Doubly Robust Network Treatment Effects

ISEF Category: Mathematics

Subcategory: Probability and Statistics  ·  Difficulty: Advanced  ·  Setup: Home Setup  ·  Time: Full Year

The Hook

One person's treatment can change another person's outcome. That breaks the usual rules of causal inference fast. In a social network, a rumor, app invite, or health behavior can spill over to friends, too. Your project can test how well a doubly robust estimator survives that mess.

What Is It?

This project studies how to measure cause and effect when people are connected. In a simple experiment, each person is treated or not treated, and you compare the two groups. In a network, that logic gets messy because one person's treatment can affect someone else nearby. That extra effect is called interference.

A doubly robust estimator is a method that stays reliable if at least one of two models is correct. One model predicts who gets treated. The other predicts the outcome. Think of it like using two backups on a long hike. If one map is a little wrong, the other can still keep you on track. In this topic, you test whether that idea still works when treatment spills across a network.

Why This Is a Good Topic

This is a strong science fair topic because it is mathematical, testable, and tied to a real problem. Social networks, public health campaigns, and online platforms all create interference, so the question matters outside class. You can study it with public network data, simulated data, or both. You will learn causal inference, estimation error, confidence intervals, and how assumptions change results.

Research Questions

• How does interference change the bias of a standard treatment effect estimator?
• What is the effect of network density on the accuracy of a doubly robust estimator?
• Does the doubly robust estimator stay close to the true treatment effect when the outcome model is misspecified?
• To what extent does treatment assignment imbalance affect estimator variance under spillovers?
• Which network structures, such as clustered, scale-free, or random graphs, lead to the largest estimation error?
• How does the coverage of confidence intervals change as spillover strength increases?

Basic Materials

• Laptop or desktop computer.
• Python installed on your computer.
• Jupyter Notebook or Google Colab.
• Public network data from Stanford SNAP.
• Spreadsheet software for organizing results.
• Graph visualization tool such as Gephi or NetworkX plots.
• Basic statistics reference, such as an AP Statistics or undergraduate probability text.

Advanced Materials

• Laptop or desktop computer.
• Python with NumPy, pandas, SciPy, statsmodels, and NetworkX.
• Jupyter Notebook or Google Colab.
• Public network data from Stanford SNAP or other open network datasets.
• Simulation code for treatment assignment and outcome generation.
• A reference implementation of causal inference methods.
• Access to a statistics textbook or research papers on interference and doubly robust estimation.

Software & Tools

• Python: Runs simulations, fits models, and computes estimator error across many network settings.
• Jupyter Notebook: Keeps code, notes, and results together in one place.
• NetworkX: Builds and analyzes graph structures for interference experiments.
• pandas: Organizes node-level, edge-level, and treatment outcome data.
• Matplotlib: Plots bias, variance, and confidence interval coverage.

Experiment Steps

1. Define the causal question you want to estimate, including who counts as treated and what spillover means in your network.
2. Choose a network setting to study, such as a public dataset or simulated graphs with known structure.
3. Decide which nuisance models you will fit, one for treatment assignment and one for outcomes.
4. Build a simulation plan that lets you compare the doubly robust estimator with simpler estimators under the same conditions.
5. Select evaluation metrics before running code, such as bias, variance, root mean squared error, and confidence interval coverage.
6. Plan sensitivity checks that change network structure, spillover strength, and model misspecification one at a time.

Common Pitfalls

• Ignoring interference and treating connected people as if they were independent, which can make the effect estimate look cleaner than it really is.
• Using a network dataset without checking whether nodes, edges, and attributes are complete, which can distort the treatment mechanism.
• Comparing estimators on different simulated data draws, which makes one method look better for the wrong reason.
• Fitting overly flexible models without holdout testing, which can hide overfitting inside the doubly robust pipeline.
• Reporting only one summary statistic, which can miss whether the estimator fails in clustered or highly connected parts of the network.

What Makes This Competitive

A competitive version of this project goes past a simple simulation. You would compare several network types, test misspecified nuisance models, and report how often confidence intervals actually cover the true effect. You could also separate direct effects from spillover effects, then test whether the estimator behaves differently for each one. Strong analysis and careful assumptions matter more than fancy code.

Project Variations

• Use a public friendship network and compare estimators under different levels of spillover.
• Simulate school or online community networks and test how cluster size changes estimator accuracy.
• Study whether the estimator behaves differently when treatment is binary versus continuous.

Learn More

• Stanford SNAP: Search the Stanford Network Analysis Project for open network datasets and graph benchmarks.
• NIH PubMed: Search for review articles on causal inference with interference and network spillovers.
• Journal of the American Statistical Association: Search for papers on doubly robust estimation and treatment effects under interference.
• MIT OpenCourseWare: Look for probability, statistics, and causal inference course materials from MIT.
• NIST/SEMATECH e-Handbook of Statistical Methods: Use it for confidence intervals, model checking, and regression basics.