stablemarkets/intro_bayesian_causal

Repository for Introduction to Bayesian Estimation of Causal Effects

A Practical Introduction to Bayesian Estimation of Causal Effects: Parametric and Nonparametric Approaches

This is the companion GitHub repository for the paper here: https://onlinelibrary.wiley.com/doi/10.1002/sim.8761.

Please cite the code examples here and discussed in the paper by citing the paper. The BibTex is

@article{doi:10.1002/sim.8761,
author = {Oganisian, Arman and Roy, Jason A.},
title = {A practical introduction to Bayesian estimation of causal effects: Parametric and nonparametric approaches},
journal = {Statistics in Medicine},
volume = {n/a},
number = {n/a},
pages = {1-34},
keywords = {BART, Bayesian, Bayesian nonparametric, causal inference, confounding, Dirichlet process, g-computation, Gaussian process},
doi = {10.1002/sim.8761},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.8761},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.8761}}

Software Dependencies

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All code and analyses generated in R version 3.6.3. We particularly rely on

• Stan to fit GPs and parametric causal models.
• ChiRP (https://stablemarkets.github.io/ChiRPsite/index.html) to fit DP models.
• BayesTree to fit BART models.

Directory

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• dose_response: contains code implementing model discussed in Section 3.1 of the paper. Code generates Figure 1a.
• partial_pool: contains code implementing model discussed in Section 3.2. Code generates Figure 1b.
• partial_pool: contains code implementing model discussed in Section 3.2. Code generates Figure 1b.
• g_comp: contains code estimating model discussed in Section 4.1 using Ridge prior in Equation (10). Generates Figure 3a.
• sensitivity: contains code implementing sensitivity analysis for ignorability violations (Section 5). Generates Figure 3b.
• Nonparametrics: contains code implementing DP, GP, and BART models. The file npbayes.R generates Figure 4a-c. The filte npbayes_ATE.R uses specified models to estimate average treatment effects (ATEs) and generates Figure 4d.

Causal and Bayesian Topics

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The paper touches on the following topics

• Standardization (i.e. g-computation in the point-treatment setting).
• G-computation for time-varying treatments.
  • Estimating effects of static regimes.
  • Estimating effects of dynamic regimes.
• Performing sensitivity analyses around causal assumptions via priors.

In terms of Bayesian models we touch upon

• Bayesian bootstrapping.
• Ridge-like and horseshoe priors for sparsity in high-dimensional regressions.
• Hierarchical priors that induce partial pooling of conditional causal effects.
• Dirichlet Process (DP) priors.
• Bayesian Additive Regression Trees (BART).
• Gaussian process (GP) priors.