Theory and Inference for Regression Models with Missing Responses and Covariates.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Missing data in regression models pose challenges for accurate statistical inference.
• Existing research often addresses either missing covariates or missing responses, but not both simultaneously.
• Handling both missing response and covariate data requires robust theoretical frameworks.

Purpose of the Study:

• To conduct a theoretical investigation of statistical inference for general regression models with both missing response and covariate data.
• To evaluate and compare three distinct estimation methods: complete case (CC), complete response (CR), and all case (AC) analysis.
• To analyze the theoretical properties, information loss, and asymptotic variances of these methods under MAR and MCAR assumptions.

Main Methods:

• Development of general likelihood expressions for each estimation scenario (CC, CR, AC).
• Application of the Expectation-Maximization (EM) algorithm for estimation scheme development.
• Theoretical analysis within the normal linear model framework, including bias investigation for CC.
• Derivation and comparison of asymptotic variances under MAR and MCAR missing data mechanisms.

Main Results:

• Analytical characterization of information loss for CC, CR, and AC methods.
• Comparison of asymptotic variances across the three methods, highlighting their relative efficiencies.
• Investigation into the potential bias introduced by the complete case analysis method.
• Validation of theoretical findings through a simulation study and a real-world dataset.

Conclusions:

• The study provides a comprehensive theoretical framework for handling missing data in regression models.
• Different missing data handling strategies (CC, CR, AC) exhibit varying levels of efficiency and potential bias.
• The findings offer guidance on selecting appropriate methods for statistical inference in the presence of incomplete response and covariate data.