Package 'drtmle' reference manual

Title:	Doubly-Robust Nonparametric Estimation and Inference
Description:	Targeted minimum loss-based estimators of counterfactual means and causal effects that are doubly-robust with respect both to consistency and asymptotic normality (Benkeser et al (2017), <doi:10.1093/biomet/asx053>; MJ van der Laan (2014), <doi:10.1515/ijb-2012-0038>).
Authors:	David Benkeser [aut, cre, cph] , Nima Hejazi [ctb]
Maintainer:	David Benkeser <[email protected]>
License:	MIT + file LICENSE
Version:	1.1.2
Built:	2024-09-04 05:07:30 UTC
Source:	https://github.com/benkeser/drtmle

Compute asymptotically linear IPTW estimators with super learning for the propensity score

Description

Compute asymptotically linear IPTW estimators with super learning for the propensity score

Usage

adaptive_iptw(W, A, Y, DeltaY = as.numeric(!is.na(Y)),
  DeltaA = as.numeric(!is.na(A)), stratify = FALSE, family = if (all(Y
  %in% c(0, 1))) {     stats::binomial() } else {     stats::gaussian() },
  a_0 = unique(A[!is.na(A)]), SL_g = NULL, glm_g = NULL, SL_Qr = NULL,
  glm_Qr = NULL, returnModels = TRUE, verbose = FALSE, maxIter = 2,
  tolIC = 1/length(Y), tolg = 0.01, cvFolds = 1, gn = NULL, ...)
adaptive_iptw(W, A, Y, DeltaY = as.numeric(!is.na(Y)),
  DeltaA = as.numeric(!is.na(A)), stratify = FALSE, family = if (all(Y
  %in% c(0, 1))) {     stats::binomial() } else {     stats::gaussian() },
  a_0 = unique(A[!is.na(A)]), SL_g = NULL, glm_g = NULL, SL_Qr = NULL,
  glm_Qr = NULL, returnModels = TRUE, verbose = FALSE, maxIter = 2,
  tolIC = 1/length(Y), tolg = 0.01, cvFolds = 1, gn = NULL, ...)

Arguments

`W`	A `data.frame` of named covariates
`A`	A `numeric` vector of binary treatment assignment (assumed to be equal to 0 or 1)
`Y`	A `numeric` numeric of continuous or binary outcomes.
`DeltaY`	A `numeric` indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	A `numeric` indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`stratify`	A `logical` indicating whether to estimate the missing outcome regression separately for observations with different levels of `A` (if `TRUE`) or to pool across `A` (if `FALSE`).
`family`	A `family` object equal to either `binomial()` or `gaussian()`, to be passed to the `SuperLearner` or `glm` function.
`a_0`	A vector of `numeric` treatment values at which to return marginal mean estimates.
`SL_g`	A vector of characters describing the super learner library to be used for each of the propensity score regressions (`DeltaA`, `A`, and `DeltaY`). To use the same library for each of the regressions (or if there is no missing data in `A` nor `Y`), a single library may be input. See `link{SuperLearner::SuperLearner}` for details on how super learner libraries can be specified.
`glm_g`	A list of characters describing the formulas to be used for each of the propensity score regressions (`DeltaA`, `A`, and `DeltaY`). To use the same formula for each of the regressions (or if there is no missing data in `A` nor `Y`), a single character formula may be input.
`SL_Qr`	A vector of characters or a list describing the Super Learner library to be used for the reduced-dimension outcome regression.
`glm_Qr`	A character describing a formula to be used in the call to `glm` for reduced-dimension outcome regression. Ignored if `SL_Qr!=NULL`. The formula should use the variable name `'gn'`.
`returnModels`	A logical indicating whether to return model fits for the propensity score and reduced-dimension regressions.
`verbose`	A logical indicating whether to print status updates.
`maxIter`	A numeric that sets the maximum number of iterations the TMLE can perform in its fluctuation step.
`tolIC`	A numeric that defines the stopping criteria based on the empirical mean of the influence function.
`tolg`	A numeric indicating the minimum value for estimates of the propensity score.
`cvFolds`	A numeric equal to the number of folds to be used in cross-validated fitting of nuisance parameters. If `cvFolds = 1`, no cross-validation is used.
`gn`	An optional list of propensity score estimates. If specified, the function will ignore the nuisance parameter estimation specified by `SL_g` and `glm_g`. The entries in the list should correspond to the propensity for the observed values of `W`, with order determined by the input to `a_0` (e.g., if `a_0 = c(0,1)` then `gn[[1]]` should be propensity of `A` = 0 and `gn[[2]]` should be propensity of `A` = 1).
`...`	Other options (not currently used).

Value

An object of class "adaptive_iptw".

iptw_tmle: A list of point estimates and covariance matrix for the IPTW estimator based on a targeted propensity score.
iptw_tmle_nuisance: A list of the final TMLE estimates of the propensity score ($gnStar) and reduced-dimension regression ($QrnStar) evaluated at the observed data values.
iptw_os: A list of point estimates and covariance matrix for the one-step correct IPTW estimator.
iptw_os_nuisance: A list of the initial estimates of the propensity score and reduced-dimension regression evaluated at the observed data values.
iptw: A list of point estimates for the standard IPTW estimator. No estimate of the covariance matrix is provided because theory does not support asymptotic Normality of the IPTW estimator if super learning is used to estimate the propensity score.
gnMod: The fitted object for the propensity score. Returns NULL if returnModels = FALSE.
QrnMod: The fitted object for the reduced-dimension regression that guards against misspecification of the outcome regression. Returns NULL if returnModels = FALSE.
a_0: The treatment levels that were requested for computation of covariate-adjusted means.
call: The call to adaptive_iptw.

Examples

# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# fit iptw with maxIter = 1 to run fast

fit1 <- adaptive_iptw(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  SL_g = c("SL.glm", "SL.mean", "SL.step"),
  SL_Qr = "SL.npreg", maxIter = 1
)

# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# fit iptw with maxIter = 1 to run fast

fit1 <- adaptive_iptw(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  SL_g = c("SL.glm", "SL.mean", "SL.step"),
  SL_Qr = "SL.npreg", maxIter = 1
)

Helper function for averaging lists of estimates generated in the main `for` loop of `drtmle`

Description

Helper function for averaging lists of estimates generated in the main for loop of drtmle

Usage

average_est_cov_list(est_cov_list)
average_est_cov_list(est_cov_list)

Arguments

est_cov_list

A list with named entries est and cov

Helper function to average convergence results and drtmle influence function estimates over multiple fits

Description

Helper function to average convergence results and drtmle influence function estimates over multiple fits

Usage

average_ic_list(ic_list)
average_ic_list(ic_list)

Arguments

ic_list

List of influence function estimates

Compute confidence intervals for drtmle and adaptive_iptw@

Description

Compute confidence intervals for drtmle and adaptive_iptw@

Usage

ci(...)
ci(...)

Arguments

...

Arguments to be passed to method

Confidence intervals for adaptive_iptw objects

Description

Estimate confidence intervals for objects of class "adaptive_iptw"

Usage

## S3 method for class 'adaptive_iptw'
ci(object, est = c("iptw_tmle"), level = 0.95, contrast = NULL, ...)
## S3 method for class 'adaptive_iptw'
ci(object, est = c("iptw_tmle"), level = 0.95, contrast = NULL, ...)

