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Instrumental Variable Estimation for Causal Inference in Longitudinal Data with Time-Dependent Latent Confounders

AAAI 2024 · Probabilistic and scientific modeling › Treatment effects · approach: Instrumental variable estimation · 10 citations (OpenAlex)

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Proposes TIFM, an LSTM-based latent factor model that infers a substitute for a time-dependent instrumental variable from covariate history, then plugs it into TSLS to estimate time-varying causal effects under latent time-dependent confounding.

Problem

Estimating time-varying causal effects from longitudinal observational data when time-dependent latent confounders affect both treatment and outcome, where a valid time-dependent instrumental variable is usually unavailable.

Approach

Learn a substitute of the unobserved time-dependent IV as a latent factor sequence produced by an LSTM over covariate and treatment history (a sequential factor model with a Kallenberg-style construction), then use it as the instrument in TSLS (or other IV estimators) at each time step.

Key results

• On synthetic data with 5k samples and p=1, TIFM's absolute error at time-step 10 is 0.005±0.001 versus 0.251 for the uncadjusted baseline.
• In the 6k p=1 table, TIFM at time-step 5 achieves 0.013±0.001 vs. best comparison (Xlearner) 0.028±0.000 and LDML 0.172±0.025.
• On the climate case study, TIFM identifies skin temperature as the most significant treatment effect on US precipitation, consistent with domain knowledge (qualitative result only).

Measured effects reported in the paper

Surprising findings

• Reported errors for the comparison estimators are not monotonic with time-step, and TIFM's error at p=3 rises at later steps (0.058 at step 20 for 5k).

Limitations

• Relies on the untestable assumption that history of covariates serves as a proxy for the latent IV; the no-single-cause-confounder assumption is required.
• Baseline in tables is an unadjusted estimate and comparisons are on synthetic data generated by the authors' own process.
• Evaluation on a single climate dataset is only qualitative and lacks ground truth.

Experimental setup

Datasets: Synthetic longitudinal data (AR(p) generation following Bica et al.) NCEP-NCAR Reanalysis 1

Benchmarks: Synthetic longitudinal datasets (p=1, p=3) NCEP-NCAR Reanalysis 1 case study

Metrics: absolute error |beta_hat - beta|

Baselines: LinearDML NonParamDML SparseLinearDML CausalForestDML KernelDML X-learner DRL KDRL

Builds on: Two-Stage Least Squares Time series deconfounder Counterfactual recurrent network DeepIV Kallenberg construction

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