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,
...
)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.modelis 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
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)
#> Estimate Std.Err 2.5% 97.5% P-value
#> E[y(1)] 1.8508 0.04186 1.7687 1.9328 0.000e+00
#> E[y(0)] 0.8279 0.02054 0.7876 0.8681 0.000e+00
#> ───────────
#> (Intercept) 1.0229 0.04768 0.9295 1.1164 4.287e-102
## CATE
cate(cate.model=~1+w2,
response.model=y~a*(w1+w2),
propensity.model=a~w1+w2,
data=d)
#> Estimate Std.Err 2.5% 97.5% P-value
#> E[y(1)] 1.8508 0.04186 1.7687 1.9328 0.000e+00
#> E[y(0)] 0.8279 0.02054 0.7876 0.8681 0.000e+00
#> ───────────
#> (Intercept) 0.9999 0.04654 0.9087 1.0911 2.146e-102
#> w2 0.9879 0.04304 0.9035 1.0723 1.451e-116
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)
#> Error: object 'mod1' not found
cate(cate.model=~1,
response.model=s1,
propensity.model=learner_glm(a~w1+w2, family=binomial),
data=d,
stratify=TRUE)
#> Error: object 's1' not found
# \dontrun{}