Arguments

`object`	An object of class `"adaptive_iptw"`
`est`	A vector indicating for which estimators to return a confidence interval. Possible estimators include the TMLE IPTW (`"iptw_tmle"`, recommended), the one-step IPTW (`"iptw_os"`, not recommended), the standard IPTW (`"iptw"`, recommended only for comparison to the other two estimators).
`level`	The nominal coverage probability of the desired confidence interval (should be between 0 and 1). Default computes 95\ intervals.
`contrast`	Specifies the parameter for which to return confidence intervals. If `contrast=NULL`, then confidence intervals for the marginal means are computed. If instead, `contrast` is a numeric vector of ones, negative ones, and zeros to define linear combinations of the various means (e.g., to estimate an average treatment effect, see example). Finally, `contrast` can be a list with named functions `f`, `f_inv`, `h`, and `fh_grad`. The first two functions should take as input argument `eff`. Respectively, these specify which transformation of the effect measure to compute the confidence interval for and the inverse transformation to put the confidence interval back on the original scale. The function `h` defines the contrast to be estimated and should take as input `est`, a vector of the same length as `object$a_0`, and output the desired contrast. The function `fh_grad` is the gradient of the function `h`. See examples and vignette for more information.
`...`	Other options (not currently used).

Value

An object of class "ci.adaptive_iptw" with point estimates and confidence intervals of the specified level.

Examples

# load super learner
library(SuperLearner)
# fit adaptive_iptw
set.seed(123456)
n <- 200
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))

fit1 <- adaptive_iptw(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  SL_g = c("SL.glm", "SL.mean", "SL.step"),
  SL_Qr = "SL.glm"
)

# get confidence intervals for each mean
ci_mean <- ci(fit1)

# get confidence intervals for ATE
ci_ATE <- ci(fit1, contrast = c(1, -1))

# get confidence intervals for risk ratio
# by inputting own contrast function
# this computes CI on log scale and back transforms
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  },
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
ci_RR <- ci(fit1, contrast = myContrast)
# load super learner
library(SuperLearner)
# fit adaptive_iptw
set.seed(123456)
n <- 200
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))

fit1 <- adaptive_iptw(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  SL_g = c("SL.glm", "SL.mean", "SL.step"),
  SL_Qr = "SL.glm"
)

# get confidence intervals for each mean
ci_mean <- ci(fit1)

# get confidence intervals for ATE
ci_ATE <- ci(fit1, contrast = c(1, -1))

# get confidence intervals for risk ratio
# by inputting own contrast function
# this computes CI on log scale and back transforms
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  },
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
ci_RR <- ci(fit1, contrast = myContrast)

Confidence intervals for drtmle objects

Description

Confidence intervals for drtmle objects

Usage

## S3 method for class 'drtmle'
ci(object, est = c("drtmle"), level = 0.95, contrast = NULL, ...)
## S3 method for class 'drtmle'
ci(object, est = c("drtmle"), level = 0.95, contrast = NULL, ...)

Arguments

`object`	An object of class `"drtmle"`
`est`	A vector indicating for which estimators to return a confidence interval. Possible estimators include the TMLE with doubly robust inference (`"drtmle"`, recommended), the AIPTW with additional correction for misspecification (`"aiptw_c"`, not recommended), the standard TMLE (`"tmle"`, recommended only for comparison to "drtmle"), the standard AIPTW (`"aiptw"`, recommended only for comparison to "drtmle"), and G-computation (`"gcomp"`, not recommended).
`level`	The nominal coverage probability of the desired confidence interval (should be between 0 and 1). Default computes 95\ intervals.
`contrast`	Specifies the parameter for which to return confidence intervals. If `contrast=NULL`, then confidence intervals for the marginal means are computed. If instead, `contrast` is a numeric vector of ones, negative ones, and zeros to define linear combinations of the various means (e.g., to estimate an average treatment effect, see example). Finally, `contrast` can be a list with named functions `f`, `f_inv`, `h`, and `fh_grad`. The first two functions should take as input argument `eff`. Respectively, these specify which transformation of the effect measure to compute the confidence interval for and the inverse transformation to put the confidence interval back on the original scale. The function `h` defines the contrast to be estimated and should take as input `est`, a vector of the same length as `object$a_0`, and output the desired contrast. The function `fh_grad` is the gradient of the function `h`. See examples and vignette for more information.
`...`	Other options (not currently used).

Value

An object of class "ci.drtmle" with point estimates and confidence intervals of the specified level.

Examples

# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))

# fit drtmle with maxIter = 1 to run fast
fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean"),
  SL_g = c("SL.glm", "SL.mean"),
  SL_Qr = "SL.npreg",
  SL_gr = "SL.npreg", maxIter = 1
)

# get confidence intervals for each mean
ci_mean <- ci(fit1)

# get confidence intervals for ATE
ci_ATE <- ci(fit1, contrast = c(1, -1))

# get confidence intervals for risk ratio by
# computing CI on log scale and back-transforming
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  },
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
ci_RR <- ci(fit1, contrast = myContrast)

# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))

# fit drtmle with maxIter = 1 to run fast
fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean"),
  SL_g = c("SL.glm", "SL.mean"),
  SL_Qr = "SL.npreg",
  SL_gr = "SL.npreg", maxIter = 1
)

# get confidence intervals for each mean
ci_mean <- ci(fit1)

# get confidence intervals for ATE
ci_ATE <- ci(fit1, contrast = c(1, -1))

# get confidence intervals for risk ratio by
# computing CI on log scale and back-transforming
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  },
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
ci_RR <- ci(fit1, contrast = myContrast)

TMLE estimate of the average treatment effect with doubly-robust inference

Description

TMLE estimate of the average treatment effect with doubly-robust inference

Usage

drtmle(Y, A, W, DeltaA = as.numeric(!is.na(A)),
  DeltaY = as.numeric(!is.na(Y)), a_0 = unique(A[!is.na(A)]), family = if
  (all(Y %in% c(0, 1))) {     stats::binomial() } else {    
  stats::gaussian() }, stratify = FALSE, SL_Q = NULL, SL_g = NULL,
  SL_Qr = NULL, SL_gr = NULL, n_SL = 1, avg_over = "drtmle",
  se_cv = "none", se_cvFolds = ifelse(se_cv == "partial", 10, 1),
  targeted_se = se_cv != "partial", glm_Q = NULL, glm_g = NULL,
  glm_Qr = NULL, glm_gr = NULL, adapt_g = FALSE, guard = c("Q", "g"),
  reduction = "univariate", returnModels = FALSE, returnNuisance = TRUE,
  cvFolds = 1, maxIter = 3, tolIC = 1/length(Y), tolg = 0.01,
  verbose = FALSE, Qsteps = 2, Qn = NULL, gn = NULL,
  use_future = FALSE, ...)
drtmle(Y, A, W, DeltaA = as.numeric(!is.na(A)),
  DeltaY = as.numeric(!is.na(Y)), a_0 = unique(A[!is.na(A)]), family = if
  (all(Y %in% c(0, 1))) {     stats::binomial() } else {    
  stats::gaussian() }, stratify = FALSE, SL_Q = NULL, SL_g = NULL,
  SL_Qr = NULL, SL_gr = NULL, n_SL = 1, avg_over = "drtmle",
  se_cv = "none", se_cvFolds = ifelse(se_cv == "partial", 10, 1),
  targeted_se = se_cv != "partial", glm_Q = NULL, glm_g = NULL,
  glm_Qr = NULL, glm_gr = NULL, adapt_g = FALSE, guard = c("Q", "g"),
  reduction = "univariate", returnModels = FALSE, returnNuisance = TRUE,
  cvFolds = 1, maxIter = 3, tolIC = 1/length(Y), tolg = 0.01,
  verbose = FALSE, Qsteps = 2, Qn = NULL, gn = NULL,
  use_future = FALSE, ...)

