Deconfounded and debiased estimation for high-dimensional linear regression under hidden confounding with application...

Area of Science:

• Statistics
• Bioinformatics
• Causal Inference

Background:

• Observational studies face challenges with hidden confounders in high-dimensional data, leading to biased causal effect estimates.
• Existing deconfounding methods often fail in high-dimensional settings or require prior knowledge of confounders.

Purpose of the Study:

• To propose a two-step deconfounded and debiased estimation method for high-dimensional linear regression with hidden confounding.
• To develop a technique that does not require prior knowledge of hidden confounders.

Main Methods:

• A two-step approach involving spectral transformation for deconfounding.
• Bias correction using convex optimization by inverting Karush-Kuhn-Tucker conditions, without assuming a sparse precision matrix.

Main Results:

• The proposed method effectively reduces hidden confounding and corrects estimation bias.
• Simulations demonstrate improved precision of coefficient estimates compared to existing methods.
• The method was applied to a dataset investigating Alzheimer's disease severity and cerebrospinal fluid tau levels.

Conclusions:

• The novel deconfounding and debiasing technique offers a robust solution for high-dimensional data with hidden confounders.
• This approach enhances causal inference accuracy in complex datasets.