targeted (version 0.6)

cate: Conditional Average Treatment Effect estimation

Description

Conditional Average Treatment Effect estimation with cross-fitting.

Usage

cate(
  response.model,
  propensity.model,
  cate.model = ~1,
  calibration.model = NULL,
  data,
  contrast,
  nfolds = 1,
  rep = 1,
  silent = FALSE,
  stratify = FALSE,
  mc.cores = NULL,
  rep.type = c("nuisance", "average"),
  var.type = "IC",
  second.order = TRUE,
  response_model = deprecated,
  cate_model = deprecated,
  propensity_model = deprecated,
  treatment = deprecated,
  ...
)

Value

cate.targeted object

Arguments

response.model

formula or learner object (formula => learner_glm)

propensity.model

formula or learner object (formula => learner_glm)

cate.model

formula specifying regression design for conditional average treatment effects

calibration.model

linear calibration model. Specify covariates in addition to predicted potential outcomes to include in the calibration.

data

data.frame

contrast

treatment contrast (default 1 vs 0)

nfolds

number of folds

rep

number of replications of cross-fitting procedure

silent

suppress all messages and progressbars

stratify

if TRUE the response.model will be stratified by treatment

mc.cores

(optional) number of cores. parallel::mcmapply used instead of future

rep.type

repeated cross-fitting applied by averaging nuisance models (rep.type="nuisance") or by average estimates from each replication (rep.type="average").

var.type

when equal to "IC" the asymptotic variance is derived from the influence function. Otherwise, based on expressions in Bannick et al. (2025) valid under different covariate-adaptive randomization schemes (only available for ATE and when calibration.model is also specified)

second.order

add seconder order term to IF to handle misspecification of outcome models

response_model

Deprecated. Use response.model instead.

cate_model

Deprecated. Use cate.model instead.

propensity_model

Deprecated. Use propensity.model instead.

treatment

Deprecated. Use cate.model instead.

...

additional arguments to future.apply::future_mapply

Author

Klaus Kähler Holst, Andreas Nordland

Details

We have observed data \((Y,A,W)\) where \(Y\) is the response variable, \(A\) the binary treatment, and \(W\) covariates. We further let \(V\) be a subset of the covariates. Define the conditional potential mean outcome $$\psi_{a}(P)(V) = E_{P}[E_{P}(Y\mid A=a, W)|V]$$ and let \(m(V; \beta)\) denote a parametric working model, then the target parameter is the mean-squared error $$\beta(P) = \operatorname{argmin}_{\beta} E_{P}[\{\Psi_{1}(P)(V)-\Psi_{0}(P)(V)\} - m(V; \beta)]^{2}$$

References

Mark J. van der Laan (2006) Statistical Inference for Variable Importance, The International Journal of Biostatistics.

Examples

sim1 <- function(n=1000, ...) {
  w1 <- rnorm(n)
  w2 <- rnorm(n)
  a <- rbinom(n, 1, plogis(-1 + w1))
  y <- cos(w1) + w2*a + 0.2*w2^2 + a + rnorm(n)
  data.frame(y, a, w1, w2)
}

d <- sim1(5000)
## ATE
cate(cate.model=~1,
     response.model=y~a*(w1+w2),
     propensity.model=a~w1+w2,
     data=d)
## CATE
cate(cate.model=~1+w2,
     response.model=y~a*(w1+w2),
     propensity.model=a~w1+w2,
     data=d)

if (FALSE)  ## superlearner example
mod1 <- list(
   glm = learner_glm(y~w1+w2),
   gam = learner_gam(y~s(w1) + s(w2))
)
s1 <- learner_sl(mod1, nfolds=5)
cate(cate.model=~1,
     response.model=s1,
     propensity.model=learner_glm(a~w1+w2, family=binomial),
     data=d,
     stratify=TRUE)