Metabolomic Age (MileAge) predicts health and lifespan: a comparison of multiple machine learning algorithms

20

Molecular ageing clocks estimate an individual’s biological age. Our aim was 21 to compare multiple machine learning algorithms for developing ageing clocks from nuclear 22 magnetic resonance (NMR) spectroscopy metabolomics data. To validate how well each 23 ageing clock predicted age-related morbidity and lifespan, we assessed their associations with 24 multiple health indicators (e.g., telomere length and frailty) and all-cause mortality. 25

The UK Biobank is a multicentre observational health study of middle-aged and 26 older adults. The Nightingale Health platform was used to quantify 168 circulating plasma 27 metabolites at the baseline assessment from 2006 to 2010. We trained and internally 28 validated 17 machine learning algorithms including regularised regression, kernel-based 29

and ensembles. Metabolomic age (MileAge) delta was defined as the difference 30 between predicted and chronological age. 31

The sample included 101,359 participants (mean age = 56.53 years, SD = 8.10). 32 Most metabolite levels varied by chronological age. The nested cross-validation mean 33 absolute error (MAE) ranged from 5.31 to 6.36 years. 31.76% of participants had an age-bias 34 adjusted MileAge more than one standard deviation (3.75 years) above or below the mean. A 35 Cubist rule-based regression model overall performed best at predicting health outcomes. The 36 all-cause mortality hazard ratio (HR) comparing individuals with a MileAge delta more than 37 one standard deviation above and below the mean was HR = 1.52 (95% CI 1.41-1.64, p < 38 0.001) over a median follow-up of 13.87 years. Individuals with an older MileAge were 39 frailer, had shorter telomeres, were more likely to have a chronic illness and rated their health 40 worse. 41

Metabolomic ageing clocks derived from multiple machine learning algorithms 42 were robustly associated with health indicators and mortality. Our metabolomic ageing clock 43 (MileAge) derived from a Cubist rule-based regression model can be incorporated in 44 research, and may find applications in health assessments, risk stratification and proactive 45 health tracking. 46 47

ageing clocks; biological age; biomarkers; machine learning; metabolomics 48 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 3

49 Chronological age, the time elapsed since birth, is a powerful predictor of health and disease 50 (Mutz, Roscoe, & Lewis, 2021). However, there is considerable heterogeneity in health 51 status, lifestyle and the physical signs of ageing between individuals of the same 52 chronological age. This variability may partly reflect individual differences in biological 53 ageing, which is the process of accumulating molecular and cellular damage that results in a 54 progressive decline in physiological functioning (Moqri et al., 2023). While our 55 chronological age cannot be altered, biological ageing trajectories in humans may be 56 modifiable, or even reversible. Therefore, developing reliable measures of biological age is 57 an important priority in biomedical research and population health. 58 59 Although there is no single biological marker of biological ageing, several hallmarks such as 60 telomere length shortening have been identified (López-Otín, Blasco, Partridge, Serrano, & 61 Kroemer, 2023). Clinical and population studies of age-related biological changes have also 62 examined physiological measures of grip strength and cardiovascular function (Mutz, 63 Hoppen, Fabbri, & Lewis, 2022; Mutz & Lewis, 2021; Mutz, Young, & Lewis, 2022), blood-64 based biomarkers (Nakamura, Miyao, & Ozeki, 1988), inflammatory markers (Franceschi, 65 Garagnani, Parini, Giuliani, & Santoro, 2018) and frailty (Hoogendijk et al., 2019). 66 67 Molecular “omics” and neuroimaging data such as DNA methylation (Hannum et al., 2013; 68 Horvath & Raj, 2018; Lu et al., 2019) and structural magnetic resonance imaging (Cole & 69 Franke, 2017) have facilitated the development of biological ageing clocks (Rutledge, Oh, & 70 Wyss-Coray, 2022; Solovev, Shaposhnikov, & Moskalev, 2020). Ageing clocks are usually 71 developed using machine learning algorithms that identify relationships between 72 chronological age and molecular data. The difference between predicted age, which 73 approximates biological age, and chronological age is associated with health outcomes 74 (Macdonald-Dunlop et al., 2022). Ageing clocks provide a more holistic picture of a person’s 75 health and are conceptually easier to understand than most individual molecular markers as 76 they are expressed in unit of years. 