A New Mutual Information Estimator for Continuous Censored Variables

Estimating dependency relationships between variables is an important issue in statistics. Mutual information (MI) is a measure of dependency which quantifies the amount of shared information between two variables. It is free of distribution assumption and captures both linear and non-linear dependencies. MI estimation methods were primarily developed for datasets with exclusively discrete variables, exclusively continuous variables, or a mixture of both. In practice, complex variables containing both discrete and continuous values (discrete-continuous variables), specifically continuous censored variables, are often present in real datasets (e.g., biological measures from analytical tools with lower detection limit). Methods have been developed to handle discrete-continuous data, but their effectiveness on the specific case of continuous censored data has not yet been evaluated. We propose a new estimation method based on the decomposition of the MI formula, with a first part handling the censoring status of the data, and a second part handling its continuous section. This estimation method works as a correction, as it takes in parameter one MI estimator for continuous data, and makes it able to handling censoring. We constructed different simulation scenarios of pairs of correlated censored log-normal variables, by varying the censoring rate, correlation, and sample size. We evaluated our correction on a few existing estimators previously developed for continuous, mixed or discrete-continuous data. We compared the selected estimators, with and without the correction, on these different scenarios. We found that the correction globally enables to reduce bias, and allows convergence towards the true MI value as the number of observations increases.