targeted (version 0.5)

alean: Assumption Lean inference for generalized linear model parameters

Description

Assumption lean inference via cross-fitting (Double ML). See <doi:10.1111/rssb.12504

Usage

alean(
  response_model,
  exposure_model,
  data,
  link = "identity",
  g_model,
  nfolds = 1,
  silent = FALSE,
  mc.cores,
  ...
)

Value

alean.targeted object

Arguments

response_model

formula or ml_model object (formula => glm)

exposure_model

model for the exposure

data

data.frame

link

Link function (g)

g_model

Model for \(E[g(Y|A,W)|W]\)

nfolds

Number of folds

silent

supress all messages and progressbars

mc.cores

mc.cores Optional number of cores. parallel::mcmapply used instead of future

...

additional arguments to future.apply::future_mapply

Author

Klaus Kähler Holst

Details

Let \(Y\) be the response variable, \(A\) the exposure and \(W\) covariates. The target parameter is: $$\Psi(P) = \frac{E(Cov[A, g\{E(Y|A,W)\}\mid W])} {E\{Var(A\mid W)\}} $$

The response_model is the model for \(E(Y|A,W)\), and exposure_model is the model for \(E(A|W)\). link specifies \(g\).

Examples

sim1 <- function(n, family=gaussian(), ...) {
   m <- lvm() |>
     distribution(~ y, binomial.lvm()) |>
     regression('a', value=function(l) l) |>
     regression('y', value=function(a,l) a + l)
     if (family$family=="binomial")
        distribution(m, ~a) <- binomial.lvm()
   sim(m, n)
}

library(splines)
f <- binomial()
d <- sim1(1e4, family=f)
e <- alean(response_model=ML(y ~ a + bs(l, df=3), family=binomial),
           exposure_model=ML(a ~ bs(l, df=3), family=f),
           data=d,
           link = "logit", mc.cores=1, nfolds=1)
e

e <- alean(response_model=ML(y ~ a + l, family=binomial),
           exposure_model=ML(a ~ l),
           data=d,
           link = "logit", mc.cores=1, nfolds=1)
e