• Introduction to the folders
• Introduction to files
• How to run the code

This repository contains code for implementing the simulation studies discussed in the paper. The four folders, namely sim1-consistency, sim2-weak-overlap, sim3-misspecification, and sim4-crossfitting-HD, correspond to the four subsections under the Simulation section in the paper.

Introduction to the folders

• sim1-consistency: This folder contains code for the simulation 1, which is about validating the statistical properties, such as consistency and asymptotic linearity, of the estimators.
• sim2-weak-overlap: This folder contains code for the simulation 2, which is about understanding the behaviors of the estimators under weak overlap.
• sim3-misspecification: This folder contains code for the simulation 3, which is about understanding the behaviors of the estimators under model misspecification.
• sim4-crossfitting-HD: This folder contains code for the simulation 4, which is about understanding the behaviors of the estimators when applied with cross-fitting.

Under each of these folders, there are three subfolders, namely DGPs, YinL, and YnotL.

• DGPs: This folder contains the data generating code and code for empirically computing the true ACE and its variance. The true ACE and its variance are stored at YinL-truth.Rdata and YnotL-truth.Rdata.
• YinL: This folder contains the code for estimating the ACE under the graphical model depicted in Figure 2(a), where the outcome $Y$ is within the district of the treatment $A$.
• YnotL: This folder contains the code for estimating the ACE under the graphical model depicted in Figure 2(c), where the outcome $Y$ is not within the district of the treatment $A$.

Apart from these folders, under sim1-consistency, there is one more folder, namely YinL-groupML.

• YinL-groupML: This folder contains the code for estimating the ACE under the graphical model depicted in Figure 2(a). In estimation, we treat the mediators $M$ and $L$ as a single multivariate variable, thereby simplifying the DGP to the front-door model, whereas for YinL, we strictly adhere to the DGP shown in Figure 2(a), treating the mediators $M$ and $L$ as separate variables.

Under each of these subfolders, there are seven more estimator subfolders:

• dsq: This folder save the messages generated when executing the code for estimation
• Onestep-dnorm: This folder contains the code for estimating the ACE using the one-step estimator $\psi^+_\text{dnorm}(\hat{Q})$.
• Onestep-densratio: This folder contains the code for estimating the ACE using the one-step estimator $\psi^+_\text{densratio}(\hat{Q})$.
• Onestep-bayes: This folder contains the code for estimating the ACE using the one-step estimator $\psi^+_\text{bayes}(\hat{Q})$.
• TMLE-dnorm: This folder contains the code for estimating the ACE using the TMLE estimator $\psi_\text{dnorm}(\hat{Q}^*)$.
• TMLE-densratio: This folder contains the code for estimating the ACE using the TMLE estimator $\psi_\text{densratio}(\hat{Q}^*)$.
• TMLE-bayes: This folder contains the code for estimating the ACE using the TMLE estimator $\psi_\text{bayes}(\hat{Q}^*)$.

The output from these estimators are saved in the output folder under each of these subfolders. Considering the large amount of output files generated, we omit the output files from this repository. However, the output files are summarized and stored in result.Rdata under each estimator folder.

For folders, sim3-misspecification and sim4-crossfitting-HD, there are several parent folders of these estimator folders:

• CF: This folder contains the code for implementing the cross-fitting procedure.
• Linear: This folder contains the code for estimating the ACE under linearity assumption.
• RF: This folder contains the code for estimating the ACE using the random forest algorithm.
• SL: This folder contains the code for estimating the ACE using the super learner algorithm.

Introduction to files

• joblist*.txt: This is the job file for simulation. Each line corresponds to one simulation. It is recommended to execute the job lists using parallel computing.
• write_job.R: This is the R script for producing the joblist*.txt files.
• main.R: Each line in the job list calls this main.R function to perform TMLE and one-step estimation. This file calls the flexCausal package for estimation and saves estimation results to the output folders, located under subfolders named after the estimators.
• organize.R: This file is used for organizing the output file from one-step estimators and TMLEs. It is called by the organize.txt file within each estimator folder.
• organize.txt: This file contains code for summarizing the files in the output folder. Run bash organize.txt in terminal to execute.
• plot.R: This is used for generating plots for sim1-consistency. This file calls plot-sub.R for generating smaller plots.
• plot-sub.R: This function is called by plot.R for generating smaller plots.
• table.R: This is used for generating tables in the paper.

How to run the code

We recommend running the code in parallel. To do so, follow these steps:

1. Under each estimator folder, run write_job.R to generate the job list file: Rscript write_job.R.
2. Submit the job list file to the cluster for parallel computing.
3. After the job is done, run organize.txt in the output folder to summarize the results: bash organize.txt.
4. Run plot.R to generate plots for sim1-consistency: Rscript plot.R. OR run table.R to generate tables for the paper: Rscript table.R. Note, remember to change the working directory to your local directory in the code before running the code.