ife

S7 class for influence function estimands with forward mode automatic differentiation for variance estimation.

Installation

You can install the development version of ife from GitHub with:

# install.packages("pak")
pak::pak("nt-williams/ife")

Example

Consider estimating the population mean outcome under treatment $E[E[Y \mid A=1,W]]$ and control $E[E[Y \mid A=0,W]]$ using augmented inverse probability weighting (AIPW).

library(ife)

# Generate simulated data
n <- 500
w <- runif(n)                                   # confounder
a <- rbinom(n, 1, 0.5)                          # treatment (randomized)
y <- rbinom(n, 1, plogis(-0.75 + a + w))        # outcome

# Create data-frames for counterfactual predictions
foo <- data.frame(w, a, y)
foo1 <- foo0 <- foo
foo1$a <- 1  # everyone treated
foo0$a <- 0  # everyone untreated

# Fit outcome model and generate predictions
pi <- 0.5  # known propensity score
m <- glm(y ~ a + w, data = foo, family = binomial())
Qa <- predict(m, type = "response")                    # predicted outcomes
Q1 <- predict(m, newdata = foo1, type = "response")    # under treatment
Q0 <- predict(m, newdata = foo0, type = "response")    # under control

# Calculate un-centered influence functions
if1 <- a / pi * (y - Qa) + Q1              
if0 <- (1 - a) / (1 - pi) * (y - Qa) + Q0  

Create ife objects for these estimates using influence_func_estimate() or ife():

ife1 <- influence_func_estimate(mean(if1), if1)
ife0 <- ife(mean(if0), if0)

ife then allows you to estimate contrasts between estimates, with variance estimated using automatic differentiation. The additive effect (risk difference) can be calculated as:

ife1 - ife0
#>       Estimate: 0.254
#>     Std. error: 0.042
#> 95% Conf. int.: 0.172, 0.336

The multiplicative effect (risk ratio) can be estimated as:

ife1 / ife0
#>       Estimate: 1.583
#>     Std. error: 0.129
#> 95% Conf. int.: 1.33, 1.837

For the risk ratio, which is strictly positive, you can estimate the effect on the log scale and exponentiate the confidence intervals to ensure the lower bound is always positive:

exp(log(ife1 / ife0)@conf_int)
#> [1] 1.35 1.86