High-dimensional inference for dynamic treatment effects

Estimating dynamic treatment effects is a crucial endeavor in causal inference, particularly when confronted with high-dimensional confounders. Doubly robust (DR) approaches have emerged as promising tools for estimating treatment effects due to their flexibility. However, we showcase that the traditional DR approaches that only focus on the DR representation of the expected outcomes may fall short of delivering optimal results. In this paper, we propose a novel DR representation for intermediate conditional outcome models that leads to superior robustness guarantees. The proposed method achieves consistency even with high-dimensional confounders, as long as at least one nuisance function is appropriately parametrized for each exposure time and treatment path. Our results represent a significant step forward as they provide faster convergence rates and new robustness guarantees. The key to achieving these results lies in utilizing DR representations for intermediate conditional outcome models, which offer superior inferential performance while requiring weaker assumptions. Lastly, we examine finite sample behavior through simulations and a real data application.