Network Causal Effect Estimation in the Presence of Contagion and Latent Confounding: A Likelihood-Based Approach

Core Concepts

This paper addresses the challenge of distinguishing between contagion and latent confounding when estimating causal effects in network settings, proposing novel likelihood ratio tests and an extension of auto-g-computation to account for both mechanisms.

Abstract

Bibliographic Information:

Wu, Y., & Bhattacharya, R. (2024). Network Causal Effect Estimation In Graphical Models Of Contagion And Latent Confounding. arXiv preprint arXiv:2411.01371v1.

Research Objective:

This research paper aims to develop a method for accurately estimating causal effects in network settings where both contagion (peer-to-peer influence) and latent confounding (unobserved background factors) may be present. The authors seek to distinguish between these two mechanisms and propose appropriate estimation strategies for different scenarios.

Methodology:

The authors utilize segregated graphical models (SGs) to represent both contagion and latent confounding within a network. They propose asymptotically valid likelihood ratio tests based on coding likelihoods to differentiate between dependence arising from contagion versus latent confounding. For causal effect estimation, they extend the auto-g-computation method to handle latent confounding by incorporating local structure parameterization and outcome regression modeling.

Key Findings:

• The proposed likelihood ratio tests demonstrate good calibration and power in distinguishing between contagion and latent confounding, with power increasing as the size of the network grows.
• The extended auto-g-computation method provides consistent and asymptotically normal estimates of causal effects, even in the presence of latent confounding, under certain network asymptotic conditions.
• The study highlights the importance of considering both contagion and latent confounding in network causal inference, as ignoring either mechanism can lead to biased estimates.

Main Conclusions:

The authors conclude that their proposed methods offer a robust framework for estimating causal effects in networks with full interference, accounting for both contagion and latent confounding. The likelihood ratio tests enable researchers to identify the underlying dependence mechanism, while the extended auto-g-computation method provides accurate effect estimates under different scenarios.

Significance:

This research significantly contributes to the field of causal inference in network settings by providing practical tools for addressing the challenge of disentangling contagion from latent confounding. The proposed methods have broad applicability in various domains, including social science, epidemiology, and public health, where understanding causal relationships within networks is crucial for effective intervention design.

Limitations and Future Research:

The study acknowledges limitations regarding the assumption that contagion and latent confounding cannot co-occur within the same layer of the SG. Future research could explore methods for handling such co-occurrences and develop sensitivity analysis techniques to assess the robustness of the proposed methods to this assumption. Additionally, investigating more sample-efficient estimators and methods robust to network uncertainty are promising avenues for future work.

Stats

Effective sample sizes of 200, 500, 1000, 2000, 3000, 4000, and 5000 were used to evaluate the likelihood ratio tests.
Synthetic networks of 200,000 units were generated, with each unit having 1 to 6 randomly assigned neighbors.
Ten real-world networks from the Stanford Large Network Dataset Collection (SNAP) were analyzed to assess the feasibility of obtaining sufficiently large 6-degree separated sets.
Node usage for the tests varied from 0.02% in the dense Twitch Gamers network to 2.85% in the sparser Deezer RO network.
Friendship networks of sizes 500, 1000, 2000, 3000, 4000, and 5000 were generated to evaluate the causal effect estimation method, with units having an average of 5 and at most 10 neighbors.

Quotes

Key Insights Distilled From

Network Causal Effect Estimation In Graphical Models Of Contagion And Latent Confounding

by Yufeng Wu, R... at arxiv.org 11-05-2024

https://arxiv.org/pdf/2411.01371.pdf

Deeper Inquiries

How can these methods be adapted to handle dynamic networks where connections evolve over time?

Adapting the methods to dynamic networks where connections evolve over time presents a significant challenge and would require substantial extensions. Here's a breakdown of the key considerations and potential approaches:
Challenges:

Time-varying Confounding: In dynamic settings, confounding factors can change over time and influence both network structure and outcomes. This necessitates more sophisticated methods for confounding control, potentially drawing upon techniques from longitudinal causal inference like marginal structural models or g-estimation.
Temporal Dependence: Outcomes and treatments in a dynamic network are not only influenced by current network structure but also by past interactions. This temporal dependence needs to be explicitly modeled, possibly through time-series analysis or dynamic Bayesian networks.
Causal Interpretation of Evolving Networks: Defining and identifying causal effects in dynamic networks is complex. The timing and nature of network changes can themselves be influenced by prior treatments and outcomes, leading to intricate feedback loops.
Potential Adaptations:

