Personalized Imputation in metric spaces via conformal prediction: Applications in Predicting Diabetes Development with Continuous Glucose Monitoring Information

TL;DR

This paper introduces a personalized imputation framework for metric space data using conformal prediction, applied to improve diabetes onset prediction from continuous glucose monitoring data, demonstrating significant accuracy gains.

Contribution

It presents a novel two-step imputation and personalization framework for metric space data, specifically applied to functional glucose monitoring data in diabetes prediction.

Findings

Personalized imputation improves diabetes prediction accuracy by over 10%.

New conformal prediction algorithms tailored for metric spaces are developed.

The framework effectively handles missing distributional data in health monitoring applications.

Abstract

The challenge of handling missing data is widespread in modern data analysis, particularly during the preprocessing phase and in various inferential modeling tasks. Although numerous algorithms exist for imputing missing data, the assessment of imputation quality at the patient level often lacks personalized statistical approaches. Moreover, there is a scarcity of imputation methods for metric space based statistical objects. The aim of this paper is to introduce a novel two-step framework that comprises: (i) a imputation methods for statistical objects taking values in metrics spaces, and (ii) a criterion for personalizing imputation using conformal inference techniques. This work is motivated by the need to impute distributional functional representations of continuous glucose monitoring (CGM) data within the context of a longitudinal study on diabetes, where a significant fraction of patients do not have available CGM profiles. The importance of these methods is illustrated by evaluating the effectiveness of CGM data as new digital biomarkers to predict the time to diabetes onset in healthy populations. To address these scientific challenges, we propose: (i) a new regression algorithm for missing responses; (ii) novel conformal prediction algorithms tailored for metric spaces with a focus on density responses within the 2-Wasserstein geometry; (iii) a broadly applicable personalized imputation method criterion, designed to enhance both of the aforementioned strategies, yet valid across any statistical model and data structure. Our findings reveal that incorporating CGM data into diabetes time-to-event analysis, augmented with a novel personalization phase of imputation, significantly enhances predictive accuracy by over ten percent compared to traditional predictive models for time to diabetes.