D1,
  DgivenGXQ.Pred,
  Y0givenQ.Pred_G0,
  Y0givenQ.Pred_G1,
  Y1givenQ.Pred_G0,
  Y1givenQ.Pred_G1,
  DgivenQ.Pred_G0,
  DgivenQ.Pred_G1,
  GgivenQ.Pred,
  data,
  alpha = 0.05
)
cdgd1_manual(
  Y,
  D,
  G,
  YgivenGXQ.Pred_D0,
  YgivenGXQ.Pred_D1,
  DgivenGXQ.Pred,
  Y0givenQ.Pred_G0,
  Y0givenQ.Pred_G1,
  Y1givenQ.Pred_G0,
  Y1givenQ.Pred_G1,
  DgivenQ.Pred_G0,
  DgivenQ.Pred_G1,
  GgivenQ.Pred,
  data,
  alpha = 0.05
)

Arguments

`Y`	Outcome. The name of a numeric variable.
`D`	Treatment status. The name of a binary numeric variable taking values of 0 and 1.
`G`	Advantaged group membership. The name of a binary numeric variable taking values of 0 and 1.
`YgivenGXQ.Pred_D0`	A numeric vector of predicted Y values given X, G, and D=0. Vector length=nrow(data).
`YgivenGXQ.Pred_D1`	A numeric vector of predicted Y values given X, G, and D=1. Vector length=nrow(data).
`DgivenGXQ.Pred`	A numeric vector of predicted D values given X and G. Vector length=nrow(data).
`Y0givenQ.Pred_G0`	A numeric vector of predicted Y(0) values given Q and G=0. Vector length=nrow(data).
`Y0givenQ.Pred_G1`	A numeric vector of predicted Y(0) values given Q and G=0. Vector length=nrow(data).
`Y1givenQ.Pred_G0`	A numeric vector of predicted Y(1) values given Q and G=0. Vector length=nrow(data).
`Y1givenQ.Pred_G1`	A numeric vector of predicted Y(1) values given Q and G=1. Vector length=nrow(data).
`DgivenQ.Pred_G0`	A numeric vector of predicted D values given Q and G=0. Vector length=nrow(data).
`DgivenQ.Pred_G1`	A numeric vector of predicted D values given Q and G=0. Vector length=nrow(data).
`GgivenQ.Pred`	A numeric vector of predicted G values given Q. Vector length=nrow(data).
`data`	A data frame.
`alpha`	1-alpha confidence interval.

Value

A dataframe of estimates.

Examples

# This example will take a minute to run.

data(exp_data)

Y="outcome"
D="treatment"
G="group_a"
X="confounder"
Q="Q"
data=exp_data

set.seed(1)

### estimate the nuisance functions with cross-fitting
sample1 <- sample(nrow(data), floor(nrow(data)/2), replace=FALSE)
sample2 <- setdiff(1:nrow(data), sample1)

### outcome regression model

message <- utils::capture.output( YgivenDGXQ.Model.sample1 <-
  caret::train(stats::as.formula(paste(Y, paste(D,G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
               data=data[sample1,], method="ranger",
               trControl=caret::trainControl(method="cv"),
               tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )
message <- utils::capture.output( YgivenDGXQ.Model.sample2 <-
  caret::train(stats::as.formula(paste(Y, paste(D,G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
               data=data[sample2,], method="ranger",
               trControl=caret::trainControl(method="cv"),
               tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )

### propensity score model
data[,D] <- as.factor(data[,D])
levels(data[,D]) <- c("D0","D1")  # necessary for caret implementation of ranger

message <- utils::capture.output( DgivenGXQ.Model.sample1 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
                 data=data[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )
message <- utils::capture.output( DgivenGXQ.Model.sample2 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
                 data=data[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )

data[,D] <- as.numeric(data[,D])-1

### cross-fitted predictions
YgivenGXQ.Pred_D0 <- YgivenGXQ.Pred_D1 <- DgivenGXQ.Pred <- rep(NA, nrow(data))

pred_data <- data
pred_data[,D] <- 0
YgivenGXQ.Pred_D0[sample2] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample2,])
YgivenGXQ.Pred_D0[sample1] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample1,])

pred_data <- data
pred_data[,D] <- 1
YgivenGXQ.Pred_D1[sample2] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample2,])
YgivenGXQ.Pred_D1[sample1] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample1,])

pred_data <- data
DgivenGXQ.Pred[sample2] <- stats::predict(DgivenGXQ.Model.sample1,
    newdata = pred_data[sample2,], type="prob")[,2]
DgivenGXQ.Pred[sample1] <- stats::predict(DgivenGXQ.Model.sample2,
    newdata = pred_data[sample1,], type="prob")[,2]