77 78 Population-scale metabolomics, the study of small molecules, i.e., metabolites, within cells, 79 tissues or organisms, is increasingly incorporated into biological ageing research (Panyard, 80 Yu, & Snyder, 2022). Metabolites are the products of metabolism, for example when food is 81 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 4 converted to energy. While many initial metabolomics studies were limited to few 82 metabolites and small samples, technological advancements have enabled the population-83 scale profiling of multiple molecular pathways (Soininen, Kangas, Würtz, Suna, & Ala-84 Korpela, 2015). Simultaneously quantifying hundreds or thousands of metabolites can 85 provide unprecedented snapshots of an individual’s physiological state. Metabolomic profiles 86 predict many common incident diseases (Buergel et al., 2022) and mortality risk (Deelen et 87 al., 2019). Over the past decade, studies have characterised associations between 88 chronological age and metabolomic biomarkers (Lawton et al., 2008; Menni et al., 2013; Yu 89 et al., 2012). The first study to develop a “metabolite-derived age variable” showed that a 90 panel of 22 metabolites explained 59% of the variance in chronological age. A linear 91 combination of these metabolites was correlated with age-related clinical measures 92 independent of chronological age (Menni et al., 2013). The first study to develop a biological 93 ageing clock from metabolomics data showed that the difference between predicted and 94 chronological age, metabolomic age delta, was associated with a higher disease burden and 95 higher mortality (Hertel et al., 2016). Analyses in other samples, for example the Airwave 96 Health Monitoring Study in the UK (Robinson et al., 2020) and the Dutch BBMRI-NL 97 consortium (van den Akker et al., 2020), have since replicated some of these findings. 98 Metabolomics is amongst the most powerful omics data for biological age estimation 99 (Solovev et al., 2020) and prediction of disease (Macdonald-Dunlop et al., 2022). 100 101 The aim of this study was to compare multiple machine learning algorithms for developing 102 ageing clocks from nuclear magnetic resonance (NMR) spectroscopy metabolomics data in 103 more than 100,000 participants in the UK Biobank (Bycroft et al., 2018). These data provide 104 an unprecedented resource to develop ageing clocks and represent one of the largest single 105 NMR metabolomics databases to date. To validate how well each ageing clock predicted age-106 related morbidity and lifespan, and captured biological signal beyond that approximated by 107 chronological age (Hertel et al., 2019), we assessed their associations with multiple health 108 indicators (e.g., telomere length and frailty) and all-cause mortality. 109 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 5

110 Study population 111 The UK Biobank is a prospective health study of over 500,000 UK residents aged 37–73 who 112 were recruited between 2006 and 2010. Individuals registered with the UK National Health 113 Service (NHS) and living within a 25-mile (~40 km) radius of one of 22 assessment centres 114 were invited to participate (Bycroft et al., 2018). Participants provided data on their 115 sociodemographic characteristics, health behaviours and medical history, underwent physical 116 examination and had blood and urine samples taken. There is extensive record linkage, for 117 example with national death registries, hospital inpatient records and primary care data. 118 119 Metabolomic biomarker quantification 120 Nuclear magnetic resonance (NMR) spectroscopy metabolomic biomarkers were quantified 121 in non-fasting blood plasma samples taken at the baseline assessment. The Nightingale 122 Health platform ascertains 168 circulating metabolites using a high-throughput standardized 123 protocol for sample quality control, preparation, data storage and automated analyses (Würtz 124 et al., 2017). The metabolites span multiple pathways, including lipoprotein lipids in 14 125 subclasses, circulating fatty acids and fatty acid compositions, as well as low-molecular 126 weight metabolites, such as amino acids, ketone bodies and glycolysis metabolites. Most 127 measures are highly correlated (r > 0.9) with routine clinical chemistry assays (Würtz et al., 128 2017). For further details on sample preparation and quality control procedures, see 129 https://biobank.ndph.ox.ac.uk/ukb/ukb/docs/nmrm_companion_doc.pdf. We used the first 130 release of metabolomics data (March 2021) on a random subset of 118,019 participants. 