Post-selection inference in regression models for group testing data.

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Variable selection is crucial in logistic regression.
• Partially observed or error-prone response data presents inference challenges.
• Existing methods may lack reliability when combining variable selection and inference.

Purpose of the Study:

• To develop a robust methodology for valid statistical inference after variable selection.
• To address challenges posed by partially observed response data in logistic regression.
• To improve the reliability of covariate effect estimation in the presence of measurement error.

Main Methods:

• Utilized the expectation-maximization algorithm for maximum likelihood estimation.
• Applied LASSO penalization for effective variable selection.
• Extended post-selection inference techniques using the polyhedral lemma.

Main Results:

• The proposed methodology enables valid inference after variable selection with partially observed responses.
• The expectation-maximization algorithm with LASSO effectively handles missing information.
• Simulation studies demonstrate superior reliability compared to naive inference methods.

Conclusions:

• The developed method provides a reliable framework for statistical inference in complex logistic regression scenarios.
• Accounting for variable selection and response error is essential for accurate results.
• This approach enhances the trustworthiness of findings in data with imperfect response measurements.