Evaluating methods for Lasso selective inference in biomedical research: a comparative simulation study.

Area of Science:

• Biostatistics
• Statistical Inference
• Machine Learning in Healthcare

Background:

• Variable selection in regression is vital for biomedical data analysis.
• Classical frequentist theory does not cover inference after variable selection, leading to issues.
• Over-optimistic selection and replicability problems arise from ignoring post-selection inference.

Purpose of the Study:

• Compare selective inference methods for Lasso and adaptive Lasso.
• Evaluate confidence intervals from sample splitting, SI, and PoSI.
• Assess practical usability through simulations and real-data application.

Main Methods:

• Comparative simulation study of sample splitting, SI, and PoSI.
• Analysis of selective confidence intervals using R packages.
• Application to a publicly available biomedical dataset.

Main Results:

• SI showed acceptable frequentist properties but did not always attain claimed coverage, especially with adaptive Lasso.
• PoSI was overly conservative, exceeding nominal coverage but requiring significant computation.
• Sample splitting achieved acceptable coverage but was inefficient and yielded less accurate estimates.

Conclusions:

• Conditional inference (SI) is recommended for most Lasso applications.
• Sample splitting is a simpler alternative if efficiency is not paramount.
• PoSI is suitable for few predictors or controlling false positives; recommended for adaptive Lasso.
• Selective inference is valuable for assessing predictor importance uncertainty.