Handling the uncertainty issue of missingness via a mixture-structure-based method.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Missing data are prevalent in real-world studies, posing challenges due to unknown missingness structures.
• Uncertainty arises from both the missing mechanism and the functional form of the missing data model.
• Missing not at random (MNAR) data presents particular difficulties for reliable statistical inference.

Purpose of the Study:

• To systematically examine sources of uncertainty in missing data, focusing on MNAR data.
• To propose a unified method for handling missing data uncertainty and conducting inference.
• To establish an identification framework for finite mixture models with MNAR data.

Main Methods:

• A two-step mixture-structure-based method is proposed, incorporating a model filtering pre-screening step.
• An expectation-maximization (EM)-based framework unifies uncertainty handling and inference.
• A two-layer postulated mixture is constructed to enhance flexibility and robustness.

Main Results:

• The method effectively handles uncertainty from both missing mechanisms and model forms.
• An identification framework is established for finite mixture models under MNAR.
• Demonstrated performance through simulation studies and application to the Medical Expenditure Panel Survey (MEPS).

Conclusions:

• The proposed method offers a robust approach to statistical inference with complex missing data structures.
• It addresses key uncertainties in missing data analysis, particularly for MNAR data.
• The unified framework simplifies the process of handling missing data and drawing reliable conclusions.