carts (version 0.1.0)

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

Description

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). The implementation is a one-step estimator as described by Van Lancker et al (2024).

Usage

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

Value

function

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.

Author

Klaus Kähler Holst

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.

References

Van Lancker et al (2024) Automated, efficient and model-free inference for randomized clinical trials via data-driven covariate adjustment, arXiv:2404.11150

See Also

Trial est_glm

Examples

# \donttest{
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)

# 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))


# 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))

# 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)

dd_factor <- dd
# 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))
estimator(dd_factor) # E[Y(1)] - E[Y(0)]

dd_factor$a <- factor(dd_factor$a, levels = c(1, 0))
estimator(dd_factor) # E[Y(1)] - E[Y(0)]
# }