A New Mutual Information Estimator for Continuous Censored Variables.

Area of Science:

• Statistics
• Information Theory
• Biostatistics

Background:

• Estimating dependency between variables is crucial in statistics.
• Mutual Information (MI) quantifies shared information, capturing linear and non-linear dependencies.
• Existing MI estimators often struggle with complex data types like censored continuous variables.

Purpose of the Study:

• To develop and evaluate a novel method for estimating mutual information in the presence of continuous censored data.
• To assess the effectiveness of this correction method on existing MI estimators.
• To improve dependency estimation for real-world datasets with detection limits.

Main Methods:

• Proposed a new MI estimation method by decomposing the MI formula into parts addressing censoring status and continuous data.
• Applied this correction to existing MI estimators for continuous, mixed, and discrete-continuous data.
• Evaluated performance using simulations with varying censoring rates, correlations, and sample sizes for censored log-normal variables.

Main Results:

• The proposed correction method globally reduced bias in MI estimation.
• Corrected estimators demonstrated improved convergence towards true MI values with increasing sample size.
• Effectiveness was observed across different simulation scenarios and tested estimators.

Conclusions:

• The developed correction method enhances the ability of existing MI estimators to handle continuous censored data.
• This approach offers a valuable tool for more accurate dependency analysis in fields with censored measurements.
• The findings support the use of this correction for improved statistical modeling with complex data.