Efficient Estimation of the Causal Effects of Stochastic Interventions

Authors: Nima Hejazi and David Benkeser

## What’s txshift?

The txshift R package is designed to provide facilities for the construction of efficient estimators of a causal parameter defined as the counterfactual mean of an outcome under stochastic mechanisms for treatment assignment (Dı́az and van der Laan 2012). txshift implements and builds upon a simplified algorithm for the targeted maximum likelihood (TML) estimator of such a causal parameter, originally proposed by Dı́az and van der Laan (2018), and makes use of analogous machinery to compute an efficient one-step estimator (Pfanzagl and Wefelmeyer 1985). txshift integrates with the sl3 package (Coyle et al. 2020) to allow for ensemble machine learning to be leveraged in the estimation procedure.

For many practical applications (e.g., vaccine efficacy trials), observed data is often subject to a two-phase sampling mechanism (i.e., through the use of a two-stage design). In such cases, efficient estimators (of both varieties) must be augmented to construct unbiased estimates of the population-level causal parameter. Rose and van der Laan (2011) first introduced an augmentation procedure that relies on introducing inverse probability of censoring (IPC) weights directly to an appropriate loss function or to the efficient influence function estimating equation. txshift extends this approach to compute IPC-weighted one-step and TML estimators of the counterfactual mean outcome under a shift stochastic treatment regime. The package is designed to implement the statistical methodology described in Hejazi et al. (2020) and extensions thereof.

## Installation

For standard use, we recommend installing the package from CRAN via

install.packages("txshift")

Note: If txshift is installed from CRAN, the sl3, an enhancing dependency that allows ensemble machine learning to be used for nuisance parameter estimation, won’t be included. We highly recommend additionally installing sl3 from GitHub via remotes:

remotes::install_github("tlverse/sl3@master")

For the latest features, install the most recent stable version of txshift from GitHub via remotes:

remotes::install_github("nhejazi/txshift@master")

To contribute, install the development version of txshift from GitHub via remotes:

remotes::install_github("nhejazi/txshift@devel")

## Example

To illustrate how txshift may be used to ascertain the effect of a treatment, consider the following example:

library(txshift)
#> txshift v0.3.6: Efficient Estimation of the Causal Effects of Stochastic
#> Interventions
library(sl3)
set.seed(429153)

# simulate simple data
n_obs <- 500
W <- replicate(2, rbinom(n_obs, 1, 0.5))
A <- rnorm(n_obs, mean = 2 * W, sd = 1)
Y <- rbinom(n_obs, 1, plogis(A + W + rnorm(n_obs, mean = 0, sd = 1)))

# now, let's introduce a a two-stage sampling process
C_samp <- rbinom(n_obs, 1, plogis(W + Y))

# fit the full-data TMLE (ignoring two-phase sampling)
tmle <- txshift(
W = W, A = A, Y = Y, delta = 0.5,
estimator = "tmle",
g_exp_fit_args = list(
fit_type = "sl",
sl_learners_density = Lrnr_density_hse$new(Lrnr_hal9001$new())
),
Q_fit_args = list(fit_type = "glm", glm_formula = "Y ~ .")
)
tmle
#> Counterfactual Mean of Shifted Treatment
#> Intervention: Treatment + 0.5
#> txshift Estimator: tmle
#> Estimate: 0.7672
#> Std. Error: 0.0192
#> 95% CI: [0.7275, 0.8027]

# fit a full-data one-step estimator for comparison (again, no sampling)
os <- txshift(
W = W, A = A, Y = Y, delta = 0.5,
estimator = "onestep",
g_exp_fit_args = list(
fit_type = "sl",
sl_learners_density = Lrnr_density_hse$new(Lrnr_hal9001$new())
),
Q_fit_args = list(fit_type = "glm", glm_formula = "Y ~ .")
)
os
#> Counterfactual Mean of Shifted Treatment
#> Intervention: Treatment + 0.5
#> txshift Estimator: onestep
#> Estimate: 0.7671
#> Std. Error: 0.0192
#> 95% CI: [0.7274, 0.8027]

# fit an IPCW-TMLE to account for the two-phase sampling process
tmle_ipcw <- txshift(
W = W, A = A, Y = Y, delta = 0.5, C_samp = C_samp, V = c("W", "Y"),
estimator = "tmle", max_iter = 5, eif_reg_type = "glm",
samp_fit_args = list(fit_type = "glm"),
g_exp_fit_args = list(
fit_type = "sl",
sl_learners_density = Lrnr_density_hse$new(Lrnr_hal9001$new())
),
Q_fit_args = list(fit_type = "glm", glm_formula = "Y ~ .")
)
tmle_ipcw
#> Counterfactual Mean of Shifted Treatment
#> Intervention: Treatment + 0.5
#> txshift Estimator: tmle
#> Estimate: 0.7602
#> Std. Error: 0.0203
#> 95% CI: [0.7181, 0.7978]

