Conditional Average Treatment Effect estimation

Conditional Average Treatment Effect estimation with cross-fitting.

cate(
  response.model,
  propensity.model,
  cate.model = ~1,
  contrast = c(1, 0),
  data,
  nfolds = 1,
  rep = 1,
  rep.type = c("nuisance", "average"),
  silent = FALSE,
  stratify = FALSE,
  mc.cores = NULL,
  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
contrast: treatment contrast (default 1 vs 0)
data: data.frame
nfolds: number of folds
rep: number of replications of cross-fitting procedure
rep.type: repeated cross-fitting applied by averaging nuisance models (rep.type="nuisance") or by average estimates from each replication (rep.type="average").
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
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

Value

cate.targeted object

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.

Author

Klaus Kähler Holst, Andreas Nordland

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{}