## 1 Introduction: Background and Objective of the Work  
Biological age and its subsequent estimation are concepts that have found great interest in the bioinformatics literature over the last 50 years [1]. The dichotomy between \"real chronological age\" and the age expressed by the \"true global state\" [1] of the organisms has in fact been shown to be one of the most crucial biomarkers for possible pathological states. It is well known that chronological age represents one of the most important risk factors when it comes to predicting negative clinical outcomes [2]. At the same time, individuals of the same chronological age can present extremely different biological aging states, which can lead to completely different likelihood predictions when it comes to evaluating mortality and negative outcome risk. To generalize and to give a more comprehensive definition, biological age can be defined as the age resulting from a prediction produced by a statistical model incorporating a set of age-dependent variables and biomarkers. In recent years, several studies have explored the dichotomy between biological age and chronological age, focusing on different types of omics and imaging biomarkers. To give an example, [PERSON] et al. [3] estimated biological age using brain MRI scans. In the paper, they introduced the concept of brain aging which represents a crucial step to investigate specific pathologies and diseases that might affect brain structure and cognition. A further notable example in the literature is the seminal Horvath clock, built using methylation information [4]. This sets the ground for the new concept of biological age estimation from molecular data. Since then, other estimators based on epigenetics and DNA methylation have been developed such as PhenoAGE [5] and GrimAge [6]. These models are currently representing a relevant field of research in the area of epigenetics and aging. Analogously, metabolomics is currently seeing an increasing trend of interest in the development and study of models that could predict biological age starting from serum or plasma metabolomic data. The human metabolome has been in fact proven to correlate with (and possibly to predict) several phenotypical factors, such as gender [7; 8], BMI [9], and age-related pathological conditions, for example, Parkinson's [10; 11] and Alzheimer's [12; 13] diseases. Considering the interdependence between age and metabolism, some studies have concentrated on this research topic. For example, linear regression models were used [14] to grasp the relationship between age and the levels of a panel of metabolites, using also BMI as a covariate. Other similar approaches have been developed [15; 16; 17; 18; 19]. Due to the established correlations between age and metabolomic data, a few later studies have focused on the development of predictive models to estimate biological age. In ref. [2], the authors presented a study where urine metabolome data were used as a biological age estimator. The authors started with a healthy cohort and then tested the regression model in a sample of obese individuals undergoing bariatric surgery [2]. In [20], instead, the authors focused on the estimation of age from urine samples analyzed in a cohort of 301 healthy individuals. Here, we present an attempt to estimate the biological age using metabolomic data acquired on serum samples. A strength of our approach is the use of a collection of different cohorts of Parkinson's disease (PD) patients plus control individuals, recruited through the PROPAG-AGEING Horizon 2020 Project [21]. Previous results obtained with the PROPAG-AGEING cohorts have already identified promising biomarkers for the discrimination between controls and PD patients using miRNA [22], metabolites, and lipoproteins [23]. In this study, the aim was to develop a biological age prediction model to study the discrepancies observed between age estimated in control individuals and age predicted in patients, using a nuclear magnetic resonance (NMR)-based metabolomic approach.