### Estimate E(Y_d | Q,g)
YgivenGXQ.Pred_D1_ncf <- YgivenGXQ.Pred_D0_ncf <- DgivenGXQ.Pred_ncf <- rep(NA, nrow(data))
# ncf stands for non-cross-fitted

pred_data <- data
pred_data[,D] <- 1
YgivenGXQ.Pred_D1_ncf[sample1] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample1,])
YgivenGXQ.Pred_D1_ncf[sample2] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample2,])

pred_data <- data
pred_data[,D] <- 0
YgivenGXQ.Pred_D0_ncf[sample1] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample1,])
YgivenGXQ.Pred_D0_ncf[sample2] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample2,])

DgivenGXQ.Pred_ncf[sample1] <- stats::predict(DgivenGXQ.Model.sample1,
    newdata = pred_data[sample1,], type="prob")[,2]
DgivenGXQ.Pred_ncf[sample2] <- stats::predict(DgivenGXQ.Model.sample2,
    newdata = pred_data[sample2,], type="prob")[,2]

# IPOs for modelling E(Y_d | Q,g)
IPO_D0_ncf <- (1-data[,D])/(1-DgivenGXQ.Pred_ncf)/mean((1-data[,D])/(1-DgivenGXQ.Pred_ncf))*
    (data[,Y]-YgivenGXQ.Pred_D0_ncf) + YgivenGXQ.Pred_D0_ncf
IPO_D1_ncf <- data[,D]/DgivenGXQ.Pred_ncf/mean(data[,D]/DgivenGXQ.Pred_ncf)*
    (data[,Y]-YgivenGXQ.Pred_D1_ncf) + YgivenGXQ.Pred_D1_ncf

data_temp <- data[,c(G,Q)]
data_temp$IPO_D0_ncf <- IPO_D0_ncf
data_temp$IPO_D1_ncf <- IPO_D1_ncf

message <- utils::capture.output( Y0givenGQ.Model.sample1 <-
    caret::train(stats::as.formula(paste("IPO_D0_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )
message <- utils::capture.output( Y0givenGQ.Model.sample2 <-
    caret::train(stats::as.formula(paste("IPO_D0_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )
message <- utils::capture.output( Y1givenGQ.Model.sample1 <-
    caret::train(stats::as.formula(paste("IPO_D1_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )
message <- utils::capture.output( Y1givenGQ.Model.sample2 <-
    caret::train(stats::as.formula(paste("IPO_D1_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )

Y0givenQ.Pred_G0 <- Y0givenQ.Pred_G1 <- Y1givenQ.Pred_G0 <- Y1givenQ.Pred_G1 <- rep(NA, nrow(data))

pred_data <- data
pred_data[,G] <- 1
# cross-fitting is used
Y0givenQ.Pred_G1[sample2] <- stats::predict(Y0givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y0givenQ.Pred_G1[sample1] <- stats::predict(Y0givenGQ.Model.sample2, newdata = pred_data[sample1,])
Y1givenQ.Pred_G1[sample2] <- stats::predict(Y1givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y1givenQ.Pred_G1[sample1] <- stats::predict(Y1givenGQ.Model.sample2, newdata = pred_data[sample1,])

pred_data <- data
pred_data[,G] <- 0
# cross-fitting is used
Y0givenQ.Pred_G0[sample2] <- stats::predict(Y0givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y0givenQ.Pred_G0[sample1] <- stats::predict(Y0givenGQ.Model.sample2, newdata = pred_data[sample1,])
Y1givenQ.Pred_G0[sample2] <- stats::predict(Y1givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y1givenQ.Pred_G0[sample1] <- stats::predict(Y1givenGQ.Model.sample2, newdata = pred_data[sample1,])

