Construct evaluation scores via inverse-propensity weighting.

Source: R/get_ipw_scores.R

A simple convenience function to construct an evaluation score matrix via IPW, where entry (i, k) equals $$\frac{\mathbf{1}(W_i=k)Y_i}{P[W_i=k | X_i]} - \frac{\mathbf{1}(W_i=0)Y_i}{P[W_i=0 | X_i]},$$ where \(W_i\) is the treatment assignment of unit i and \(Y_i\) the observed outcome. \(k = 1 \ldots K\) are one of K treatment arms and k = 0 is the control arm.

get_ipw_scores(Y, W, W.hat = NULL)

Arguments

Y

The observed outcome.
W

The observed treatment assignment (must be a factor vector, where the first factor level is the control arm).
W.hat

Optional treatment propensities. If these vary by unit and arm, then this should be a matrix with the treatment assignment probability of units to arms, with columns corresponding to the levels of W. If these only vary by arm, a vector can also be supplied. If W.hat is NULL (Default), then the assignment probabilities are assumed to be uniform and the same for each arm.

Value

An \(n \cdot K\) matrix of evaluation scores.

Examples

# \donttest{
# Draw some equally likely samples from control arm A and treatment arms B and C.
n <- 5000
W <- as.factor(sample(c("A", "B", "C"), n, replace = TRUE))
Y <- 42 * (W == "B") - 42 * (W == "C") + rnorm(n)
IPW.scores <- get_ipw_scores(Y, W)
# An IPW-based estimate of E[Y(B) - Y(A)] and E[Y(C) - Y(A)]. Should be approx 42 and -42.
colMeans(IPW.scores)
#>     B - A     C - A 
#>  41.22642 -41.86194 

# Draw non-uniformly from the different arms.
W.hat <- c(0.2, 0.2, 0.6)
W <- as.factor(sample(c("A", "B", "C"), n, replace = TRUE, prob = W.hat))
Y <- 42 * (W == "B") - 42 * (W == "C") + rnorm(n)
IPW.scores <- get_ipw_scores(Y, W, W.hat = W.hat)
# Should still be approx 42 and -42.
colMeans(IPW.scores)
#>     B - A     C - A 
#>  42.87608 -41.79971 
# }