Personalized Imputation in metric spaces via conformal prediction: Applications in Predicting Diabetes Development with Continuous Glucose Monitoring Information
arxiv(2024)
摘要
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.
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