Bayesian Frameworks for Explicit Biological Age Estimation

ABSTRACT Biological age (BA) is a quantity of interest in insurance, and this paper explores the statistical foundations for estimating an individual's BA, proposing a semi‐parametric Bayesian model for its estimation using multiple quantitative and qualitative phenotypes. BA is modeled explicitly as a latent biological state that influences observable phenotypes. The proposed approach employs hierarchical Bayesian models based on a deep learning (DL) model to accommodate potential non‐linear relationships between phenotypes and BA. To explore the statistical features, we start by investigating the identifiability issues and deriving the Fisher information. Then, models are becoming increasingly complicated compared to the Bayesian DL model. A numerical illustration for clarity in the exposition, along with applications to both simulated and real datasets, is used to demonstrate the main insights from this study: explicit estimation of BA under a Bayesian approach avoids the identifiability problem and leads to more precise and interpretable estimation with respect to implicit approaches where BA is the implicit response of the individual's observed phenotypes.