### Estimate E(D | Q,g')
data[,D] <- as.factor(data[,D])
levels(data[,D]) <- c("D0","D1")  # necessary for caret implementation of ranger

message <- utils::capture.output( DgivenGQ.Model.sample1 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,sep="+"), sep="~")),
                 data=data[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )
message <- utils::capture.output( DgivenGQ.Model.sample2 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,sep="+"), sep="~")),
                 data=data[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )

data[,D] <- as.numeric(data[,D])-1

DgivenQ.Pred_G0 <- DgivenQ.Pred_G1 <- rep(NA, nrow(data))

pred_data <- data
pred_data[,G] <- 0
DgivenQ.Pred_G0[sample2] <- stats::predict(DgivenGQ.Model.sample1,
    newdata = pred_data[sample2,], type="prob")[,2]
DgivenQ.Pred_G0[sample1] <- stats::predict(DgivenGQ.Model.sample2,
    newdata = pred_data[sample1,], type="prob")[,2]

pred_data <- data
pred_data[,G] <- 1
DgivenQ.Pred_G1[sample2] <- stats::predict(DgivenGQ.Model.sample1,
   newdata = pred_data[sample2,], type="prob")[,2]
DgivenQ.Pred_G1[sample1] <- stats::predict(DgivenGQ.Model.sample2,
   newdata = pred_data[sample1,], type="prob")[,2]

### Estimate p_g(Q)=Pr(G=g | Q)
data[,G] <- as.factor(data[,G])
levels(data[,G]) <- c("G0","G1")  # necessary for caret implementation of ranger

message <- utils::capture.output( GgivenQ.Model.sample1 <-
    caret::train(stats::as.formula(paste(G, paste(Q,sep="+"), sep="~")),
                 data=data[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )
message <- utils::capture.output( GgivenQ.Model.sample2 <-
    caret::train(stats::as.formula(paste(G, paste(Q,sep="+"), sep="~")),
                 data=data[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )

data[,G] <- as.numeric(data[,G])-1

GgivenQ.Pred <- rep(NA, nrow(data))
GgivenQ.Pred[sample2] <- stats::predict(GgivenQ.Model.sample1,
    newdata = data[sample2,], type="prob")[,2]
GgivenQ.Pred[sample1] <- stats::predict(GgivenQ.Model.sample2,
    newdata = data[sample1,], type="prob")[,2]


results <- cdgd1_manual(Y=Y,D=D,G=G,
                        YgivenGXQ.Pred_D0=YgivenGXQ.Pred_D0,
                        YgivenGXQ.Pred_D1=YgivenGXQ.Pred_D1,
                        DgivenGXQ.Pred=DgivenGXQ.Pred,
                        Y0givenQ.Pred_G0=Y0givenQ.Pred_G0,
                        Y0givenQ.Pred_G1=Y0givenQ.Pred_G1,
                        Y1givenQ.Pred_G0=Y1givenQ.Pred_G0,
                        Y1givenQ.Pred_G1=Y1givenQ.Pred_G1,
                        DgivenQ.Pred_G0=DgivenQ.Pred_G0,
                        DgivenQ.Pred_G1=DgivenQ.Pred_G1,
                        GgivenQ.Pred=GgivenQ.Pred,
                        data,alpha=0.05)

results
# This example will take a minute to run.

data(exp_data)

Y="outcome"
D="treatment"
G="group_a"
X="confounder"
Q="Q"
data=exp_data

set.seed(1)

### estimate the nuisance functions with cross-fitting
sample1 <- sample(nrow(data), floor(nrow(data)/2), replace=FALSE)
sample2 <- setdiff(1:nrow(data), sample1)

### outcome regression model

message <- utils::capture.output( YgivenDGXQ.Model.sample1 <-
  caret::train(stats::as.formula(paste(Y, paste(D,G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
               data=data[sample1,], method="ranger",
               trControl=caret::trainControl(method="cv"),
               tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )
message <- utils::capture.output( YgivenDGXQ.Model.sample2 <-
  caret::train(stats::as.formula(paste(Y, paste(D,G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
               data=data[sample2,], method="ranger",
               trControl=caret::trainControl(method="cv"),
               tuneGrid=expand.grid(mtry=c(2,4),splitrule=c("variance"),min.node.size=c(50,100))) )

