Debiased inference for heterogeneous subpopulations in a high-dimensional logistic regression model

Area of Science:

• Statistics
• Bioinformatics
• Computational Biology

Background:

• Data heterogeneity is common in scientific studies, particularly with complex datasets and subpopulations.
• Analyzing high-dimensional binary responses in heterogeneous data presents significant inferential challenges.
• Existing methods often struggle to effectively quantify covariate effects across subpopulations.

Purpose of the Study:

• To develop a novel statistical inference method for high-dimensional logistic regression in the presence of heterogeneous subpopulations.
• To investigate and quantify heterogeneity in covariate effects across subpopulations.
• To test the equivalence and significance of covariate effects in complex datasets.

Main Methods:

• Proposed a fused group Lasso penalization method for overall sparsity and coefficient fusion.
• Developed a bias-corrected statistical inference method.
• Adapted proximal gradient and alternating direction method of multipliers (ADMM) for computational efficiency.
• Provided non-asymptotic analyses for the fused group Lasso and chi-squared approximations for debiased test statistics.

Main Results:

• The proposed method effectively accounts for data heterogeneity in high-dimensional logistic regression.
• Simulations demonstrated superior performance compared to existing methods.
• The fused group Lasso achieved sparsity and fusion of coefficients across subpopulations.
• Debiased test statistics were shown to admit chi-squared approximations.

Conclusions:

• The novel statistical inference method offers a robust approach for analyzing heterogeneous subpopulations with high-dimensional binary data.
• The method provides accurate and efficient statistical inference, outperforming existing techniques.
• Demonstrated practical utility through analysis of Cancer Cell Line Encyclopedia (CCLE) data.