Glucose values prediction five years ahead with a new framework of missing responses in reproducing kernel Hilbert spaces, and the use of continuous glucose monitoring technology

AEGIS study possesses unique information on longitudinal changes in circulating glucose from a random sample. However, some five-year outcomes, such as glycosylated hemoglobin (A1C), are over 40\% missing data. To alleviate this problem, this article proposes a new data analysis framework based on learning in reproducing kernel Hilbert spaces (RKHS) with missing responses. In particular, we extend the Hilbert-Schmidt dependence measure to this context introducing a new bootstrap procedure in which we prove to be consistent. In addition, we adapt or use existing algorithms/models of variable selection, regression, or conformal inference to acquire new clinical findings with the AEGIS study data. The fitted models allow: i) to identify new factors associated with long-term glucose changes; ii) to highly the usefulness of CGM technology predictive capacity; and iii) to improve and optimize clinical interventions based on expected glucose changes according to patients' baseline characteristics.