### propensity score model
data[,D] <- as.factor(data[,D])
levels(data[,D]) <- c("D0","D1")  # necessary for caret implementation of ranger

message <- utils::capture.output( DgivenGXQ.Model.sample1 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
                 data=data[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )
message <- utils::capture.output( DgivenGXQ.Model.sample2 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,paste(X,collapse="+"),sep="+"), sep="~")),
                 data=data[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=c(1,2),splitrule=c("gini"),min.node.size=c(50,100))) )

data[,D] <- as.numeric(data[,D])-1

### cross-fitted predictions
YgivenGXQ.Pred_D0 <- YgivenGXQ.Pred_D1 <- DgivenGXQ.Pred <- rep(NA, nrow(data))

pred_data <- data
pred_data[,D] <- 0
YgivenGXQ.Pred_D0[sample2] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample2,])
YgivenGXQ.Pred_D0[sample1] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample1,])

pred_data <- data
pred_data[,D] <- 1
YgivenGXQ.Pred_D1[sample2] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample2,])
YgivenGXQ.Pred_D1[sample1] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample1,])

pred_data <- data
DgivenGXQ.Pred[sample2] <- stats::predict(DgivenGXQ.Model.sample1,
    newdata = pred_data[sample2,], type="prob")[,2]
DgivenGXQ.Pred[sample1] <- stats::predict(DgivenGXQ.Model.sample2,
    newdata = pred_data[sample1,], type="prob")[,2]

### Estimate E(Y_d | Q,g)
YgivenGXQ.Pred_D1_ncf <- YgivenGXQ.Pred_D0_ncf <- DgivenGXQ.Pred_ncf <- rep(NA, nrow(data))
# ncf stands for non-cross-fitted

pred_data <- data
pred_data[,D] <- 1
YgivenGXQ.Pred_D1_ncf[sample1] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample1,])
YgivenGXQ.Pred_D1_ncf[sample2] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample2,])

pred_data <- data
pred_data[,D] <- 0
YgivenGXQ.Pred_D0_ncf[sample1] <- stats::predict(YgivenDGXQ.Model.sample1,
    newdata = pred_data[sample1,])
YgivenGXQ.Pred_D0_ncf[sample2] <- stats::predict(YgivenDGXQ.Model.sample2,
    newdata = pred_data[sample2,])

DgivenGXQ.Pred_ncf[sample1] <- stats::predict(DgivenGXQ.Model.sample1,
    newdata = pred_data[sample1,], type="prob")[,2]
DgivenGXQ.Pred_ncf[sample2] <- stats::predict(DgivenGXQ.Model.sample2,
    newdata = pred_data[sample2,], type="prob")[,2]

# IPOs for modelling E(Y_d | Q,g)
IPO_D0_ncf <- (1-data[,D])/(1-DgivenGXQ.Pred_ncf)/mean((1-data[,D])/(1-DgivenGXQ.Pred_ncf))*
    (data[,Y]-YgivenGXQ.Pred_D0_ncf) + YgivenGXQ.Pred_D0_ncf
IPO_D1_ncf <- data[,D]/DgivenGXQ.Pred_ncf/mean(data[,D]/DgivenGXQ.Pred_ncf)*
    (data[,Y]-YgivenGXQ.Pred_D1_ncf) + YgivenGXQ.Pred_D1_ncf

data_temp <- data[,c(G,Q)]
data_temp$IPO_D0_ncf <- IPO_D0_ncf
data_temp$IPO_D1_ncf <- IPO_D1_ncf

message <- utils::capture.output( Y0givenGQ.Model.sample1 <-
    caret::train(stats::as.formula(paste("IPO_D0_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )
message <- utils::capture.output( Y0givenGQ.Model.sample2 <-
    caret::train(stats::as.formula(paste("IPO_D0_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )
message <- utils::capture.output( Y1givenGQ.Model.sample1 <-
    caret::train(stats::as.formula(paste("IPO_D1_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )
message <- utils::capture.output( Y1givenGQ.Model.sample2 <-
    caret::train(stats::as.formula(paste("IPO_D1_ncf", paste(G,Q,sep="+"), sep="~")),
                 data=data_temp[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv"),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("variance"),min.node.size=c(25,50))) )