Arguments

`Y`	A `numeric` continuous or binary outcomes.
`A`	A `numeric` vector of discrete-valued treatment assignment.
`W`	A `data.frame` of named covariates.
`DeltaA`	A `numeric` vector of missing treatment indicator (assumed to be equal to 0 if missing 1 if observed).
`DeltaY`	A `numeric` vector of missing outcome indicator (assumed to be equal to 0 if missing 1 if observed).
`a_0`	A `numeric` vector of fixed treatment values at which to return marginal mean estimates.
`family`	A `family` object equal to either `binomial()` or `gaussian()`, to be passed to the `SuperLearner` or `glm` function.
`stratify`	A `boolean` indicating whether to estimate the outcome regression separately for different values of `A` (if `TRUE`) or to pool across `A` (if `FALSE`).
`SL_Q`	A vector of characters or a list describing the Super Learner library to be used for the outcome regression. See `SuperLearner` for details.
`SL_g`	A vector of characters describing the super learner library to be used for each of the propensity score regressions (`DeltaA`, `A`, and `DeltaY`). To use the same library for each of the regressions (or if there is no missing data in `A` nor `Y`), a single library may be input. See `SuperLearner` for details on how super learner libraries can be specified.
`SL_Qr`	A vector of characters or a list describing the Super Learner library to be used for the reduced-dimension outcome regression.
`SL_gr`	A vector of characters or a list describing the Super Learner library to be used for the reduced-dimension propensity score.
`n_SL`	Number of repeated Super Learners to run (default 1) for the each nuisance parameter. Repeat Super Learners more times to obtain more stable inference.
`avg_over`	If multiple Super Learners are run, on which scale should the results be aggregated. Options include: `"SL"` = repeated nuisance parameter estimates are averaged before subsequently generating a single vector of point estimates based on the averaged models; `"drtmle"` = repeated vectors of point estimates are generated and averaged. Both can be specified, recognizing that this adds considerable computational expense. In this case, the final estimates are the average of `n_SL` point estimates where each is built by averaging `n_SL` fits. If `NULL`, no averaging is performed (in which case `n_SL` should be set equal to 1).
`se_cv`	Should cross-validated nuisance parameter estimates be used for computing standard errors? Options are `"none"` = no cross-validation is performed; `"partial"` = only applicable if Super Learner is used for nuisance parameter estimates; `"full"` = full cross-validation is performed. See vignette for further details. Ignored if `cvFolds > 1`, since then cross-validated nuisance parameter estimates are used by default and it is assumed that you want full cross-validated standard errors.
`se_cvFolds`	If cross-validated nuisance parameter estimates are used to compute standard errors, how many folds should be used in this computation. If `se_cv = "partial"`, then this option sets the number of folds used by the `SuperLearner` fitting procedure.
`targeted_se`	A boolean indicating whether the targeted nuisance parameters should be used in standard error computation or the initial estimators. If `se_cv` is not set to `"none"`, this option is ignored and standard errors are computed based on non-targeted, cross-validated nuisance parameter fits.
`glm_Q`	A character describing a formula to be used in the call to `glm` for the outcome regression. Ignored if `SL_Q!=NULL`.
`glm_g`	A list of characters describing the formulas to be used for each of the propensity score regressions (`DeltaA`, `A`, and `DeltaY`). To use the same formula for each of the regressions (or if there are no missing data in `A` nor `Y`), a single character formula may be input. In general the formulas can reference any variable in `colnames(W)`, unless `adapt_g = TRUE` in which case the formulas should reference variables `QaW` where `a` takes values in `a_0`.
`glm_Qr`	A character describing a formula to be used in the call to `glm` for reduced-dimension outcome regression. Ignored if `SL_Qr!=NULL`. The formula should use the variable name `'gn'`.
`glm_gr`	A character describing a formula to be used in the call to `glm` for the reduced-dimension propensity score. Ignored if `SL_gr!=NULL`. The formula should use the variable name `'Qn'` and `'gn'` if `reduction='bivariate'` and `'Qn'` otherwise.
`adapt_g`	A boolean indicating whether the propensity score should be outcome adaptive. If `TRUE` then the propensity score is estimated as the regression of `A` onto covariates `QaW` for `a` in each value contained in `a_0`. See vignette for more details.
`guard`	A character vector indicating what pattern of misspecifications to guard against. If `guard` contains `"Q"`, then the TMLE guards against misspecification of the outcome regression by estimating the reduced-dimension outcome regression specified by `glm_Qr` or `SL_Qr`. If `guard` contains `"g"` then the TMLE (additionally) guards against misspecification of the propensity score by estimating the reduced-dimension propensity score specified by `glm_gr` or `SL_gr`. If `guard` is set to `NULL`, then only standard TMLE and one-step estimators are computed.
`reduction`	A character equal to `"univariate"` for a univariate misspecification correction (default) or `"bivariate"` for the bivariate version.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`returnNuisance`	A boolean indicating whether to return the estimated nuisance regressions evaluated on the observed data. Defaults to `TRUE`. If `n_SL` is large and `"drtmle"` is in `avg_over`, then consider setting to `FALSE` in order to reduce size of resultant object.
`cvFolds`	A numeric equal to the number of folds to be used in cross-validated fitting of nuisance parameters. If `cvFolds = 1`, no cross-validation is used. Alternatively, `cvFolds` may be entered as a vector of fold assignments for observations, in which case its length should be the same length as `Y`.
`maxIter`	A numeric that sets the maximum number of iterations the TMLE can perform in its fluctuation step.
`tolIC`	A numeric that defines the stopping criteria based on the empirical mean of the influence function.
`tolg`	A numeric indicating the minimum value for estimates of the propensity score.
`verbose`	A boolean indicating whether to print status updates.
`Qsteps`	A numeric equal to 1 or 2 indicating whether the fluctuation submodel for the outcome regression should be fit using a single minimization (`Qsteps = 1`) or a backfitting-type minimization (`Qsteps=2`). The latter was found to be more stable in simulations and is the default.
`Qn`	An optional list of outcome regression estimates. If specified, the function will ignore the nuisance parameter estimation specified by `SL_Q` and `glm_Q`. The entries in the list should correspond to the outcome regression evaluated at `A` and the observed values of `W`, with order determined by the input to `a_0` (e.g., if `a_0 = c(0, 1)` then `Qn[[1]]` should be outcome regression at `A` = 0 and `Qn[[2]]` should be outcome regression at `A` = 1).
`gn`	An optional list of propensity score estimates. If specified, the function will ignore the nuisance parameter estimation specified by `SL_g` and `glm_g`. The entries in the list should correspond to the propensity for the observed values of `W`, with order determined by the input to `a_0` (e.g., if `a_0 = c(0,1)` then `gn[[1]]` should be propensity of `A` = 0 and `gn[[2]]` should be propensity of `A` = 1).
`use_future`	Boolean indicating whether to use `future_lapply` or instead to just use lapply. The latter can be easier to run down errors.
`...`	Other options (not currently used).

Value

An object of class "drtmle".

drtmle: A list of doubly-robust point estimates and a doubly-robust covariance matrix
nuisance_drtmle: A list of the final TMLE estimates of the outcome regression ($QnStar), propensity score ($gnStar), and reduced-dimension regressions ($QrnStar, $grnStar) evaluated at the observed data values.
ic_drtmle: A list of the empirical mean of the efficient influence function ($eif) and the extra pieces of the influence function resulting from misspecification. All should be smaller than tolIC (unless maxIter was reached first). Also includes a matrix of the influence function values at the estimated nuisance parameters evaluated at the observed data.
aiptw_c: A list of doubly-robust point estimates and a non-doubly-robust covariance matrix. Theory does not guarantee performance of inference for these estimators, but simulation studies showed they often perform adequately.
nuisance_aiptw: A list of the initial estimates of the outcome regression, propensity score, and reduced-dimension regressions evaluated at the observed data values.
tmle: A list of doubly-robust point estimates and non-doubly-robust covariance for the standard TMLE estimator.
aiptw: A list of doubly-robust point estimates and non-doubly-robust covariance matrix for the standard AIPTW estimator.
gcomp: A list of non-doubly-robust point estimates and non-doubly-robust covariance matrix for the standard G-computation estimator. If super learner is used there is no guarantee of correct inference for this estimator.
QnMod: The fitted object for the outcome regression. Returns NULL if returnModels = FALSE.
gnMod: The fitted object for the propensity score. Returns NULL if returnModels = FALSE.
QrnMod: The fitted object for the reduced-dimension regression that guards against misspecification of the outcome regression. Returns NULL if returnModels = FALSE.
grnMod: The fitted object for the reduced-dimension regression that guards against misspecification of the propensity score. Returns NULL if returnModels = FALSE.
a_0: The treatment levels that were requested for computation of covariate-adjusted means.

