Fast and efficient causal inference in large-scale data via subsampling and projection calibration

Estimating the average treatment effect in large-scale datasets faces significant computational and storage challenges. Subsampling has emerged as a critical strategy to mitigate these issues. This paper proposes a novel subsampling method that builds on the G-estimation method offering the double robustness property. The proposed method uses a small subset of data to estimate computationally complex nuisance parameters, while leveraging the full dataset for the computationally simple final estimation. To ensure that the resulting estimator remains first-order insensitive to variations in nuisance parameters, a projection approach is introduced to optimize the estimation of the outcome regression function and treatment regression function such that the Neyman orthogonality conditions are satisfied. It is shown that the resulting estimator is asymptotically normal and achieves the same convergence rate as the full data-based estimator when either the treatment or the outcome models is correctly specified. Additionally, when both models are correctly specified, the proposed estimator achieves the same asymptotic variance as the full data-based estimator. The finite sample performance of the proposed method is demonstrated through simulation studies and an application to birth data, comprising over 30 million observations collected over the past eight years. Numerical results indicate that the proposed estimator is nearly as computationally efficient as the uniform subsampling estimator, while achieving similar estimation efficiency to the full data-based G-estimator.