Estimation and Inference for High-Dimensional Generalized Linear Models with Knowledge Transfer

Area of Science:

• Epidemiology
• Biostatistics
• Computational Biology

Background:

• Transfer learning enhances epidemiological and medical studies by leveraging data from related diseases and populations.
• High-dimensional generalized linear models (GLMs) are crucial for analyzing complex biological data but can be limited by sample size.
• Integrating external data sources can improve the accuracy and robustness of statistical models.

Purpose of the Study:

• To propose a novel transfer learning algorithm, TransHDGLM, for high-dimensional generalized linear models (GLMs).
• To establish theoretical guarantees for the proposed method, including minimax rates of convergence and rate-optimality.
• To develop statistical inference procedures for regression coefficients and demonstrate improved accuracy in estimation and classification.

Main Methods:

• Development of the TransHDGLM algorithm for integrating target and source study data within a high-dimensional GLM framework.
• Theoretical analysis to establish minimax rates of convergence for parameter estimation.
• Derivation of asymptotic normality for a debiased estimator to enable statistical inference and confidence interval construction.

Main Results:

• The proposed TransHDGLM estimator is shown to be rate-optimal in terms of estimation accuracy.
• Statistical inference methods provide reliable confidence intervals for regression coefficients.
• Numerical simulations demonstrate significant improvements in estimation and inference accuracy compared to standard GLMs using only target data.

Conclusions:

• TransHDGLM effectively utilizes information from related studies to enhance high-dimensional GLMs.
• The method offers improved accuracy for disease classification, as evidenced by its application to colorectal cancer data.
• Transfer learning provides a powerful approach for leveraging multi-study data in epidemiological and medical research.