Construct estimator for the treatment effect in RCT based on covariate adjustment

Efficient estimator of the treatment effect based on the efficient influence function. This involves a model for the conditional mean of the outcome variable given covariates (Q-model).

Usage

est_adj(
  response = "y",
  treatment = "a",
  covariates = NULL,
  offset = NULL,
  id = NULL,
  family = gaussian(),
  level = 0.95,
  treatment.effect = "absolute",
  nfolds = 1,
  ...
)

Arguments

response: (character, formula, targeted::learner) The default behavior when providing a character is to use a glm with treatment-covariate interactions for the Q-model. The covariates are specified via the covariates argument, where the default behavior is to use no covariates. When providing a formula, a glm is used for the Q-model, where the design matrix is specified by the formula. The last option is to provide a targeted::learner object that specifies the Q-model (see examples).
treatment: (character) Treatment variable. Additional care must be taken when the treatment variable is encoded as a factor (see examples).
covariates: (character) List of covariates. Only applicable when response is a character.
offset: (character) Optional offset to include in the glm model when response is a character.
id: (character) Subject id variable
family: (family) Family argument used in the glm when response is a character or formula.
level: (numeric) Confidence interval level
treatment.effect: (character, function) Default is the average treatment effect, i.e. difference in expected outcomes (x, y) -> x - y, with x = E[Y(1)] and y = E[Y(0)]). Other options are "logrr" (x, y) -> log(x / y) ) and "logor" (x, y) -> log(x / (1 - x) * y / (1 - y)). A user-defined function can alternatively be provided to target a population parameter other than the absolute difference, log rate ratio or log odds ratio (see details).
nfolds: (integer) Number of folds for estimating the conditional average treatment effect with double machine learning.
...: Additional arguments to targeted::learner_glm when response is a character or formula.

Value

function

Details

The user-defined function for treatment.effect needs to accept a single argument x of estimates of (E[Y(1)],E[Y(0)]). The estimates are a vector, where the order of E[Y(1)] and E[Y(0)] depends on the encoding of the treatment variable. E[Y(0)] is the first element when the treatment variable is drawn from a Bernoulli distribution and kept as a numeric variable or corresponds to the first level when the treatment variable is encoded as a factor.

Author

Klaus Kähler Holst

Examples

if (FALSE)  # don't run because of high computational time
trial <- Trial$new(
    covariates = function(n) data.frame(a = rbinom(n, 1, 0.5), x = rnorm(n)),
    outcome = setargs(outcome_count,
      mean = ~ 1 + a*x,
      par = c(1, -0.1, 0.5, 0.2),
      overdispersion = 2)
)
dd <- trial$simulate(1e4)
#> Error: object 'trial' not found

# equivalent specifications to estimate log(E[Y(1)] / E[Y(0)])
estimators <- list(
  est_adj(family = poisson, treatment.effect = "logrr"),
  est_glm(family = poisson),
  est_adj(response = y ~ a, family = poisson, treatment.effect = "logrr"),
  est_adj(response = targeted::learner_glm(y ~ a, family = poisson),
    treatment.effect = "logrr"
  )
)
lapply(estimators, \(est) est(dd))
#> Error in FUN(X[[i]], ...): object 'dd' not found


# now with covariates, estimating E[Y(1)] - E[Y(0)]
estimators <- list(
  est_adj(covariates = "x", family = poisson),
  est_adj(response = y ~ a * x, family = poisson),
  est_adj(response = targeted::learner_glm(y ~ a * x, family = poisson))
)
lapply(estimators, \(est) est(dd))
#> Error in FUN(X[[i]], ...): object 'dd' not found

# custom treatment.effect function
estimator <- est_adj(response = y ~ a * x, family = poisson,
  treatment.effect = \(x) x[2] - x[1] # x[1] contains the estimate of E[Y(0)]
)
estimator(dd)
#> Error: object 'dd' not found

dd_factor <- dd
#> Error: object 'dd' not found
# when using factors, the control/comparator treatment needs to be the first
# level to estimate the contrasts defined by the `treatment.level` argument
estimator <- est_adj(response = y ~ a * x, family = poisson)
dd_factor$a <- factor(dd_factor$a, levels = c(0, 1))
#> Error: object 'dd_factor' not found
estimator(dd_factor) # E[Y(1)] - E[Y(0)]
#> Error: object 'dd_factor' not found

dd_factor$a <- factor(dd_factor$a, levels = c(1, 0))
#> Error: object 'dd_factor' not found
estimator(dd_factor) # E[Y(1)] - E[Y(0)]
#> Error: object 'dd_factor' not found
 # \dontrun{}