Y0givenQ.Pred_G0 <- Y0givenQ.Pred_G1 <- Y1givenQ.Pred_G0 <- Y1givenQ.Pred_G1 <- rep(NA, nrow(data))

pred_data <- data
pred_data[,G] <- 1
# cross-fitting is used
Y0givenQ.Pred_G1[sample2] <- stats::predict(Y0givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y0givenQ.Pred_G1[sample1] <- stats::predict(Y0givenGQ.Model.sample2, newdata = pred_data[sample1,])
Y1givenQ.Pred_G1[sample2] <- stats::predict(Y1givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y1givenQ.Pred_G1[sample1] <- stats::predict(Y1givenGQ.Model.sample2, newdata = pred_data[sample1,])

pred_data <- data
pred_data[,G] <- 0
# cross-fitting is used
Y0givenQ.Pred_G0[sample2] <- stats::predict(Y0givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y0givenQ.Pred_G0[sample1] <- stats::predict(Y0givenGQ.Model.sample2, newdata = pred_data[sample1,])
Y1givenQ.Pred_G0[sample2] <- stats::predict(Y1givenGQ.Model.sample1, newdata = pred_data[sample2,])
Y1givenQ.Pred_G0[sample1] <- stats::predict(Y1givenGQ.Model.sample2, newdata = pred_data[sample1,])

### Estimate E(D | Q,g')
data[,D] <- as.factor(data[,D])
levels(data[,D]) <- c("D0","D1")  # necessary for caret implementation of ranger

message <- utils::capture.output( DgivenGQ.Model.sample1 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,sep="+"), sep="~")),
                 data=data[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )
message <- utils::capture.output( DgivenGQ.Model.sample2 <-
    caret::train(stats::as.formula(paste(D, paste(G,Q,sep="+"), sep="~")),
                 data=data[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )

data[,D] <- as.numeric(data[,D])-1

DgivenQ.Pred_G0 <- DgivenQ.Pred_G1 <- rep(NA, nrow(data))

pred_data <- data
pred_data[,G] <- 0
DgivenQ.Pred_G0[sample2] <- stats::predict(DgivenGQ.Model.sample1,
    newdata = pred_data[sample2,], type="prob")[,2]
DgivenQ.Pred_G0[sample1] <- stats::predict(DgivenGQ.Model.sample2,
    newdata = pred_data[sample1,], type="prob")[,2]

pred_data <- data
pred_data[,G] <- 1
DgivenQ.Pred_G1[sample2] <- stats::predict(DgivenGQ.Model.sample1,
   newdata = pred_data[sample2,], type="prob")[,2]
DgivenQ.Pred_G1[sample1] <- stats::predict(DgivenGQ.Model.sample2,
   newdata = pred_data[sample1,], type="prob")[,2]

### Estimate p_g(Q)=Pr(G=g | Q)
data[,G] <- as.factor(data[,G])
levels(data[,G]) <- c("G0","G1")  # necessary for caret implementation of ranger

message <- utils::capture.output( GgivenQ.Model.sample1 <-
    caret::train(stats::as.formula(paste(G, paste(Q,sep="+"), sep="~")),
                 data=data[sample1,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )
message <- utils::capture.output( GgivenQ.Model.sample2 <-
    caret::train(stats::as.formula(paste(G, paste(Q,sep="+"), sep="~")),
                 data=data[sample2,], method="ranger",
                 trControl=caret::trainControl(method="cv", classProbs=TRUE),
                 tuneGrid=expand.grid(mtry=1,splitrule=c("gini"),min.node.size=c(25,50))) )

data[,G] <- as.numeric(data[,G])-1

GgivenQ.Pred <- rep(NA, nrow(data))
GgivenQ.Pred[sample2] <- stats::predict(GgivenQ.Model.sample1,
    newdata = data[sample2,], type="prob")[,2]
GgivenQ.Pred[sample1] <- stats::predict(GgivenQ.Model.sample2,
    newdata = data[sample1,], type="prob")[,2]


results <- cdgd1_manual(Y=Y,D=D,G=G,
                        YgivenGXQ.Pred_D0=YgivenGXQ.Pred_D0,
                        YgivenGXQ.Pred_D1=YgivenGXQ.Pred_D1,
                        DgivenGXQ.Pred=DgivenGXQ.Pred,
                        Y0givenQ.Pred_G0=Y0givenQ.Pred_G0,
                        Y0givenQ.Pred_G1=Y0givenQ.Pred_G1,
                        Y1givenQ.Pred_G0=Y1givenQ.Pred_G0,
                        Y1givenQ.Pred_G1=Y1givenQ.Pred_G1,
                        DgivenQ.Pred_G0=DgivenQ.Pred_G0,
                        DgivenQ.Pred_G1=DgivenQ.Pred_G1,
                        GgivenQ.Pred=GgivenQ.Pred,
                        data,alpha=0.05)

results

Perform conditional decomposition via machine learning

Description

Perform conditional decomposition via machine learning

Usage

cdgd1_ml(Y, D, G, X, Q, data, algorithm, alpha = 0.05, trim1 = 0, trim2 = 0)
cdgd1_ml(Y, D, G, X, Q, data, algorithm, alpha = 0.05, trim1 = 0, trim2 = 0)