131 132 Machine learning 133 We evaluated 17 machine learning algorithms, including regularised linear regression, latent 134 variable modelling, instance-based learning, non-parametric regression, kernel-based 135 methods, tree-based models, rule-based models and ensemble methods (Panel 1). To 136 internally validate each algorithm in predicting chronological age from plasma metabolites, 137 we implemented 10×5 nested cross-validation (Figure 1a). Nested cross-validation is 138 preferred for internal validation over other existing approaches as it provides more accurate 139 error estimation (Bates, Hastie, & Tibshirani). We split the data into 10 folds of equal size, to 140 which individuals were allocated at random while preserving the chronological age 141 distribution of the full analytical sample (Figure 1b). 142 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 6 Panel 1. Overview of the machine learning algorithms used in this study. 143 144 Ridge regression: linear regression model with a penalty term (L2 regularization) to shrink the 145 magnitude of coefficient estimates towards zero (Hoerl & Kennard, 1970). 146 147 Least Absolute Shrinkage and Selection Operator (LASSO): linear regression model with a 148 penalty term (L1 regularization) to shrink the magnitude of coefficient estimates towards 149 zero. This technique can result in sparse models as variable selection is performed by 150 reducing some coefficient estimates exactly equal to zero (Tibshirani, 1996). 151 152 Elastic net: linear regression model that combines the L1 and L2 penalty terms of LASSO and 153 Ridge regression. This technique reduces the magnitude of some coefficient estimates 154 towards zero and can perform variable selection by reducing some coefficient estimates 155 exactly equal to zero (Zou & Hastie, 2005). 156 157 Partial least squares regression (PLSR): latent variable model that extracts a set of latent 158 factors that best explain the covariance between the predictors and outcome. These factors 159 are then used as predictors in a linear regression model (Wold, Sjöström, & Eriksson, 2001). 160 161 K-nearest neighbors (KNN): instance-based learning model which uses the weighted average 162 outcome of the k nearest data points to make predictions. In this context, “nearest” is usually 163 determined by a distance metric such as the Minkowski distance (Cover & Hart, 1967). 164 165 Multivariate adaptive regression splines (MARS): non-parametric regression model that 166 creates piecewise linear approximations of the relationship between the predictors and 167 outcome. This technique can model non-linear associations and interactions between the 168 predictors (J. Friedman, H., 1991). 169 170 MARS ensemble: ensemble method that combines the predictions of multiple MARS models 171 to improve the predictive accuracy and stability of the model (Kuhn & Johnson, 2013a). 172 173 Support vector regression (SVR): kernel-based method that seeks to identify a hyperplane 174 that best models the relationships between the predictors and outcome. This variation of the 175 support vector machine algorithm (Boser, Guyon, & Vapnik, 1992) was adapted for 176 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 7 regression and can employ a range of kernels to transform the data to a higher-dimensional 177 space, allowing for complex non-linear associations (Drucker, Burges, Kaufman, Smola, & 178 Vapnik, 1996). We tested linear, polynomial and radial basis function kernels. 179 180 Regression tree: technique that models the relationship between the predictors and outcome 181 by creating a tree-like structure of decision rules based on values of the predictors. Decision 182 trees are interpretable and can incorporate non-linear relationships and higher-order 183 interactions in the data (Breiman, Friedman, Olshen, & Stone, 1984). 184 185 Bagging: ensemble method that combines the predictions of multiple regression trees. 186 Bootstrapped aggregating (“bagging”) involves training regression trees on multiple, 187 randomly selected (“bootstrapped”) samples of the data. Bagging can improve the stability 188 and accuracy of decision tree models (Breiman, 1996). 189 190 Random forest: ensemble method that combines predictions of multiple regression trees. 191 Each tree is trained on a random subset of the data and, at each split, a subset of predictors, 192 reducing the correlation between decision trees in the ensemble (Breiman, 2001). 193 194 Extreme gradient boosting (XGBoost): ensemble method that builds decision trees 195 sequentially by implementing a gradient descent algorithm that seeks to minimize errors from 196 previous models while increasing the influence (“boosting”) of highly predictive models. 197 More complex models are penalised through L1 and L2 regularization to avoid overfitting (T. 198 Chen & Guestrin, 2016). 199 200 Bayesian additive regression trees (BART): ensemble method that uses Bayesian techniques 201 to iteratively construct and update multiple decision trees. Regularization priors force each 202 tree to explain only a subset of the relationship between the predictors and outcome, thereby 203 preventing overfitting (Chipman, George, & McCulloch, 2010). 