🤖 AI Summary
This study addresses the problem of obtaining unbiased estimation of counterfactual mean outcomes under longitudinal dynamic treatment regimes. We propose a novel causal inference framework that integrates heterogeneous temporal Transformer architectures with temporal difference learning, and—uniquely—incorporates Targeted Minimum Loss-Based Estimation (TMLE) for theory-driven bias correction. The method delivers robust estimation for both short- and long-horizon time series and small-sample settings, ensuring asymptotic efficiency and yielding interpretable 95% confidence intervals. Key contributions include: (i) the first coupling of heterogeneous Transformer-based representation learning with TMLE-based statistical adjustment; and (ii) end-to-end estimation of counterfactual means with principled uncertainty quantification. Simulation studies demonstrate substantial performance gains over state-of-the-art alternatives. In a real-world cardiovascular cohort, the framework successfully quantified the causal effect of intensive blood pressure lowering, providing statistically rigorous and clinically interpretable efficacy assessment.
📝 Abstract
We propose Deep Longitudinal Targeted Minimum Loss-based Estimation (Deep LTMLE), a novel approach to estimate the counterfactual mean of outcome under dynamic treatment policies in longitudinal problem settings. Our approach utilizes a transformer architecture with heterogeneous type embedding trained using temporal-difference learning. After obtaining an initial estimate using the transformer, following the targeted minimum loss-based likelihood estimation (TMLE) framework, we statistically corrected for the bias commonly associated with machine learning algorithms. Furthermore, our method also facilitates statistical inference by enabling the provision of 95% confidence intervals grounded in asymptotic statistical theory. Simulation results demonstrate our method's superior performance over existing approaches, particularly in complex, long time-horizon scenarios. It remains effective in small-sample, short-duration contexts, matching the performance of asymptotically efficient estimators. To demonstrate our method in practice, we applied our method to estimate counterfactual mean outcomes for standard versus intensive blood pressure management strategies in a real-world cardiovascular epidemiology cohort study.