carts (version 0.1.0)

est_glm: Construct estimator for the treatment effect in RCT

Description

Regression-based covariate adjustment as described by Rosenblum & van der Laan (2010). Standard errors are estimated with the Hubert-White sandwich estimator, instead using the efficient influence function as described in the paper. Available parametric models are (stats::glm and MASS::glm.nb).

Usage

est_glm(
  response = "y",
  treatment = "a",
  covariates = NULL,
  offset = NULL,
  id = NULL,
  level = 0.95,
  family = gaussian(),
  target.parameter = treatment,
  ...
)

Value

function

Arguments

response

(character) Response variable

treatment

(character) Treatment variable. Additional care must be taken when the treatment variable is encoded as a factor (see examples).

covariates

(character; optional) Single or vector of covariates

offset

(character; optional) Model offset

id

(character; optional) Subject id variable

level

(numeric) Confidence interval level

family

(family or character) Exponential family that is supported by stats::glm and MASS::glm.nb

target.parameter

(character) Target parameter from model output

...

Additional arguments to lava::estimate

Author

Klaus Kähler Holst

References

Rosenblum & van der Laan (2010) Simple, Efficient Estimators of Treatment Effects in Randomized Trials Using Generalized Linear Models to Leverage Baseline Variables, The International Journal of Biostatistics

See Also

Trial

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(3e2)

# crude mean comparison between arms (default behavior; y ~ a)
est <- est_glm(family = poisson)
est(dd)

# linear adjustment with one covariate (y ~ a + x)
est <- est_glm(family = poisson, covariates = "x")
est(dd)

# return estimates of all linear coefficients (useful for debugging)
est <- est_glm(family = poisson, covariates = "x", target.parameter = NULL)
est(dd)

# comparing robust and non-robust standard errors of poisson estimator by
# passing robust argument via ... to lava::estimate
estimators <- list(
  robust = est_glm(family = poisson),
  non.robust = est_glm(family = poisson, robust = FALSE)
)
res <- do.call(rbind, lapply(estimators, \(est) est(dd)$coefmat))
rownames(res) <- names(estimators)
res

dd_factor <- dd
dd_factor$a <- as.factor(dd_factor$a)
# target parameter needs to be changed because the name of the estimated
# regression coefficient changes when encoding the treatment variable as a
# factor
est_glm(family = poisson, target.parameter = "a1")(dd_factor)
# }