204 205 Cubist rule-based regression: ensemble model that that derives rules from decision trees and 206 fits linear regression models for the subset of the data defined by each rule. The model 207 incorporates boosting techniques and may adjust predictions based on k-nearest neighbors 208 (Kuhn & Johnson, 2013b; Quinlan, 1992). 209 210 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 8 RuleFit ensemble: ensemble method that uses a tree-based model (XGBoost) to predict an 211 outcome and subsequently derives rules. LASSO is then used to select the most predictive 212 rules, resulting in a sparse linear model (J. H. Friedman & Popescu, 2008). 213 214 For each iteration of the outer loop of the nested cross-validation, 9/10 folds combined served 215 as the training set and the tenth fold served as the test set. The 90% training sets were further 216 divided into five equal size sets, and we performed 5-fold cross validation to empirically 217 identify, for each algorithm, the hyperparameter combination that resulted in the lowest 218 cross-validation mean absolute error (MAE). Tuning grids were set up using a maximum 219 entropy space-filling design. The size of each tuning grid was determined by the number of 220 available hyperparameters, type of hyperparameter (continuous, discrete or categorical) and 221 computational constraints. We tested up to ten values for each hyperparameter, resulting in 222 tuning grid sizes between ten (for Ridge regression) and 3125 (for XGBoost). Further details, 223 including pre-processing requirements, are available in Table S1. The model specifications 224 with the lowest 5-fold cross-validation MAE were subsequently fit in the 90% training sets, 225 and performance was assessed by calculating the MAE, root-mean-square error (RMSE), 226 Pearson correlation coefficient (r) and the coefficient of determination (R2) in the 10% test 227 sets. We also examined the average magnitude of discrepancy in predictive performance 228 between the training and test sets, extrapolation beyond the chronological age range in the 229 data and the computing hours required for hyperparameter tuning for each model. 230 231 Metabolomic ageing clocks 232 Individual-level age predictions for all participants were obtained by aggregating the 233 predictions of the ten test sets of the outer loop of the nested cross-validation. Metabolomic 234 age delta (MileAge delta) was calculated as the difference between predicted and 235 chronological age, with positive values representing an older predicted than chronological 236 age and negative values representing a younger predicted than chronological age. Given that 237 ageing clocks overestimate age in young individuals and underestimate age in older 238 individuals, we regressed predicted age (MileAge) on chronological age and used the 239 resulting intercept (β ) and slope coefficient (α ) estimates to apply a statistical correction to 240 the age prediction: M i le A g e ( a g e bi as ad ju ste d) = Mi l e A g e + [ A g e /g3398/g4666α × A ge + β /g4667/g4671 (de 241 Lange & Cole, 2020). 242 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 9 Health indicators and mortality 243 We tested associations between MileAge delta (adj.) and multiple health indicators: having a 244 long-standing illness, disability or infirmity (yes/no), self-rated health (“poor”, “fair”, “good” 245 or “excellent”) and overall health status (unhealthy/healthy) derived from 81 cancer and 443 246 non-cancer illnesses (Mutz & Lewis, 2022; Mutz et al., 2021). Next we examined 247 associations with the frailty phenotype and frailty index (Mutz, Choudhury, Zhao, & Dregan, 248 2022). The frailty phenotype summarises data on weight loss, exhaustion, physical activity, 249 walking speed and hand-grip strength. The frailty index was derived from 49 variables 250 obtained at the baseline assessment, including cardiometabolic, cranial, immunological, 251 musculoskeletal, respiratory and sensory traits, well-being, infirmity, cancer and pain. We 252 also tested associations between MileAge delta (adj.) and telomere length, measured using a 253 validated quantitative polymerase chain reaction assay that expresses telomere length as the 254 ratio of the telomere repeat copy number (T) relative to a single-copy gene (S) that encodes 255 haemoglobin subunit beta. T/S ratio is proportional to an individual’s average telomere length 256 (Lai, Wright, & Shay, 2018). Finally, we examined prospective associations with all-cause 257 mortality. The date of death was obtained through linkage with national death registries, NHS 258 Digital (England and Wales) and the NHS Central Register (Scotland). The censoring date 259 was 30 November 2022. 