Examples

# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# A quick example of drtmle:
# We note that more flexible super learner libraries
# are available, and that we recommend the user use more flexible
# libraries for SL_Qr and SL_gr for general use.
fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_g = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_Qr = "SL.glm",
  SL_gr = "SL.glm", maxIter = 1
)
# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# A quick example of drtmle:
# We note that more flexible super learner libraries
# are available, and that we recommend the user use more flexible
# libraries for SL_Qr and SL_gr for general use.
fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_g = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_Qr = "SL.glm",
  SL_gr = "SL.glm", maxIter = 1
)

estimateG

Description

Function to estimate propensity score

Usage

estimateG(A, W, DeltaY, DeltaA, SL_g, glm_g, a_0, tolg, stratify = FALSE,
  validRows = NULL, verbose = FALSE, returnModels = FALSE, Qn = NULL,
  adapt_g = FALSE, se_cv = "none", se_cvFolds = 10)
estimateG(A, W, DeltaY, DeltaA, SL_g, glm_g, a_0, tolg, stratify = FALSE,
  validRows = NULL, verbose = FALSE, returnModels = FALSE, Qn = NULL,
  adapt_g = FALSE, se_cv = "none", se_cvFolds = 10)

Arguments

`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`W`	A `data.frame` of named covariates
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`SL_g`	A vector of characters describing the super learner library to be used for each of the regression (`DeltaA`, `A`, and `DeltaY`). To use the same regression for each of the regressions (or if there is no missing data in `A` nor `Y`), a single library may be input.
`glm_g`	A character describing a formula to be used in the call to `glm` for the propensity score.
`a_0`	A vector of fixed treatment values at which to return marginal mean estimates.
`tolg`	A numeric indicating the minimum value for estimates of the propensity score.
`stratify`	A `boolean` indicating whether to estimate the missing outcome regression separately for observations with `A` equal to 0/1 (if `TRUE`) or to pool across `A` (if `FALSE`).
`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.
`verbose`	A boolean indicating whether to print status updates.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`Qn`	A `list` of estimates of the outcome regression for each value in `a_0`. Only needed if `adapt_g = TRUE`.
`adapt_g`	A boolean indicating whether propensity score is adaptive to outcome regression.
`se_cv`	Should cross-validated nuisance parameter estimates be used for computing standard errors? Options are `"none"` = no cross-validation is performed; `"partial"` = only applicable if Super Learner is used for nuisance parameter estimates; `"full"` = full cross-validation is performed. See vignette for further details. Ignored if `cvFolds > 1`, since then cross-validated nuisance parameter estimates are used by default and it is assumed that you want full cross-validated standard errors.
`se_cvFolds`	If cross-validated nuisance parameter estimates are used to compute standard errors, how many folds should be used in this computation. If `se_cv = "partial"`, then this option sets the number of folds used by the `SuperLearner` fitting procedure.

estimateG_loop

Description

Helper function to clean up internals of drtmle function

Usage

estimateG_loop(validRows, A, W, DeltaA, DeltaY, tolg, verbose, stratify,
  returnModels, SL_g, glm_g, a_0, Qn, adapt_g, use_future, se_cv = "none",
  se_cvFolds = 10)
estimateG_loop(validRows, A, W, DeltaA, DeltaY, tolg, verbose, stratify,
  returnModels, SL_g, glm_g, a_0, Qn, adapt_g, use_future, se_cv = "none",
  se_cvFolds = 10)

Arguments

`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.
`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`W`	A `data.frame` of named covariates
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`tolg`	A numeric indicating the minimum value for estimates of the propensity score.
`verbose`	A boolean indicating whether to print status updates.
`stratify`	A `boolean` indicating whether to estimate the missing outcome regression separately for observations with `A` equal to 0/1 (if `TRUE`) or to pool across `A` (if `FALSE`).
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`SL_g`	A vector of characters describing the super learner library to be used for each of the regression (`DeltaA`, `A`, and `DeltaY`). To use the same regression for each of the regressions (or if there is no missing data in `A` nor `Y`), a single library may be input.
`glm_g`	A character describing a formula to be used in the call to `glm` for the propensity score.
`a_0`	A vector of fixed treatment values at which to return marginal mean estimates.
`Qn`	A `list` of estimates of the outcome regression for each value in `a_0`. Only needed if `adapt_g = TRUE`.
`adapt_g`	A boolean indicating whether propensity score is adaptive to outcome regression.
`use_future`	Should `future` be used for parallelization?
`se_cv`	Should cross-validated nuisance parameter estimates be used for computing standard errors? Options are `"none"` = no cross-validation is performed; `"partial"` = only applicable if Super Learner is used for nuisance parameter estimates; `"full"` = full cross-validation is performed. See vignette for further details. Ignored if `cvFolds > 1`, since then cross-validated nuisance parameter estimates are used by default and it is assumed that you want full cross-validated standard errors.
`se_cvFolds`	If cross-validated nuisance parameter estimates are used to compute standard errors, how many folds should be used in this computation. If `se_cv = "partial"`, then this option sets the number of folds used by the `SuperLearner` fitting procedure.

estimategrn

Description

Estimates the reduced dimension regressions necessary for the additional fluctuations.

Usage

estimategrn(Y, A, W, DeltaA, DeltaY, Qn, gn, SL_gr, tolg, glm_gr, a_0,
  reduction, returnModels, validRows)
estimategrn(Y, A, W, DeltaA, DeltaY, Qn, gn, SL_gr, tolg, glm_gr, a_0,
  reduction, returnModels, validRows)

Arguments

`Y`	A vector of continuous or binary outcomes.
`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1).
`W`	A `data.frame` of named covariates.
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed).
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed).
`Qn`	A list of outcome regression estimates evaluated on observed data.
`gn`	A list of propensity regression estimates evaluated on observed data.
`SL_gr`	A vector of characters or a list describing the Super Learner library to be used for the reduced-dimension propensity score.
`tolg`	A numeric indicating the minimum value for estimates of the propensity score.
`glm_gr`	A character describing a formula to be used in the call to `glm` for the second reduced-dimension regression. Ignored if `SL_gr!=NULL`.
`a_0`	A list of fixed treatment values .
`reduction`	A character equal to `'univariate'` for a univariate misspecification correction or `'bivariate'` for the bivariate version.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.

estimategrn_loop

Description

Helper function to clean up the internal code of drtmle

Usage

estimategrn_loop(validRows, Y, A, W, DeltaA, DeltaY, tolg, Qn, gn, glm_gr,
  SL_gr, a_0, reduction, returnModels, use_future)
estimategrn_loop(validRows, Y, A, W, DeltaA, DeltaY, tolg, Qn, gn, glm_gr,
  SL_gr, a_0, reduction, returnModels, use_future)

Arguments

`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.
`Y`	A vector of continuous or binary outcomes.
`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1).
`W`	A `data.frame` of named covariates.
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed).
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed).
`tolg`	A numeric indicating the minimum value for estimates of the propensity score.
`Qn`	A list of outcome regression estimates evaluated on observed data.
`gn`	A list of propensity regression estimates evaluated on observed data.
`glm_gr`	A character describing a formula to be used in the call to `glm` for the second reduced-dimension regression. Ignored if `SL_gr!=NULL`.
`SL_gr`	A vector of characters or a list describing the Super Learner library to be used for the reduced-dimension propensity score.
`a_0`	A list of fixed treatment values .
`reduction`	A character equal to `'univariate'` for a univariate misspecification correction or `'bivariate'` for the bivariate version.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`use_future`	Should `future` be used to parallelize?

estimateQ

Description

Function to estimate initial outcome regression

Usage

estimateQ(Y, A, W, DeltaA, DeltaY, SL_Q, glm_Q, a_0, stratify, family,
  verbose = FALSE, returnModels = FALSE, se_cv = "none",
  se_cvFolds = 10, validRows = NULL, ...)
estimateQ(Y, A, W, DeltaA, DeltaY, SL_Q, glm_Q, a_0, stratify, family,
  verbose = FALSE, returnModels = FALSE, se_cv = "none",
  se_cvFolds = 10, validRows = NULL, ...)

