Estimating the treatment effect over time under general interference through deep learner integrated TMLE

TL;DR

This work addresses estimating time-dependent treatment effects under general interference in networked populations using observational data. It introduces DeepNetTMLE, a framework that embeds a deep learning outcome model within TMLE and employs domain adversarial training to learn intervention-invariant representations, mitigating time-varying confounding. Through extensive SIR-based simulations of quarantine policies, DeepNetTMLE demonstrates lower bias, tighter confidence intervals, and better coverage than baseline methods, enabling more reliable and cost-aware quarantine recommendations. The approach offers a principled path for causal inference with interference in dynamic networks and has potential for informing public health interventions when randomized trials are infeasible.

Abstract

Understanding the effects of quarantine policies in populations with underlying social networks is crucial for public health, yet most causal inference methods fail here due to their assumption of independent individuals. We introduce DeepNetTMLE, a deep-learning-enhanced Targeted Maximum Likelihood Estimation (TMLE) method designed to estimate time-sensitive treatment effects in observational data. DeepNetTMLE mitigates bias from time-varying confounders under general interference by incorporating a temporal module and domain adversarial training to build intervention-invariant representations. This process removes associations between current treatments and historical variables, while the targeting step maintains the bias-variance trade-off, enhancing the reliability of counterfactual predictions. Using simulations of a ``Susceptible-Infected-Recovered'' model with varied quarantine coverages, we show that DeepNetTMLE achieves lower bias and more precise confidence intervals in counterfactual estimates, enabling optimal quarantine recommendations within budget constraints, surpassing state-of-the-art methods.

Figures (7)

• Figure 1: Current challenge for estimating causal effect under interference with time-dependent intervention assignments. By changing the order of quarantine treatment, the potential outcome differs. The cross-sectional analysis at the last time point fails to illustrate the difference between two treatment plans.
• Figure 2: Network structure of outcome model. The solid and dashed lines indicate forward and backward propagation, respectively.
• Figure 3: Performance comparison between linear regression and deep learning model in predicting the cumulative infliction of disease for uniform and power-law random graph with $N=500, 1000$ and $2000$ under constant strategy with budget covering all population. The deep learning model has a reception field over the last nine time steps of observational data. Bias and ESE are viewed using the left y-axis in red. The cover is shown in blue on the right y-axis. The grey horizontal dash indicated the zero as a benchmark line for bias estimation.
• Figure 4: Performance comparison between linear regression and deep learning model in predicting the cumulative infliction of disease for uniform and power-law random graph with $N=500, 1000$ and $2000$ under constant strategy with budget covering $50\%$ population and most connected are exposed. The deep learning model has a reception field over the last ten time steps of observational data. Bias and ESE are viewed using the left y-axis in red. The cover is shown in blue on the right y-axis. The grey horizontal dash indicated the zero as a benchmark line for bias estimation.
• Figure 5: Average performance improvement comparing DeepNetTMLE over linear regression w/ and w/o unsupervised domain adaptation, respectively. The results are averaged over four scenarios (CC, CW, WC, Flexible) and all exposure probability levels. The grey horizontal line indicated the zero as a benchmark line for improvement.