# compare with an IPCW-agumented one-step estimator under two-phase sampling
os_ipcw <- txshift(
W = W, A = A, Y = Y, delta = 0.5, C_samp = C_samp, V = c("W", "Y"),
estimator = "onestep", eif_reg_type = "glm",
samp_fit_args = list(fit_type = "glm"),
g_exp_fit_args = list(
fit_type = "sl",
sl_learners_density = Lrnr_density_hse$new(Lrnr_hal9001$new())
),
Q_fit_args = list(fit_type = "glm", glm_formula = "Y ~ .")
)
os_ipcw
#> Counterfactual Mean of Shifted Treatment
#> Intervention: Treatment + 0.5
#> txshift Estimator: onestep
#> Estimate: 0.76
#> Std. Error: 0.0204
#> 95% CI: [0.7179, 0.7976]

## Issues

If you encounter any bugs or have any specific feature requests, please file an issue. Further details on filing issues are provided in our contribution guidelines.

## Contributions

Contributions are very welcome. Interested contributors should consult our contribution guidelines prior to submitting a pull request.

## Citation

After using the txshift R package, please cite the following:

    @article{hejazi2020efficient,
author = {Hejazi, Nima S and {van der Laan}, Mark J and Janes, Holly
E and Gilbert, Peter B and Benkeser, David C},
title = {Efficient nonparametric inference on the effects of
stochastic interventions under two-phase sampling, with
applications to vaccine efficacy trials},
year = {2020},
doi = {10.1111/biom.13375},
url = {https://doi.org/10.1111/biom.13375},
journal = {Biometrics},
publisher = {Wiley Online Library}
}

@article{hejazi2020txshift-joss,
author = {Hejazi, Nima S and Benkeser, David C},
title = {{txshift}: Efficient estimation of the causal effects of
stochastic interventions in {R}},
year  = {2020},
doi = {10.21105/joss.02447},
url = {https://10.21105.joss.02447},
journal = {Journal of Open Source Software},
publisher = {The Open Journal}
}

@software{hejazi2020txshift-rpkg,
author = {Hejazi, Nima S and Benkeser, David C},
title = {{txshift}: Efficient Estimation of the Causal Effects of
Stochastic Interventions},
year  = {2020},
doi = {10.5281/zenodo.4070042},
url = {https://CRAN.R-project.org/package=txshift},
note = {R package version 0.3.4}
}

## Funding

The development of this software was supported in part through a grant from the National Institutes of Health: T32 LM012417-02.

MIT License

Copyright (c) 2017-2021 Nima S. Hejazi

Permission is hereby granted, free of charge, to any person obtaining a copy
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SOFTWARE.

## References

Coyle, Jeremy R, Nima S Hejazi, Ivana Malenica, and Oleg Sofrygin. 2020. sl3: Modern Pipelines for Machine Learning and Super Learning. https://github.com/tlverse/sl3. https://doi.org/10.5281/zenodo.1342293.

Coyle, Jeremy R, Nima S Hejazi, and Mark J van der Laan. 2020. hal9001: The Scalable Highly Adaptive Lasso. https://github.com/tlverse/hal9001. https://doi.org/10.5281/zenodo.3558313.

Dı́az, Iván, and Nima S Hejazi. 2020. “Causal Mediation Analysis for Stochastic Interventions.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 82 (3): 661–83. https://doi.org/10.1111/rssb.12362.

Dı́az, Iván, and Mark J van der Laan. 2011. “Super Learner Based Conditional Density Estimation with Application to Marginal Structural Models.” The International Journal of Biostatistics 7 (1): 1–20.

———. 2012. “Population Intervention Causal Effects Based on Stochastic Interventions.” Biometrics 68 (2): 541–49.

———. 2018. “Stochastic Treatment Regimes.” In Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies, 167–80. Springer Science & Business Media.

Hejazi, Nima S, Jeremy R Coyle, and Mark J van der Laan. 2020. “hal9001: Scalable Highly Adaptive Lasso Regression in R.” Journal of Open Source Software 5 (53): 2526. https://doi.org/10.21105/joss.02526.

Hejazi, Nima S, Mark J van der Laan, Holly E Janes, Peter B Gilbert, and David C Benkeser. 2020. “Efficient Nonparametric Inference on the Effects of Stochastic Interventions Under Two-Phase Sampling, with Applications to Vaccine Efficacy Trials.” Biometrics. https://doi.org/10.1111/biom.13375.

Pfanzagl, J, and W Wefelmeyer. 1985. “Contributions to a General Asymptotic Statistical Theory.” Statistics & Risk Modeling 3 (3-4): 379–88.

Rose, Sherri, and Mark J van der Laan. 2011. “A Targeted Maximum Likelihood Estimator for Two-Stage Designs.” The International Journal of Biostatistics 7 (1): 1–21.