Arguments

`Y`	A vector of continuous or binary outcomes.
`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1).
`W`	A `data.frame` of named covariates.
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed).
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed).
`SL_Q`	A vector of characters or a list describing the Super Learner library to be used for the outcome regression.
`glm_Q`	A character describing a formula to be used in the call to `glm` for the outcome regression.
`a_0`	A list of fixed treatment values
`stratify`	A `boolean` indicating whether to estimate the outcome regression separately for observations with `A` equal to 0/1 (if `TRUE`) or to pool across `A` (if `FALSE`).
`family`	A character passed to `SuperLearner`
`verbose`	A boolean indicating whether to print status updates.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`se_cv`	Should cross-validated nuisance parameter estimates be used for computing standard errors? Options are `"none"` = no cross-validation is performed; `"partial"` = only applicable if Super Learner is used for nuisance parameter estimates; `"full"` = full cross-validation is performed. See vignette for further details. Ignored if `cvFolds > 1`, since then cross-validated nuisance parameter estimates are used by default and it is assumed that you want full cross-validated standard errors.
`se_cvFolds`	If cross-validated nuisance parameter estimates are used to compute standard errors, how many folds should be used in this computation. If `se_cv = "partial"`, then this option sets the number of folds used by the `SuperLearner` fitting procedure.
`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.
`...`	Additional arguments (not currently used)

estimateQ_loop

Description

A helper loop function to clean up the internals of drtmle function.

Usage

estimateQ_loop(validRows, Y, A, W, DeltaA, DeltaY, verbose, returnModels, SL_Q,
  a_0, stratify, glm_Q, family, use_future, se_cv, se_cvFolds)
estimateQ_loop(validRows, Y, A, W, DeltaA, DeltaY, verbose, returnModels, SL_Q,
  a_0, stratify, glm_Q, family, use_future, se_cv, se_cvFolds)

Arguments

`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.
`Y`	A vector of continuous or binary outcomes.
`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`W`	A `data.frame` of named covariates
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`verbose`	A boolean indicating whether to print status updates.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`SL_Q`	A vector of characters or a list describing the Super Learner library to be used for the outcome regression. See `SuperLearner` for details.
`a_0`	A list of fixed treatment values.
`stratify`	A `boolean` indicating whether to estimate the outcome regression separately for different values of `A` (if `TRUE`) or to pool across `A` (if `FALSE`).
`glm_Q`	A character describing a formula to be used in the call to `glm` for the outcome regression. Ignored if `SL_Q!=NULL`.
`family`	Should be gaussian() unless called from adaptive_iptw with binary `Y`.
`use_future`	Boolean indicating whether to use `future_lapply` or instead to just use lapply. The latter can be easier to run down errors.
`se_cv`	Should cross-validated nuisance parameter estimates be used for computing standard errors? Options are `"none"` = no cross-validation is performed; `"partial"` = only applicable if Super Learner is used for nuisance parameter estimates; `"full"` = full cross-validation is performed. See vignette for further details. Ignored if `cvFolds > 1`, since then cross-validated nuisance parameter estimates are used by default and it is assumed that you want full cross-validated standard errors.
`se_cvFolds`	If cross-validated nuisance parameter estimates are used to compute standard errors, how many folds should be used in this computation. If `se_cv = "partial"`, then this option sets the number of folds used by the `SuperLearner` fitting procedure.

estimateQrn

Description

Estimates the reduced dimension regressions necessary for the fluctuations of g

Usage

estimateQrn(Y, A, W, DeltaA, DeltaY, Qn, gn, glm_Qr, SL_Qr,
  family = stats::gaussian(), a_0, returnModels, validRows = NULL)
estimateQrn(Y, A, W, DeltaA, DeltaY, Qn, gn, glm_Qr, SL_Qr,
  family = stats::gaussian(), a_0, returnModels, validRows = NULL)

Arguments

`Y`	A vector of continuous or binary outcomes.
`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`W`	A `data.frame` of named covariates
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`Qn`	A list of outcome regression estimates evaluated on observed data. If NULL then 0 is used for all Qn (as is needed to estimate reduced dimension regression for adaptive_iptw)
`gn`	A list of propensity regression estimates evaluated on observed data
`glm_Qr`	A character describing a formula to be used in the call to `glm` for the first reduced-dimension regression. Ignored if `SL_gr!=NULL`.
`SL_Qr`	A vector of characters or a list describing the Super Learner library to be used for the first reduced-dimension regression.
`family`	Should be gaussian() unless called from adaptive_iptw with binary `Y`.
`a_0`	A list of fixed treatment values.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.

estimateQrn_loop

Description

Helper function to clean up internal code of drtmle function.

Usage

estimateQrn_loop(validRows, Y, A, W, DeltaA, DeltaY, Qn, gn, SL_Qr, glm_Qr,
  family, a_0, returnModels, use_future)
estimateQrn_loop(validRows, Y, A, W, DeltaA, DeltaY, Qn, gn, SL_Qr, glm_Qr,
  family, a_0, returnModels, use_future)

Arguments

`validRows`	A `list` of length `cvFolds` containing the row indexes of observations to include in validation fold.
`Y`	A vector of continuous or binary outcomes.
`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`W`	A `data.frame` of named covariates
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`Qn`	A list of outcome regression estimates evaluated on observed data. If NULL then 0 is used for all Qn (as is needed to estimate reduced dimension regression for adaptive_iptw)
`gn`	A list of propensity regression estimates evaluated on observed data
`SL_Qr`	A vector of characters or a list describing the Super Learner library to be used for the first reduced-dimension regression.
`glm_Qr`	A character describing a formula to be used in the call to `glm` for the first reduced-dimension regression. Ignored if `SL_gr!=NULL`.
`family`	Should be gaussian() unless called from adaptive_iptw with binary `Y`.
`a_0`	A list of fixed treatment values.
`returnModels`	A boolean indicating whether to return model fits for the outcome regression, propensity score, and reduced-dimension regressions.
`use_future`	Should `future` be used in the fitting process.

