Win/Loss Ratios with Distributional Random Forests

Description

drf_win_ratio() Computes the win/loss proportion, win ratio, and net benefit by estimating nuisance parameters with machine learning methods. This estimation is performed via distributional regression, implemented using distributional random forests.

Usage

drf_win_ratio(
  base,
  treatment_name,
  outcome_names,
  win_function = "lexicographic",
  n_trees_drf = 1000,
  n_of_folds = 3,
  seed = NULL
)

Arguments

Value

A list of four elements, each of which is a list structured as follows:

The first element, win_proportion, is a list with two components: value and std, where std represents the standard deviation.

The second element, lose_proportion, is a list with two components: value and std, where std represents the standard deviation.

The third element, win_ratio, is a list containing three components: value, lower_CI, and upper_CI, with lower_CI and upper_CI representing the confidence interval bounds.

The fourth element, net_benefit, is a list containing three components: value, lower_CI, and upper_CI, with lower_CI and upper_CI representing the confidence interval bounds.

The fifth and sixth elements, win_vector and lose_vector, are numeric vectors containing the nuisance function values evaluated for each individual.

Examples

## Mixed Covariates ##

set.seed(123)
n <- 100
base <- data.frame(
  X1 = rnorm(n, mean = 5, sd = 2), # numeric covariate 1
  X2 = rnorm(n, mean = 10, sd = 3), # numeric covariate 2
  X3 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  Y1 = rnorm(n, mean = 50, sd = 10), # numeric outcome 1
  Y2 = rnorm(n, mean = 100, sd = 20), # numeric outcome 2
  arm = sample(c(0, 1), n, replace = TRUE) # binary treatment arm
)
treatment_name <- "arm"
outcome_names <- c("Y1", "Y2")
res <- drf_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names
)
## Categorical Covariates ##

set.seed(123)
n <- 100
base <- data.frame(
  X1 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  X2 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  X3 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  Y1 = rnorm(n, mean = 50, sd = 10), # numeric outcome 1
  Y2 = rnorm(n, mean = 100, sd = 20), # numeric outcome 2
  arm = sample(c(0, 1), n, replace = TRUE) # binary treatment arm
)
treatment_name <- "arm"
outcome_names <- c("Y1", "Y2")
res <- drf_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names
)

Win/Loss Ratios with Efficient Influence Functions

Description

eif_win_ratio() calculates the win/loss proportion, win ratio, and net benefit by adding a correction term to drf_win_ratio() using Efficient Influence Functions.

Usage

eif_win_ratio(
  base,
  treatment_name,
  outcome_names,
  win_function = "lexicographic",
  distance = NULL,
  n_trees_drf = 1000,
  n_of_folds = 3,
  seed = NULL,
  propensity_model = "probability_forest",
  n_trees_propensity = 1000,
  propensity_scores = NULL,
  clip_propensity = 0
)

Arguments

Value

A list of six elements, each of which is a list structured as follows:

The first element, win_proportion, is a list with two components: value and std, where std represents the standard deviation.

The second element, lose_proportion, is a list with two components: value and std, where std represents the standard deviation.

The third element, win_ratio, is a list containing three components: value, lower_CI, and upper_CI, with lower_CI and upper_CI representing the confidence interval bounds.

The fourth element, net_benefit, is a list containing three components: value, lower_CI, and upper_CI, with lower_CI and upper_CI representing the confidence interval bounds.

The fifth and sixth elements, win_vector and lose_vector, are numeric vectors containing the plug-in estimator evaluated for each individual, along with the corresponding EIF correction term.

Examples

## Input Propensity Scores ##

set.seed(123)
n <- 100
base <- data.frame(
  X1 = rnorm(n, mean = 5, sd = 2), # numeric covariate 1
  X2 = rnorm(n, mean = 10, sd = 3), # numeric covariate 2
  X3 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  Y1 = rnorm(n, mean = 50, sd = 10), # numeric outcome 1
  Y2 = rnorm(n, mean = 100, sd = 20), # numeric outcome 2
  arm = sample(c(0, 1), n, replace = TRUE) # binary treatment arm
)
treatment_name <- "arm"
outcome_names <- c("Y1", "Y2")

ps_model <- stats::glm(arm ~ X1 + X3, # only consider X1 and X3 and no cross-fitting
  family = binomial(),
  data = base
)

propensity_scores <- stats::predict(ps_model, type = "response")
res <- eif_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names,
  propensity_scores = propensity_scores
)

Win/Loss Ratios with Nearest Neighbor Matching

Description

nn_win_ratio() calculates the win/loss proportion, win ratio, and net benefit by performing nearest-neighbor matching between individuals in the treatment group and those in the control group based on a specified ground distance. After matching, the outcomes of paired individuals are compared to determine winners and losers.