260 261 Exclusion criteria 262 Women who were pregnant or unsure that they were pregnant at the time of assessment were 263 excluded from the analysis given that their metabolite profiles likely changed during 264 pregnancy. Participants for whom their genetic and self-reported sex did not match were also 265 excluded as this may indicate poor data quality. We also excluded individuals with missing 266 metabolite data or potential outlier metabolite values, defined as values 4× the interquartile 267 range (IQR) above or below the median. 268 269 Statistical analyses 270 All data processing and analyses were performed in R (version 4.2). 271 272 Sample characteristics were summarised using means and standard deviations or counts and 273 percentages. Generalised additive models were used to explore the relationship between 274 chronological age and metabolite levels. We further conducted metabolome-wide association 275 analyses of chronological age and all-cause mortality to identify metabolites that were 276 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 10 statistically significantly associated with chronological age and mortality (at P < 0.05/168). 277 Correlations between the predicted age derived from each machine learning model were 278 estimated using Pearson’s correlation coefficient. 279 280 Cross-sectional associations between MileAge delta (adj.) and the frailty index and telomere 281 length were estimated using ordinary least squares regression. Associations between MileAge 282 delta and having a long-standing illness and overall health status were estimated using 283 logistic regression. Association between MileAge delta and the frailty phenotype and self-284 rated health were estimated using ordinal logistic regression. For each health indicator, higher 285 values corresponded to worse health. For the health association analyses, we fitted minimally 286 adjusted models that included chronological age and sex as covariates. For the prospective 287 analyses of all-cause mortality, we calculated person-years of follow-up and the median 288 duration of follow-up of censored individuals. Survival probabilities by MileAge delta were 289 estimated using the Kaplan-Meier (KM) method (Kaplan & Meier, 1958) and we calculated 290 log-rank p-values. Hazard ratios (HRs) and 95% confidence intervals were estimated using 291 Cox proportional hazards models (Cox, 1972). Age in years was used as the underlying time 292 axis, with age 40 as the start of follow-up. Across both cross-sectional and prospective 293 analyses, we defined MileAge delta subgroups by standard deviation from the mean. 294 Individuals with a MileAge delta equal to or smaller than one standard deviation below the 295 mean were the reference group. To discern how this analytical decision might impact results, 296 and to enable comparability with other studies, we also report associations with all-cause 297 mortality for all models with subgroups defined by the bottom and top 10% of the 298 distribution as well as negative and positive values. Finally, we used generalised additive 299 models and spline functions to explore the relationship between MileAge delta as a 300 continuous variable and health indicators and all-cause mortality, respectively. 301 302 For the Cubist rule-based regression model, which across most analyses performed best at 303 predicting health outcomes, we performed additional analyses. We calculated variable 304 importance scores to identify metabolites that strongly contributed to MileAge. We explored 305 associations between MileAge delta and all-cause mortality stratified by sex, self-rated health 306 and chronological age group (39-49, 50-59 and 60-71 years). Finally, we assessed the 307 performance of our ageing clock by benchmarking it against other ageing markers: (a) we 308 estimated the hazard ratio for all-cause mortality by MileAge delta and other ageing marker 309 (grip strength, telomere length and the frailty index) subgroups defined by standard deviation 310 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 11 from the mean, adjusted for chronological age and sex; (b) we calculated the C-index and 311 95% confidence intervals for chronological age + sex (as the base model) and for each ageing 312 marker added separately to the model, with time (in days) since the baseline assessment as 313 the underlying time axis. 314 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 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315 Sample characteristics 316 Of the 118,019 participants with metabolomics data, 110,730 had complete information on all 317 metabolites (Figure S1). After removing individuals with potential outlier metabolite values, 318 inconsistencies between self-reported and genetic sex or possible pregnancies, the analytical 319 sample included 101,359 participants (Table 1). The mean chronological age was 56.44 years 320 (SD = 8.12), with the most common age being 61 years (Figure 1b). Most metabolite levels 321 varied by chronological age (Figure 1c), showing considerable evidence of non-linear 322 relationships (Figures S2-S33). 