  Epigenetic aging clocks play a pivotal role in estimating an individual's
biological age through the examination of DNA methylation patterns at numerous
CpG (Cytosine-phosphate-Guanine) sites within their genome. However, making
valid inferences on predicted epigenetic ages, or more broadly, on predictions
derived from high-dimensional inputs, presents challenges. We introduce a novel
U-learning approach via combinatory multi-subsampling for making ensemble
predictions and constructing confidence intervals for predictions of continuous
outcomes when traditional asymptotic methods are not applicable. More
specifically, our approach conceptualizes the ensemble estimators within the
framework of generalized U-statistics and invokes the H\'ajek projection for
deriving the variances of predictions and constructing confidence intervals
with valid conditional coverage probabilities. We apply our approach to two
commonly used predictive algorithms, Lasso and deep neural networks (DNNs), and
illustrate the validity of inferences with extensive numerical studies. We have
applied these methods to predict the DNA methylation age (DNAmAge) of patients
with various health conditions, aiming to accurately characterize the aging
process and potentially guide anti-aging interventions.
