# A flexible Bayesian g-formula for causal survival analyses with time-dependent confounding

arXiv: https://arxiv.org/abs/2402.02306 · HTML: https://mlsanity.com/paper/2402.02306/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 75 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 22 of 22)

- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [Bayesian Causal Inference: A Critical Review](https://mlsanity.com/paper/2206.15460/) (2022)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [Individualized Treatment Effects with Censored Data via Fully Nonparametric Bayesian Accelerated Failure Time Models](https://mlsanity.com/paper/1706.06611/) (2017)
- [Estimation of Causal Effects of Multiple Treatments in Observational Studies with a Binary Outcome](https://mlsanity.com/paper/2001.06483/) (2020)
- [Estimating heterogeneous survival treatment effect in observational data using machine learning](https://mlsanity.com/paper/2008.07044/) (2020)
- [Challenges in Obtaining Valid Causal Effect Estimates with Machine Learning Algorithms](https://mlsanity.com/paper/1711.07137/) (2017)
- [Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs](https://mlsanity.com/paper/1302.1566/) (2013)
- [Propensity Score Matching and Subclassification in Observational Studies with Multi-level Treatments](https://mlsanity.com/paper/1508.06948/) (2015)
- [Heterogeneous causal effects with imperfect compliance: a Bayesian machine learning approach](https://mlsanity.com/paper/1905.12707/) (2019)
- [Model interpretation through lower-dimensional posterior summarization](https://mlsanity.com/paper/1905.07103/) (2019)
- [A causal framework for classical statistical estimands in failure time settings with competing events](https://mlsanity.com/paper/1806.06136/) (2018)
- [Revisiting the g-null paradox](https://mlsanity.com/paper/2103.03857/) (2021)
- [Addressing Positivity Violations in Causal Effect Estimation using Gaussian Process Priors](https://mlsanity.com/paper/2110.10266/) (2021)
- [Doubly robust estimation and sensitivity analysis for marginal structural quantile models](https://mlsanity.com/paper/2210.04100/) (2022)
- [Causal comparative effectiveness analysis of dynamic continuous-time treatment initiation rules with sparsely measured outcomes and death](https://mlsanity.com/paper/1904.01668/) (2019)
- [G-computation and doubly robust standardisation for continuous-time data: a comparison with inverse probability weighting](https://mlsanity.com/paper/2006.16859/) (2020)
- [A flexible sensitivity analysis approach for unmeasured confounding with multiple treatments and a binary outcome with application to SEER-Medicare lung cancer data](https://mlsanity.com/paper/2012.06093/) (2020)
- [Bayesian Semiparametric Model for Sequential Treatment Decisions with Informative Timing](https://mlsanity.com/paper/2211.16393/) (2022)
- [A Bayesian approach to the g-formula](https://mlsanity.com/paper/1512.04809/) (2015)

## Built on by (most cited first, 1 of 1)

- [Bayesian Mediation Analysis for Individualized Treatment Rules](https://mlsanity.com/paper/2607.28804/) (2026)

## Abstract (arXiv)

In longitudinal observational studies with time-to-event outcomes, a common objective in causal analysis is to estimate the causal survival curve under hypothetical intervention scenarios. The g-formula is a useful tool for this analysis. To enhance the traditional parametric g-formula, we developed an alternative g-formula estimator, which incorporates the Bayesian Additive Regression Trees (BART) into the modeling of the time-evolving generative components, aiming to mitigate the bias due to model misspecification. We focus on binary time-varying treatments and introduce a general class of g-formulas for discrete survival data that can incorporate the longitudinal balancing scores. The minimum sufficient formulation of these longitudinal balancing scores is linked to the nature of treatment strategies, i.e., static or dynamic. For each type of treatment strategy, we provide posterior sampling algorithms. We conducted simulations to illustrate the empirical performance of the proposed method and demonstrate its practical utility using data from the Yale New Haven Health System's electronic health records.