323 324 Table 1. Sample characteristics MileAge delta (adj.) Full sample (N=101359) ≤ 1SD below the mean (n=16204) Middle (n=69166) ≥ 1SD above the mean (n=15989) Age; mean (SD) 56.44 (8.12) 55.85 (8.33) 56.75 (8.08) 55.69 (8.00) Sex Female 54484 (53.8%) 8062 (49.8%) 37002 (53.5%) 9420 (58.9%) Male 46875 (46.2%) 8142 (50.2%) 32164 (46.5%) 6569 (41.1%) Ethnicity White 95672 (94.4%) 15163 (93.6%) 65486 (94.7%) 15023 (94.0%) Mixed-race 574 (0.6%) 103 (0.6%) 386 (0.6%) 85 (0.5%) Black 1529 (1.5%) 233 (1.4%) 975 (1.4%) 321 (2.0%) Asian 1953 (1.9%) 375 (2.3%) 1265 (1.8%) 313 (2.0%) Chinese 291 (0.3%) 77 (0.5%) 184 (0.3%) 30 (0.2%) Other 880 (0.9%) 173 (1.1%) 564 (0.8%) 143 (0.9%) Missing1 460 (0.5%) 80 (0.5%) 306 (0.4%) 74 (0.5%) Highest qualification None 17084 (16.9%) 2551 (15.7%) 11868 (17.2%) 2665 (16.7%) O levels/GCSEs/CSEs 27008 (26.6%) 4237 (26.1%) 18435 (26.7%) 4336 (27.1%) A levels/NVQ/HND/HNC2 23235 (22.9%) 3637 (22.4%) 15961 (23.1%) 3637 (22.7%) Degree 32826 (32.4%) 5577 (34.4%) 22091 (31.9%) 5158 (32.3%) Missing1 1206 (1.2%) 202 (1.2%) 811 (1.2%) 193 (1.2%) Household income3 Very low 19422 (19.2%) 2863 (17.7%) 13265 (19.2%) 3294 (20.6%) Low 22159 (21.9%) 3487 (21.5%) 15137 (21.9%) 3535 (22.1%) Medium 22634 (22.3%) 3831 (23.6%) 15417 (22.3%) 3386 (21.2%) High 17767 (17.5%) 3095 (19.1%) 12027 (17.4%) 2645 (16.5%) Very high 4725 (4.7%) 819 (5.1%) 3188 (4.6%) 718 (4.5%) Missing1 14652 (14.5%) 2109 (13.0%) 10132 (14.6%) 2411 (15.1%) Cohabitation With partner 73896 (72.9%) 12054 (74.4%) 50748 (73.4%) 11094 (69.4%) Single 8341 (8.2%) 1418 (8.8%) 5467 (7.9%) 1456 (9.1%) Missing1 19122 (18.9%) 2732 (16.9%) 12951 (18.7%) 3439 (21.5%) . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 13 Smoking status Never 55643 (54.9%) 9149 (56.5%) 37876 (54.8%) 8618 (53.9%) Former 34805 (34.3%) 5342 (33.0%) 23838 (34.5%) 5625 (35.2%) Current 10416 (10.3%) 1634 (10.1%) 7119 (10.3%) 1663 (10.4%) Missing1 495 (0.5%) 79 (0.5%) 333 (0.5%) 83 (0.5%) Menopause4 No 12986 (12.8%) 2887 (17.8%) 8096 (11.7%) 2003 (12.5%) Yes 32745 (32.3%) 4046 (25.0%) 23034 (33.3%) 5665 (35.4%) Missing1 55628 (54.9%) 9271 (57.2%) 38036 (55.0%) 8321 (52.0%) Morbidity count None 23788 (23.5%) 4459 (27.5%) 16311 (23.6%) 3018 (18.9%) One 26923 (26.6%) 4581 (28.3%) 18615 (26.9%) 3727 (23.3%) Two 20535 (20.3%) 3195 (19.7%) 14011 (20.3%) 3329 (20.8%) Three 13157 (13.0%) 1857 (11.5%) 9001 (13.0%) 2299 (14.4%) Four 7553 (7.5%) 989 (6.1%) 5077 (7.3%) 1487 (9.3%) Five+ 9387 (9.3%) 1119 (6.9%) 6141 (8.9%) 2127 (13.3%) Missing1 16 (0.0%) 4 (0.0%) 10 (0.0%) 2 (0.0%) Fasting time5; mean (SD) 3.75 (2.40) 3.74 (2.47) 3.74 (2.39) 3.79 (2.38) Body mass index6; mean (SD) 27.43 (4.73) 26.17 (4.07) 27.41 (4.57) 28.80 (5.59) Note: GCSEs = general certificate of secondary education; CSE = certificate of secondary education; NVQ = national vocational qualification; HND = higher national diploma; HNC = higher national certificate. MileAge delta (adj.) derived from the Cubist rule-based regression model. 1Missing data may also include “do not know”, “prefer not to answer”, “not applicable” or related responses. 2Also includes 'other professional qualifications'. 3Annual household income groups: very low (£100,000). 4n = 59519 females. 5n = 3 missing. 6n = 345 missing. 325 Metabolite-wide associations 326 165/168 metabolites were associated with chronological age (p < 0.05/168). While most 327 metabolite levels were elevated in older individuals (e.g., Omega 3, citrate and glucose), 328 seven, including albumin, glycine and histidine, were negatively associated with 329 chronological age (Figure S34; Additional file 1). Amongst the 119 metabolites associated 330 with all-cause mortality, GlycA was most strongly associated with a higher mortality hazard 331 (HR = 1.22, 95% CI 1.20-1.25, p < 0.001), whereas the degree of unsaturation, 332 docosahexaenoic acid (DHA) and Omega 3 were strongly associated with a lower mortality 333 hazard (Figure S35; Additional file 2). Notably, 116 metabolites associated with 334 chronological age also predicted mortality, with GlycA, Omega 3 and DHA amongst the 335 most strongly associated metabolites of both age and mortality (Figure 1d). Between 87% 336 and 95% of the metabolites that were statistically significantly associated with other health 337 indicators (e.g., frailty and health status) were associated with chronological age (Figure 338 S36). The exception was telomere length for which only 53% of statistically significant 339 metabolites were shared with chronological age. 340 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 