Evaluate usual influence function of IPTW

Description

Evaluate usual influence function of IPTW

Usage

eval_Diptw(A, Y, DeltaA, DeltaY, gn, psi_n, a_0)
eval_Diptw(A, Y, DeltaA, DeltaY, gn, psi_n, a_0)

Arguments

`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`Y`	A numeric of continuous or binary outcomes.
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`gn`	List of estimated propensity scores evaluated at observations
`psi_n`	List of estimated ATEs
`a_0`	Vector of values to return marginal mean

Evaluate extra piece of the influence function for the IPTW

Description

Evaluate extra piece of the influence function for the IPTW

Usage

eval_Diptw_g(A, DeltaA, DeltaY, Qrn, gn, a_0)
eval_Diptw_g(A, DeltaA, DeltaY, Qrn, gn, a_0)

Arguments

`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`Qrn`	List of estimated reduced-dimension outcome regression evaluated at observations
`gn`	List of estimated propensity scores evaluated at observations
`a_0`	Vector of values to return marginal mean

Evaluate usual efficient influence function

Description

Evaluate usual efficient influence function

Usage

eval_Dstar(A, Y, DeltaY, DeltaA, Qn, gn, psi_n, a_0)
eval_Dstar(A, Y, DeltaY, DeltaA, Qn, gn, psi_n, a_0)

Arguments

`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`Y`	A numeric of continuous or binary outcomes.
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`Qn`	List of estimated outcome regression evaluated at observations
`gn`	List of estimated propensity scores evaluated at observations
`psi_n`	List of estimated ATEs
`a_0`	Vector of values to return marginal mean

Evaluate extra piece of efficient influence function resulting from misspecification of outcome regression

Description

Evaluate extra piece of efficient influence function resulting from misspecification of outcome regression

Usage

eval_Dstar_g(A, DeltaY, DeltaA, Qrn, gn, a_0)
eval_Dstar_g(A, DeltaY, DeltaA, Qrn, gn, a_0)

Arguments

`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`Qrn`	List of estimated reduced-dimension outcome regression evaluated at observations
`gn`	List of estimated propensity scores evaluated at observations
`a_0`	Vector of values to return marginal mean

Evaluate extra piece of efficient influence function resulting from misspecification of propensity score

Description

Evaluate extra piece of efficient influence function resulting from misspecification of propensity score

Usage

eval_Dstar_Q(A, Y, DeltaY, DeltaA, Qn, gn, grn, a_0, reduction)
eval_Dstar_Q(A, Y, DeltaY, DeltaA, Qn, gn, grn, a_0, reduction)

Arguments

`A`	A vector of binary treatment assignment (assumed to be equal to 0 or 1)
`Y`	A numeric of continuous or binary outcomes.
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`Qn`	List of estimated outcome regression evaluated at observations
`gn`	List of estimated propensity scores evaluated at observations
`grn`	List of estimated reduced-dimension propensity scores evaluated at observations
`a_0`	Vector of values to return marginal mean
`reduction`	A character equal to `"univariate"` for a univariate misspecification correction or `"bivariate"` for the bivariate version.

Help function to extract models from fitted object

Description

Help function to extract models from fitted object

Usage

extract_models(a_list)
extract_models(a_list)

Arguments

a_list

Structured list of nuisance parameters

fluctuateG

Description

Function called internally by drtmle to perform the fluctuation of the initial estimator of g (i.e., solves the new estimating eqn that results from misspecification of Q)

Usage

fluctuateG(Y, A, W, DeltaY, DeltaA, a_0, gn, Qrn, tolg, coefTol = 1000)
fluctuateG(Y, A, W, DeltaY, DeltaA, a_0, gn, Qrn, tolg, coefTol = 1000)

Arguments

`Y`	The outcome
`A`	The treatment
`W`	The covariates
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`a_0`	A list of fixed treatment values
`gn`	A list of propensity regression estimates evaluated on observed data
`Qrn`	A list of reduced-dimension regression estimates evaluated on observed data
`tolg`	The lower bound on propensity score estimates
`coefTol`	A tolerance level on the magnitude of the coefficient that flags the result as potentially the result of numeric instability.

Function called internally by drtmle to perform simultaneous fluctuation of the initial estimator of Q (i.e., solves both EIF estimating eqn and the new estimating eqn that results from misspecification of g)

Usage

fluctuateQ(Y, A, W, DeltaY, DeltaA, Qn, gn, grn, a_0, reduction,
  coefTol = 1000)
fluctuateQ(Y, A, W, DeltaY, DeltaA, Qn, gn, grn, a_0, reduction,
  coefTol = 1000)

Arguments

`Y`	The outcome
`A`	The treatment
`W`	The covariates
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`Qn`	A list of outcome regression estimates evaluated on observed data
`gn`	A list of propensity regression estimates evaluated on observed data
`grn`	A list of reduced-dimension regression estimates evaluated on observed data
`a_0`	A list of fixed treatment values
`reduction`	A character indicating what reduced dimension regression was used.
`coefTol`	A tolerance level on the magnitude of the coefficient that flags the result as potentially the result of numeric instability.

fluctuateQ1

Description

Function called internally by drtmle to perform the first fluctuation of the initial estimator of Q (i.e., solves the original EIF estimating eqn)

Usage

fluctuateQ1(Y, A, W, DeltaA, DeltaY, Qn, gn, a_0, coefTol = 1000)
fluctuateQ1(Y, A, W, DeltaA, DeltaY, Qn, gn, a_0, coefTol = 1000)

Arguments

`Y`	The outcome
`A`	The treatment
`W`	The covariates
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`Qn`	A list of outcome regression estimates evaluated on observed data
`gn`	A list of propensity regression estimates evaluated on observed data
`a_0`	A list of fixed treatment values
`coefTol`	A tolerance level on the magnitude of the coefficient that flags the result as potentially the result of numeric instability.

fluctuateQ2

Description

Function called internally by drtmle to perform the second fluctuation of the initial estimator of Q (i.e., solves the new estimating eqn that results from misspecification of g)

Usage

fluctuateQ2(Y, A, W, DeltaY, DeltaA, Qn, gn, grn, a_0, reduction,
  coefTol = 1000)
fluctuateQ2(Y, A, W, DeltaY, DeltaA, Qn, gn, grn, a_0, reduction,
  coefTol = 1000)

Arguments

`Y`	The outcome
`A`	The treatment
`W`	The covariates
`DeltaY`	Indicator of missing outcome (assumed to be equal to 0 if missing 1 if observed)
`DeltaA`	Indicator of missing treatment (assumed to be equal to 0 if missing 1 if observed)
`Qn`	A list of outcome regression estimates evaluated on observed data
`gn`	A list of propensity regression estimates evaluated on observed data
`grn`	A list of reduced-dimension regression estimates evaluated on observed data
`a_0`	A list of fixed treatment values
`reduction`	A character indicating what reduced dimension regression was used.
`coefTol`	A tolerance level on the magnitude of the coefficient that flags the result as potentially the result of numeric instability.

Make list of rows in each validation fold.

Description

Make list of rows in each validation fold.

Usage

make_validRows(cvFolds, n, ...)
make_validRows(cvFolds, n, ...)

Arguments

`cvFolds`	Numeric number of cv folds
`n`	Number of observations
`...`	Other arguments

Helper function to properly format partially cross-validated predictions from a fitted super learner.

Description

Helper function to properly format partially cross-validated predictions from a fitted super learner.

Usage

partial_cv_preds(fit_sl, a_0, W = NULL, family, include = NULL, easy = FALSE)
partial_cv_preds(fit_sl, a_0, W = NULL, family, include = NULL, easy = FALSE)

Arguments

`fit_sl`	A fitted `SuperLearner` object with `control$saveCVFitLibrary = TRUE`
`a_0`	Treatment level to set. If `NULL`, assume this function is being used to get partially cross-validated propensity score predictions.
`W`	A `data.frame` of named covariates.
`family`	Family of prediction model
`include`	A boolean vector indicating which observations were actually used to fit the regression.
`easy`	A boolean indicating whether the predictions can be computed the "easy" way, i.e., based just on the Z matrix from SuperLearner. This is possible for propensity score models when no missing data AND no stratification.

Plot reduced dimension regression fits

Description

Plot reduced dimension regression fits

Usage

## S3 method for class 'drtmle'
plot(x, nPoints = 500, ask = TRUE, a_0 = x$a_0[1], ...)
## S3 method for class 'drtmle'
plot(x, nPoints = 500, ask = TRUE, a_0 = x$a_0[1], ...)