Arguments

`Y`	Outcome. The name of a numeric variable (can be binary and take values of 0 and 1).
`D`	Treatment status. The name of a binary numeric variable taking values of 0 and 1.
`G`	Advantaged group membership. The name of a binary numeric variable taking values of 0 and 1.
`X`	Confounders. A vector of variables names.
`Q`	Conditional set. A vector of names of numeric variables.
`data`	A data frame.
`algorithm`	The ML algorithm for modelling. "nnet" for neural network, "ranger" for random forests, "gbm" for generalized boosted models.
`alpha`	1-alpha confidence interval.
`trim1`	Threshold for trimming the propensity score. When trim1=a, individuals with propensity scores lower than a or higher than 1-a will be dropped.
`trim2`	Threshold for trimming the G given Q predictions. When trim2=a, individuals with G given Q predictions lower than a or higher than 1-a will be dropped.

Value

A dataframe of estimates.

Examples

# This example will take a minute to run.

data(exp_data)

set.seed(1)

results <- cdgd1_ml(
Y="outcome",
D="treatment",
G="group_a",
X="confounder",
Q="Q",
data=exp_data,
algorithm="gbm")

results
# This example will take a minute to run.

data(exp_data)

set.seed(1)

results <- cdgd1_ml(
Y="outcome",
D="treatment",
G="group_a",
X="confounder",
Q="Q",
data=exp_data,
algorithm="gbm")

results

Perform conditional decomposition via parametric models

Description

Perform conditional decomposition via parametric models

Usage

cdgd1_pa(Y, D, G, X, Q, data, alpha = 0.05, trim1 = 0, trim2 = 0)
cdgd1_pa(Y, D, G, X, Q, data, alpha = 0.05, trim1 = 0, trim2 = 0)

Arguments

`Y`	Outcome. The name of a numeric variable (can be binary and take values of 0 and 1).
`D`	Treatment status. The name of a binary numeric variable taking values of 0 and 1.
`G`	Advantaged group membership. The name of a binary numeric variable taking values of 0 and 1.
`X`	Confounders. A vector of variable names.
`Q`	Conditional set. A vector of variable names.
`data`	A data frame.
`alpha`	1-alpha confidence interval.
`trim1`	Threshold for trimming the propensity score. When trim1=a, individuals with propensity scores lower than a or higher than 1-a will be dropped.
`trim2`	Threshold for trimming the G given Q predictions. When trim2=a, individuals with G given Q predictions lower than a or higher than 1-a will be dropped.

Value

A dataframe of estimates.

Examples

data(exp_data)

results <- cdgd1_pa(
Y="outcome",
D="treatment",
G="group_a",
X="confounder",
Q="Q",
data=exp_data)

results
data(exp_data)

results <- cdgd1_pa(
Y="outcome",
D="treatment",
G="group_a",
X="confounder",
Q="Q",
data=exp_data)

results

Simulated example data

Description

Simulated example data

Usage

data(exp_data)
data(exp_data)

Format

An object of class data.frame with 1000 rows and 5 columns.

Package 'cdgd'

Help Index

Perform unconditional decomposition with nuisance functions estimated beforehand

Description

Usage

Arguments

Value

Examples

Perform unconditional decomposition via machine learning

Description

Usage

Arguments

Value

Examples

Perform unconditional decomposition via parametric models

Description

Usage

Arguments

Value

Examples

Perform conditional decomposition with nuisance functions estimated beforehand

Description

Usage

Arguments

Value

Examples

Perform conditional decomposition via machine learning

Description

Usage

Arguments

Value

Examples

Perform conditional decomposition via parametric models

Description

Usage

Arguments

Value

Examples

Simulated example data

Description

Usage

Format