14 341 Predictive model performance 342 Predictive performance estimates in the 90% training (n = 91,222 to 91,226) and 10% test 343 sets are shown in Table S3. The nested cross-validation mean absolute error (MAE) in the 344 test sets (n = 10,133 to 10,137) ranged from 5.31 to 6.36 years, with the support vector 345 regression with a radial basis function (SVM radial) performing best and the MARS 346 ensemble performing worst. The root-mean-square error (RMSE) ranged from 6.60 to 7.58 347 years. Correlation coefficients between predicted and chronological age ranged from 0.36 to 348 0.59, with R2 values between 0.13 and 0.35. The difference in predictive performance 349 between the training and test sets, i.e., the model’s optimism which may indicate poor 350 generalization to unseen data, was generally low (e.g., MAEdifference < 0.15 for 10/17 models). 351 However, certain tree-based models (bagging, random forest and XGBoost) and the k-nearest 352 neighbors model overfit the training data (MAEdifference = -1.51 to -5.83), with correlation 353 coefficients between predicted and chronological age of r > 0.8 in the training sets (Figure 354 S40). Figure 2a shows the nested cross-validation MAEs for all models. For comparison, 355 drawing random samples from a uniform distribution between the sample’s minimum and 356 maximum chronological age, i.e., a random prediction model, resulted in a MAE = 9.79. 357 Predicting the sample mean, i.e., a null model, resulted in a MAE = 6.96. Additional plots 358 showing other performance measures (MAE, RMSE, r and R2) in the training and test sets are 359 presented in the supplement (Figures S37-S43). There were moderate to high correlations 360 between the predicted age values of the various models (r = 0.48 to > 0.99) (Figure 2b). High 361 correlations (r > 0.87) amongst the most accurate models suggest they capture similar 362 patterns in the data. Omega 3, albumin and citrate were amongst the most important 363 contributors to predictive accuracy (Figure S44). 364 365 Age bias correction 366 All models overestimated the age of young individuals and underestimated the age of older 367 individuals (Figure S44). Applying a statistical correction (see Methods) to the predicted age 368 values removed this bias (Figures 2c-e and S45). The predicted age values were originally 369 within the chronological age range (39 to 70 years) of the sample for most individuals. 370 Across all models, 0.23% (n = 238) and 0.96% (n = 976) of predictions were below or above 371 the minimum and maximum age, respectively (Table S4). More predicted age values were 372 outside the chronological age range (up to 8.27%, n = 8382 for a single model) after the age 373 bias correction. Re-calculating the predictive performance estimates after the age bias 374 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 15 correction suggested higher accuracy (MAE = 2.12 to 3.40; Figure 2f). The overall 375 performance rankings across the models inverted, with the models that originally predicted 376 chronological age best showing reduced accuracy (Figures S46-S48). The age bias adjusted 377 MileAge delta ranged from -18.94 years younger to 16.05 years older for the Cubist rule-378 based regression model, with 15.99% (n = 16,204) and 15.77% (n = 15,989) of the sample 379 having a MileAge delta (adj.) of at least 3.75 years below or above the mean (Figure 2g; 380 Table S5). 381 382 Associations with health indicators 383 Descriptive statistics for the health indicators are shown in Table S6. Having an older 384 predicted than chronological age was associated with higher frailty index scores across all 385 models (Table S7). This extended to the frailty phenotype for all models when comparing 386 individuals with a MileAge delta (adj.) more than one standard deviation above and below 387 the mean, and for 12/17 models when comparing the middle of the distribution to individuals 388 with MileAge delta (adj.) values more than one standard deviation below the mean (Table 389 S8). For telomere length, we observed a group difference for 12/17 models when comparing 390 the tails of the distribution, and for 9/17 models when comparing the middle of the 391 distribution to the reference group (Table S9). Having an older predicted than chronological 392 age was generally associated with chronic illness and poor self-rated health (Tables S10- 393 S12). An exception to this pattern were the MARS models, for which an older predicted than 394 chronological age was associated with longer telomeres, and for which there was little 395 evidence of statistically significant differences in health between individuals with MileAge 396 delta (adj.) values in the middle of the distribution and the reference group. 