Arguments

`x`	An object of class `"drtmle"`
`nPoints`	Number of points to plot lines (increase for less bumpy plot, decrease for faster evaluation).
`ask`	Boolean indicating whether R should ask to show each plot
`a_0`	For what value of a_0 should the plot be made for?
`...`	More arguments passed to `plot`

Examples

# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# fit drtmle with maxIter = 1 to run fast

fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_g = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_Qr = "SL.npreg", SL_gr = "SL.npreg",
  maxIter = 1, returnModels = TRUE
)
# plot the reduced-dimension regression fits (not run)

plot(fit1)

#
# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# fit drtmle with maxIter = 1 to run fast

fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_g = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_Qr = "SL.npreg", SL_gr = "SL.npreg",
  maxIter = 1, returnModels = TRUE
)
# plot the reduced-dimension regression fits (not run)

plot(fit1)

#

Predict method for SL.npreg

Description

Method for predicting SL.npreg objects.

Usage

## S3 method for class 'SL.npreg'
predict(object, newdata, ...)
## S3 method for class 'SL.npreg'
predict(object, newdata, ...)

Arguments

`object`	An object of class `"SL.npreg"`.
`newdata`	The new data used to obtain predictions.
`...`	Other arguments passed to predict.

Examples

# simulate data
set.seed(1234)
n <- 100
X <- data.frame(X1 = rnorm(n))
Y <- X$X1 + rnorm(n)
# fit npreg
fit <- SL.npreg(Y = Y, X = X, newX = X)
# predict on fit
newX <- data.frame(X1 = c(-1, 0, 1))
pred <- predict(fit$fit, newdata = newX)
#
# simulate data
set.seed(1234)
n <- 100
X <- data.frame(X1 = rnorm(n))
Y <- X$X1 + rnorm(n)
# fit npreg
fit <- SL.npreg(Y = Y, X = X, newX = X)
# predict on fit
newX <- data.frame(X1 = c(-1, 0, 1))
pred <- predict(fit$fit, newdata = newX)
#

Print the output of a `"adaptive_iptw"` object.

Description

Print the output of a "adaptive_iptw" object.

Usage

## S3 method for class 'adaptive_iptw'
print(x, ...)
## S3 method for class 'adaptive_iptw'
print(x, ...)

Arguments

`x`	A `"adaptive_iptw"` object.
`...`	Other arguments (not used)

Print the output of ci.adaptive_iptw

Description

Print the output of ci.adaptive_iptw

Usage

## S3 method for class 'ci.adaptive_iptw'
print(x, digits = 3, ...)
## S3 method for class 'ci.adaptive_iptw'
print(x, digits = 3, ...)

Arguments

`x`	An object of class ci.adaptive_iptw
`digits`	Number of digits to round to
`...`	Other options (not currently used)

Print the output of ci.drtmle

Description

Print the output of ci.drtmle

Usage

## S3 method for class 'ci.drtmle'
print(x, digits = 3, ...)
## S3 method for class 'ci.drtmle'
print(x, digits = 3, ...)

Arguments

`x`	An object of class ci.drtmle
`digits`	Number of digits to round to
`...`	Other options (not currently used)

Print the output of a `"drtmle"` object.

Description

Print the output of a "drtmle" object.

Usage

## S3 method for class 'drtmle'
print(x, ...)
## S3 method for class 'drtmle'
print(x, ...)

Arguments

`x`	A `"drtmle"` object
`...`	Other arguments (not used)

Print the output of wald_test.adaptive_iptw

Description

Print the output of wald_test.adaptive_iptw

Usage

## S3 method for class 'wald_test.adaptive_iptw'
print(x, digits = 3, ...)
## S3 method for class 'wald_test.adaptive_iptw'
print(x, digits = 3, ...)

Arguments

`x`	An object of class wald_test.adaptive_iptw
`digits`	Number of digits to round to
`...`	Other options (not currently used)

Print the output of wald_test.drtmle

Description

Print the output of wald_test.drtmle

Usage

## S3 method for class 'wald_test.drtmle'
print(x, digits = 3, ...)
## S3 method for class 'wald_test.drtmle'
print(x, digits = 3, ...)

Arguments

`x`	An object of class wald_test.drtmle
`digits`	Number of digits to round to
`...`	Other options (not currently used)

Helper function to reorder lists according to cvFolds

Description

Helper function to reorder lists according to cvFolds

Usage

reorder_list(a_list, a_0, validRows, n_SL = 1, grn_ind = FALSE, n,
  for_se_cv = FALSE)
reorder_list(a_list, a_0, validRows, n_SL = 1, grn_ind = FALSE, n,
  for_se_cv = FALSE)

Arguments

`a_list`	Structured list of nuisance parameters
`a_0`	Treatment levels
`validRows`	List of rows of data in validation data for each split.
`n_SL`	Number of super learners. If >1, then predictions are averaged
`grn_ind`	Structure of grn call is slightly different
`n`	Sample size
`for_se_cv`	Is this being used to average over cross-validated standard errors? Affects index of `a_list`.

Super learner wrapper for kernel regression

Description

Kernel regression based on the np package. Uses leave-one-out cross-validation to fit a kernel regression. See ?npreg for more details.

Usage

SL.npreg(Y, X, newX, family = gaussian(), obsWeights = rep(1, length(Y)),
  rangeThresh = 1e-07, ...)
SL.npreg(Y, X, newX, family = gaussian(), obsWeights = rep(1, length(Y)),
  rangeThresh = 1e-07, ...)

Arguments

`Y`	A vector of outcomes.
`X`	A matrix or data.frame of training data predictors.
`newX`	A test set of predictors.
`family`	Not used by the function directly, but ensures compatibility with `SuperLearner`.
`obsWeights`	Not used by the function directly, but ensures compatibility with `SuperLearner`.
`rangeThresh`	If the the range of the outcomes is smaller than this number, the method returns the empirical average of the outcomes. Used for computational expediency and stability.
`...`	Other arguments (not currently used).

Examples

# simulate data
set.seed(1234)
n <- 100
X <- data.frame(X1 = rnorm(n))
Y <- X$X1 + rnorm(n)
# fit npreg
fit <- SL.npreg(Y = Y, X = X, newX = X)
#
# simulate data
set.seed(1234)
n <- 100
X <- data.frame(X1 = rnorm(n))
Y <- X$X1 + rnorm(n)
# fit npreg
fit <- SL.npreg(Y = Y, X = X, newX = X)
#

Temporary fix for convex combination method mean squared error Relative to existing implementation, we reduce the tolerance at which we declare predictions from a given algorithm the same as another

Description

Temporary fix for convex combination method mean squared error Relative to existing implementation, we reduce the tolerance at which we declare predictions from a given algorithm the same as another

Usage

tmp_method.CC_LS()
tmp_method.CC_LS()

Temporary fix for convex combination method negative log-likelihood loss Relative to existing implementation, we reduce the tolerance at which we declare predictions from a given algorithm the same as another. Note that because of the way `SuperLearner` is structure, one needs to install the optimization software separately.

Description

Temporary fix for convex combination method negative log-likelihood loss Relative to existing implementation, we reduce the tolerance at which we declare predictions from a given algorithm the same as another. Note that because of the way SuperLearner is structure, one needs to install the optimization software separately.

Usage

tmp_method.CC_nloglik()
tmp_method.CC_nloglik()

Wald tests for drtmle and adaptive_iptw objects

Description

Wald tests for drtmle and adaptive_iptw objects

Usage

wald_test(...)
wald_test(...)

Arguments

...

Arguments to be passed to method

Wald tests for adaptive_iptw objects

Description

Wald tests for adaptive_iptw objects

Usage

## S3 method for class 'adaptive_iptw'
wald_test(object, est = c("iptw_tmle"), null = 0, contrast = NULL, ...)
## S3 method for class 'adaptive_iptw'
wald_test(object, est = c("iptw_tmle"), null = 0, contrast = NULL, ...)

