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#' @param data similar as aipw_single_p() function
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#' @param exposure similar as aipw_single_p() function
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#' @param outcome similar as aipw_single_p() function
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#' @param covarsT similar as aipw_single_p() function
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#' @param covarsO similar as aipw_single_p() function
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#' @param learners similar as aipw_single_p() function
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#' @param control similar as aipw_single_p() function
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#' @param num_cf number of partitions
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#' @param n_split similar as aipw_single_p() function
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#' @param rand_split logical value; if be TRUE, discordant splits for exposure and outcome model are chosen at random ; otherwise chosen systematically.
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#' @param seed numeric value to reproduce the splits
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#' Estimate ATE using from AIPW estimator using cross-fit algorithm (multiple repetition)
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#'
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#' @param data a data frame of tibble
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#' @param exposure name of exposure variable
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#' @param outcome name of outcome variable
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#' @param covarsT a vector of names of covaraites for treatment model
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#' @param covarsO a vector of names of covaraites for outcome model
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#' @param family.y it is the family for outcome model. It can `binomial() (default)` or `"gaussian"`
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#' @param learners similar as \code{\link[Superlearner:SL.library()]{Superlearner::SL.library()}}
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#' @param control similar as \code{\link[Superlearner:cvControl()]{Superlearner::cvControl()}}
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#' @param num_cf number of repetition done. The default is 5.
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#' @param n_split number of splits used, default `n_split = 3`
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#' @param rand_split logical value; if be FALSE `(default)`, discordant splits for exposure and outcome model are chosen systematically; otherwise chosen randomly.
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#' @param seed numeric value to reproduce the splits distribution
Copy file name to clipboardExpand all lines: R/aipw_single_p.R
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#' Estimate ATE using cross-fit procedure for AIPW estimator
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#' Estimate ATE using AIPW estimator with cross-fit algorithm (single repetition)
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#'
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#' @param data a data frame of tibble
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#' @param exposure name of exposure variable
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#' @param outcome name of outcome variable
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#' @param covarsT a vector of names of covaraites for treatment model
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#' @param covarsO a vector of names of covaraites for outcome model
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#' @param family.y it is the family for outcome model. It can `binomial() (default)` or `"gaussian"`
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#' @param learners similar as \code{\link[Superlearner:SL.library()]{Superlearner::SL.library()}}
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#' @param control similar as \code{\link[Superlearner:cvControl()]{Superlearner::cvControl()}}
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#' @param n_split number of splits
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#' @param rand_split logical value; if be TRUE, discordant splits for exposure and outcome model are chosen at random ; otherwise chosen systematically.
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#' @param seed numeric value to reproduce the splits
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#' @return a tibble of estimates
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#' @param n_split number of splits used, default `n_split = 3`
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#' @param rand_split logical value; if be FALSE `(default)`, discordant splits for exposure and outcome model are chosen systematically; otherwise chosen randomly.
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#' @param seed numeric value to reproduce the splits distribution
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#' @return a tibble of estimates.
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#'
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#' @import dplyr tibble tidyr purrr furrr tmle
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#'
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#' @importFrom stats binomial coef glm median plogis predict qlogis var
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