Time-stamped Data and Temporal Models: Utilize time-stamped data on network connections, treatments, and outcomes. Employ temporal graphical models like Dynamic Bayesian Networks or time-varying Chain Graphs to represent the evolving relationships.
Sliding Window Approach: Analyze the network in overlapping time windows, treating each window as a static network and applying the proposed methods. This simplification assumes limited influence beyond the chosen window size.
Stochastic Actor-Oriented Models: These models, commonly used in social network analysis, can capture the co-evolution of network ties and individual behavior. Integrating causal inference principles into these models could provide a framework for estimating effects in dynamic networks.
Key Considerations:

Computational Complexity: Dynamic network models often involve significantly higher computational complexity compared to static models.
Data Requirements: Longitudinal data with detailed information on network changes, treatments, and outcomes over time is crucial.

Could the assumption that contagion and latent confounding cannot co-occur be relaxed by using alternative graphical models or estimation techniques?

Relaxing the assumption that contagion and latent confounding cannot co-occur within the same layer of the graph is a crucial area for future research. Here's why it's challenging and some potential avenues:
Challenges:

Identifiability: As mentioned in the paper, even for simpler linear Gaussian models, the presence of both directed and bidirected edges between the same pair of variables (forming a "bow" structure) can lead to identifiability issues. This means the model parameters cannot be uniquely determined from the observed data, making causal effect estimation unreliable.
Model Complexity: Simultaneously modeling contagion and latent confounding within the same layer significantly increases model complexity. Finding tractable and interpretable models that can capture these intertwined effects is non-trivial.
Potential Approaches:

Alternative Graphical Models:

Ancestral Graphs: These graphs can represent uncertainty about the presence of latent confounders without explicitly modeling them. Exploring their use in the context of network interference could be promising.
Nested Markov Models: These models offer a more general framework for representing causal relationships and could potentially accommodate both contagion and latent confounding.

Instrumental Variable Approaches: If variables can be identified that influence network connections (contagion) but are independent of the latent confounders, they could serve as instruments to disentangle the effects.
Sensitivity Analysis: Develop sensitivity analysis techniques to assess the robustness of the estimated causal effects to varying degrees of co-occurrence between contagion and latent confounding.
Key Considerations:

Trade-off between Flexibility and Identifiability: More flexible models often come at the cost of increased identifiability challenges.
Stronger Assumptions: Relaxing the assumption might necessitate imposing other, potentially stronger, assumptions to ensure identifiability.

How can these findings inform the development of ethical and effective interventions in real-world networks, considering potential unintended consequences?

The ability to distinguish between contagion and latent confounding in networks has significant implications for designing ethical and effective interventions:
Targeted Interventions:

Contagion: If the analysis reveals strong evidence of contagion, interventions can be designed to leverage network effects. For example, peer-led education programs or influencer marketing campaigns can be effective in promoting behavior change.
Latent Confounding: When latent confounding is the primary driver, interventions should focus on addressing the underlying factors. For instance, if socioeconomic disparities are driving both network connections and health outcomes, interventions should target these disparities directly.
Mitigating Unintended Consequences:

Displacement Effects: Interventions targeting specific individuals or groups within a network can lead to displacement effects, where the problem shifts to other parts of the network. Understanding the interplay of contagion and latent confounding can help anticipate and mitigate such effects.
Equity and Fairness: Interventions should be carefully designed to avoid exacerbating existing inequalities. By accounting for latent confounding, interventions can be tailored to ensure equitable distribution of benefits.
Ethical Considerations:

Privacy: Collecting and analyzing network data raises significant privacy concerns. Interventions should be implemented with robust privacy-preserving mechanisms in place.
Informed Consent: Obtaining informed consent from individuals in a network can be challenging, especially when interventions exploit network effects. Ethical guidelines for informed consent in network interventions are crucial.
Examples:

Public Health Campaigns: Understanding whether a health behavior spreads through social influence or shared risk factors can inform the design of more effective public health campaigns.
Criminal Justice Reform: The findings can guide interventions aimed at reducing recidivism by targeting either social networks or underlying socioeconomic factors.
Key Takeaway:
By disentangling the roles of contagion and latent confounding, these methods provide valuable insights for developing interventions that are not only effective but also ethical and sensitive to the complexities of social networks.