Arguments

`object`	An object of class `"adaptive_iptw"`
`est`	A vector indicating for which estimators to return a confidence interval. Possible estimators include the TMLE IPTW (`"iptw_tmle"`, recommended), the one-step IPTW (`"iptw_os"`, not recommended), the standard IPTW (`"iptw"`, recommended only for comparison to the other two estimators).
`null`	The null hypothesis value(s).
`contrast`	This option specifies what parameter to return confidence intervals for. If `contrast=NULL`, then test the null hypothesis that the covariate-adjusted marginal means equal the value(s) specified in `null`. `contrast` can also be a numeric vector of ones, negative ones, and zeros to define linear combinations of the various means (e.g., to estimate an average treatment effect, see examples). In this case, we test the null hypothesis that the linear combination of means equals the value specified in `null`. `contrast` can also be a list with named functions `f`, `h`, and `fh_grad`. The function `f` takes as input argument `eff` and specifies which transformation of the effect measure to test. The function `h` defines the contrast to be estimated and should take as input `est`, a vector of the same length as `object$a_0`, and output the desired contrast. The function `fh_grad` is the gradient of the function `h(f())`. The function computes a test of the null hypothesis that `h(f(object$est)) = null`. See examples.
`...`	Other options (not currently used).

Value

An object of class "ci.adaptive_iptw" with point estimates and confidence intervals of the specified level.

Examples

# load super learner
library(SuperLearner)
# fit adaptive_iptw
set.seed(123456)
n <- 200
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))

fit1 <- adaptive_iptw(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  SL_g = c("SL.glm", "SL.mean", "SL.step"),
  SL_Qr = "SL.glm"
)

# get test that each mean = 0.5
test_mean <- wald_test(fit1, null = 0.5)

# get test that the ATE = 0
ci_ATE <- ci(fit1, contrast = c(1, -1), null = 0)

# get test for risk ratio = 1 on log scale
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  }, # not necessary
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
ci_RR <- ci(fit1, contrast = myContrast, null = 1)
#
# load super learner
library(SuperLearner)
# fit adaptive_iptw
set.seed(123456)
n <- 200
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))

fit1 <- adaptive_iptw(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  SL_g = c("SL.glm", "SL.mean", "SL.step"),
  SL_Qr = "SL.glm"
)

# get test that each mean = 0.5
test_mean <- wald_test(fit1, null = 0.5)

# get test that the ATE = 0
ci_ATE <- ci(fit1, contrast = c(1, -1), null = 0)

# get test for risk ratio = 1 on log scale
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  }, # not necessary
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
ci_RR <- ci(fit1, contrast = myContrast, null = 1)
#

Wald tests for drtmle objects

Description

Wald tests for drtmle objects

Usage

## S3 method for class 'drtmle'
wald_test(object, est = c("drtmle"), null = 0, contrast = NULL, ...)
## S3 method for class 'drtmle'
wald_test(object, est = c("drtmle"), null = 0, contrast = NULL, ...)

Arguments

`object`	An object of class `"drtmle"`
`est`	A vector indicating for which estimators to return a confidence interval. Possible estimators include the TMLE with doubly robust inference (`"drtmle"`, recommended), the AIPTW with additional correction for misspecification (`"aiptw_c"`, not recommended), the standard TMLE (`"tmle"`, recommended only for comparison to "drtmle"), the standard AIPTW (`"aiptw"`, recommended only for comparison to "drtmle"), and G-computation (`"gcomp"`, not recommended).
`null`	The null hypothesis value.
`contrast`	This option specifies what parameter to return confidence intervals for. If `contrast=NULL`, then test the null hypothesis that the covariate-adjusted marginal means equal the value(s) specified in `null`. `contrast` can also be a numeric vector of ones, negative ones, and zeros to define linear combinations of the various means (e.g., to estimate an average treatment effect, see examples). In this case, we test the null hypothesis that the linear combination of means equals the value specified in `null`. `contrast` can also be a list with named functions `f`, `h`, and `fh_grad`. The function `f` takes as input argument `eff` and specifies which transformation of the effect measure to test. The function `h` defines the contrast to be estimated and should take as input `est`, a vector of the same length as `object$a_0`, and output the desired contrast. The function `fh_grad` is the gradient of the function `h(f())`. The function computes a test of the null hypothesis that `h(f(object$est)) = null`. See examples.
`...`	Other options (not currently used).

Value

An object of class "ci.drtmle" with point estimates and confidence intervals of the specified level.

Examples

# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# fit drtmle with maxIter = 1 so runs fast
fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_g = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_Qr = "SL.glm",
  SL_gr = "SL.glm", maxIter = 1
)
# get hypothesis test that each mean = 0.5
test_mean <- wald_test(fit1, null = 0.5)

# get test that ATE = 0
test_ATE <- wald_test(fit1, null = 0, contrast = c(1, -1))

# get test that risk ratio = 1, computing test on log scale
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  },
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
test_RR <- wald_test(fit1, contrast = myContrast, null = 1)
#
# load super learner
library(SuperLearner)
# simulate data
set.seed(123456)
n <- 100
W <- data.frame(W1 = runif(n), W2 = rnorm(n))
A <- rbinom(n, 1, plogis(W$W1 - W$W2))
Y <- rbinom(n, 1, plogis(W$W1 * W$W2 * A))
# fit drtmle with maxIter = 1 so runs fast
fit1 <- drtmle(
  W = W, A = A, Y = Y, a_0 = c(1, 0),
  family = binomial(),
  stratify = FALSE,
  SL_Q = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_g = c("SL.glm", "SL.mean", "SL.glm.interaction"),
  SL_Qr = "SL.glm",
  SL_gr = "SL.glm", maxIter = 1
)
# get hypothesis test that each mean = 0.5
test_mean <- wald_test(fit1, null = 0.5)

# get test that ATE = 0
test_ATE <- wald_test(fit1, null = 0, contrast = c(1, -1))

# get test that risk ratio = 1, computing test on log scale
myContrast <- list(
  f = function(eff) {
    log(eff)
  },
  f_inv = function(eff) {
    exp(eff)
  },
  h = function(est) {
    est[1] / est[2]
  },
  fh_grad = function(est) {
    c(1 / est[1], -1 / est[2])
  }
)
test_RR <- wald_test(fit1, contrast = myContrast, null = 1)
#

Package 'drtmle'

Help Index

Compute asymptotically linear IPTW estimators with super learning for the propensity score

Description

Usage

Arguments

Value

Examples

Helper function for averaging lists of estimates generated in the main for loop of drtmle

Description

Usage

Arguments

Helper function to average convergence results and drtmle influence function estimates over multiple fits

Description

Usage

Arguments

Compute confidence intervals for drtmle and adaptive_iptw@

Description

Usage

Arguments

Confidence intervals for adaptive_iptw objects

Description

Usage

Arguments

Value

Examples

Confidence intervals for drtmle objects

Description

Usage

Arguments

Value

Examples

TMLE estimate of the average treatment effect with doubly-robust inference

Description

Usage

Arguments

Value

Examples

estimateG

Description

Usage

Arguments

estimateG_loop

Description

Usage

Arguments

estimategrn

Description

Usage

Arguments

estimategrn_loop

Description

Usage

Arguments

estimateQ

Description

Usage

Arguments

estimateQ_loop

Description

Usage

Arguments

estimateQrn

Description

Usage

Arguments

estimateQrn_loop

Description

Usage

Arguments

Evaluate usual influence function of IPTW

Description

Usage

Arguments

Evaluate extra piece of the influence function for the IPTW

Description

Usage

Arguments

Evaluate usual efficient influence function

Description

Helper function for averaging lists of estimates generated in the main `for` loop of `drtmle`

Print the output of a `"adaptive_iptw"` object.

Print the output of a `"drtmle"` object.