# Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventions

arXiv: https://arxiv.org/abs/2306.09656 · HTML: https://mlsanity.com/paper/2306.09656/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 61 references that are in the map.
- First posted on arXiv 16 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [A Review of Challenges and Opportunities in Machine Learning for Health](https://mlsanity.com/paper/1806.00388/) (2018)
- [Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations](https://mlsanity.com/paper/2206.08311/) (2022)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Counterfactual Temporal Point Processes](https://mlsanity.com/paper/2111.07603/) (2021)
- [Counterfactual Neural Temporal Point Process for Estimating Causal Influence of Misinformation on Social Media](https://mlsanity.com/paper/2210.07518/) (2022)
- [A Bayesian Nonparametric Approach for Estimating Individualized Treatment-Response Curves](https://mlsanity.com/paper/1608.05182/) (2016)
- [An Interventionist Approach to Mediation Analysis](https://mlsanity.com/paper/2008.06019/) (2020)
- [Patient-Specific Effects of Medication Using Latent Force Models with Gaussian Processes](https://mlsanity.com/paper/1906.00226/) (2019)
- [Errors-in-variables Modeling of Personalized Treatment-Response Trajectories](https://mlsanity.com/paper/1906.03989/) (2019)
- [Time-dependent mediators in survival analysis: Modelling direct and indirect effects with the additive hazards model](https://mlsanity.com/paper/2011.13415/) (2020)

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

- [Learning Marked Temporal Point Process Explanations based on Counterfactual and Factual Reasoning](https://mlsanity.com/paper/2508.11943/) (2025)

## Abstract (arXiv)

Deciding on an appropriate intervention requires a causal model of a treatment, the outcome, and potential mediators. Causal mediation analysis lets us distinguish between direct and indirect effects of the intervention, but has mostly been studied in a static setting. In healthcare, data come in the form of complex, irregularly sampled time-series, with dynamic interdependencies between a treatment, outcomes, and mediators across time. Existing approaches to dynamic causal mediation analysis are limited to regular measurement intervals, simple parametric models, and disregard long-range mediator--outcome interactions. To address these limitations, we propose a non-parametric mediator--outcome model where the mediator is assumed to be a temporal point process that interacts with the outcome process. With this model, we estimate the direct and indirect effects of an external intervention on the outcome, showing how each of these affects the whole future trajectory. We demonstrate on semi-synthetic data that our method can accurately estimate direct and indirect effects. On real-world healthcare data, our model infers clinically meaningful direct and indirect effect trajectories for blood glucose after a surgery.