Doubly robust tests of exposure effects under high-dimensional confounding

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Standard inferential procedures for regression parameters can be invalid after variable selection, especially in high-dimensional settings.
• Model misspecification is common in high-dimensional data, yet existing uniformly valid hypothesis tests often assume correct model specification.
• Developing robust statistical methods is crucial for reliable causal inference in complex, high-dimensional models.

Purpose of the Study:

• To propose novel hypothesis tests for low-dimensional regression parameters that are uniformly valid under weaker sparsity conditions.
• To develop doubly robust tests that remain valid even when working models for exposure or outcome are misspecified.
• To provide practical, easy-to-implement methods for causal effect estimation in high-dimensional settings.

Main Methods:

• Developing uniformly valid hypothesis tests for regression parameters under sparsity conditions.
• Utilizing a doubly robust approach by amending nuisance parameter estimation for model misspecification.
• Leveraging existing software for penalized maximum likelihood estimation, avoiding sample splitting.

Main Results:

• The proposed tests are uniformly valid under weaker sparsity assumptions than typically required.
• The tests maintain validity even when one of the working models (exposure or outcome) is misspecified.
• The methodology is shown to be straightforward to implement and effective through simulations and real-world data analysis.

Conclusions:

• The proposed doubly robust hypothesis tests offer a significant advancement for causal inference in high-dimensional statistics.
• These methods provide reliable inferential procedures even in the presence of model misspecification, a common issue in complex datasets.
• The practical implementation using standard penalized regression software makes these tests accessible for broader application in scientific research.