Usage

nn_win_ratio(
  base,
  treatment_name,
  outcome_names,
  win_function = "lexicographic",
  distance = NULL
)

Arguments

Value

A list of six elements, each of which is a list structured as follows:

The first element, win_proportion, is a list with two components: value and std, where std represents the standard deviation.

The second element, lose_proportion, is a list with two components: value and std, where std represents the standard deviation.

The third element, win_ratio, is a list containing three components: value, lower_CI, and upper_CI, with lower_CI and upper_CI representing the confidence interval bounds.

The fourth element, net_benefit, is a list containing three components: value, lower_CI, and upper_CI, with lower_CI and upper_CI representing the confidence interval bounds.

The fifth and sixth elements, win_vector and lose_vector, are numeric vectors representing the number of wins and losses for each matched element, respectively. Their entries follow the same order as the rows in base.

Examples

## Mixed Covariates ##

set.seed(123)
n <- 100
base <- data.frame(
  X1 = rnorm(n, mean = 5, sd = 2), # numeric covariate 1
  X2 = rnorm(n, mean = 10, sd = 3), # numeric covariate 2
  X3 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  Y1 = rnorm(n, mean = 50, sd = 10), # numeric outcome 1
  Y2 = rnorm(n, mean = 100, sd = 20), # numeric outcome 2
  arm = sample(c(0, 1), n, replace = TRUE) # binary treatment arm
)
treatment_name <- "arm"
outcome_names <- c("Y1", "Y2")
res <- nn_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names
)

## Categorical Covariates ##

set.seed(123)
n <- 100
base <- data.frame(
  X1 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  X2 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  X3 = factor(sample(c("A", "B", "C"), n, replace = TRUE)), # factor covariate
  Y1 = rnorm(n, mean = 50, sd = 10), # numeric outcome 1
  Y2 = rnorm(n, mean = 100, sd = 20), # numeric outcome 2
  arm = sample(c(0, 1), n, replace = TRUE) # binary treatment arm
)
treatment_name <- "arm"
outcome_names <- c("Y1", "Y2")
res <- nn_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names
)

## Input a Distance Matrix ##

set.seed(123)
n <- 100
base <- data.frame(
  X1 = rnorm(n, mean = 5, sd = 2), # numeric covariate 1
  X2 = rnorm(n, mean = 5, sd = 2), # numeric covariate 2
  X3 = rnorm(n, mean = 5, sd = 2), # numeric covariate 3
  Y1 = rnorm(n, mean = 50, sd = 10), # numeric outcome 1
  Y2 = rnorm(n, mean = 100, sd = 20), # numeric outcome 2
  arm = sample(c(0, 1), n, replace = TRUE) # binary treatment arm
)
treatment_name <- "arm"
outcome_names <- c("Y1", "Y2")

covariate_names <- setdiff(colnames(base), c(outcome_names, treatment_name))
covariate_data <- base[, covariate_names, drop = FALSE]
distance_matrix <- as.matrix(dist(covariate_data, method = "euclidean"))

res_dist <- nn_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names,
  distance = distance_matrix
)

res <- nn_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names
)

res <- unlist(res)
res_dist <- unlist(res_dist)

print(all.equal(res, res_dist))

## Input a Win function ##

set.seed(123)
n <- 100
base <- data.frame(
  X1 = rnorm(n, mean = 5, sd = 2), # numeric covariate 1
  X2 = rnorm(n, mean = 5, sd = 2), # numeric covariate 2
  X3 = rnorm(n, mean = 5, sd = 2), # numeric covariate 3
  Y1 = rbinom(n, size = 1, prob = 0.5), # binary outcome 1 (0/1) with 50% chance
  Y2 = rbinom(n, size = 10, prob = 0.7), # counts out of 10 trials with 70% success rate
  arm = sample(c(0, 1), n, replace = TRUE) # binary treatment arm
)
treatment_name <- "arm"
outcome_names <- c("Y1", "Y2")

# Contrary to the default win function, which yields 0 for ties,
# the following win function yields 0.5.

win_function <- function(treated_row, control_row) {
  y <- as.matrix(treated_row[, outcome_names], drop = FALSE)
  z <- as.matrix(control_row[, outcome_names], drop = FALSE)
  if (all(y == z)) {
    return(0.5) # Tie, a zero in the default win function
  }
  result <- (y > z)[which.max(y != z)] * 1
  return(result)
}

res <- nn_win_ratio(
  base = base,
  treatment_name = treatment_name,
  outcome_names = outcome_names,
  win_function = win_function
)