397 398 MileAge delta (adj.) derived from the Cubist rule-based regression model was most strongly 399 associated with most health indicators (Figure 3a). Individuals with a MileAge delta (adj.) 400 greater than one standard deviation above the mean had higher frailty index scores than 401 individuals with a MileAge delta (adj.) smaller than one standard deviation below the mean 402 (β = 0.023, 95% CI 0.021–0.024, p < 0.001). This group difference was approximately 403 equivalent to an 18.3-year chronological age difference in frailty index scores (β = 0.023 404 divided by β = 0.001255 derived from a linear model, y frailty index ~ x chronological age). 405 Individuals with an older predicted than chronological age were also more likely to be 406 physically frail (OR = 1.29, 95% CI 1.23–1.35, p < 0.001) and had shorter telomeres (β = 407 0.052, 95% CI 0.030 to 0.073, p < 0.001) equivalent to a 2.2-year chronological age 408 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 16 difference in telomere length. Such individuals were also more likely to have a long-standing 409 illness (OR = 1.82, 95% CI 1.73–1.91, p < 0.001), poorer health status (OR = 1.85, 95% CI 410 1.76–1.94, p < 0.001) and worse self-rated health (OR = 1.72, 95% CI 1.65–1.80, p < 0.001). 411 Generalised additive models showed that positive MileAge delta (adj.) values, indicating 412 accelerated biological ageing, were robustly associated with unfavourable health (Figure 3b), 413 whereas negative MileAge delta (adj.) values were only weakly associated with favourable 414 health, a pattern that was consistent across most models (Figures S49-S54). 415 416 Predicting mortality 417 The median duration of follow-up of censored individuals was 13.87 years (IQR = 1.37 418 years), with 1,361,970 person-years of follow-up. There were 8113 deaths amongst 101,274 419 participants (n = 85 missing). MileAge (adj.) was strongly associated with all-cause 420 mortality, comparable to chronological age (Figures 4a-e). In the prospective analyses we 421 examined the age bias adjusted MileAge delta and models were adjusted for chronological 422 age and sex, with age (in years) as the underlying time axis (Figure S55 and Table S13). 423 424 For the Cubist rule-based regression model, the hazard ratio (HR) comparing individuals with 425 a MileAge delta (adj.) greater than one standard deviation above and below the mean was HR 426 = 1.52 (95% CI 1.41-1.64, p < 0.001). Individuals with a MileAge delta (adj.) between one 427 standard deviation above and below the mean had a statistically significantly higher mortality 428 risk for 14/17 models (p between 0.03 and < 0.001) (Table S14). Comparing the bottom and 429 top 10% of the MileAge delta (adj.) distribution, instead of one standard deviation above and 430 below the mean, resulted in greater differences (e.g., HR = 1.63, 95% CI 1.48-1.79, p < 0.001 431 for the Cubist model). Individuals in between the tails of the distribution had a higher 432 mortality risk compared to the bottom 10% for 14/17 models (Figure S56 and Table S15). 433 When comparing individuals with a positive and negative MileAge delta (adj.), we found that 434 individuals with an older predicted than chronological age had a higher mortality risk for all 435 models except the MARS models (Figure S57 and Table S16). Modelling the mortality 436 hazard as a spline function of MileAge delta (adj.) suggested that positive values were 437 strongly associated with a higher mortality hazard, while there was little evidence that 438 negative values were associated with a lower mortality hazard (Figure S58). 439 440 F emales had slightly higher MileAge delta (adj.) values than males (Figure 4f), a pattern 441 which we observed across all models (Figure S59). The mortality hazard of individuals with a 442 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 17 MileAge delta (adj.) greater than one standard deviation above the mean was elevated in both 443 females (HR = 1.26, 95% CI 1.11-1.43, p < 0.001) and males (HR = 1.73, 95% CI 1.57-1.91, 444 p < 0.001) (Figures S60-S61; Table S17). The difference in mortality between individuals 445 with a MileAge delta (adj.) in the middle of the distribution and the reference group was only 446 statistically significant in males (HR = 1.14, 95% CI 1.05-1.23, p = 0.002). Stratifying the 447 sample by self-rated health, the mortality hazard of individuals with a MileAge delta (adj.) 448 greater than one standard deviation above the mean was higher in all strata (e.g., HR = 1.41, 449 95% CI 1.11-1.78, p < 0.001 for poor self-rated health) except for individuals with excellent 450 health (Figure 4g and Table S17). The mortality hazard of individuals with a MileAge delta 451 (adj.) greater than one standard deviation above the mean was higher in the age groups above 452 50 years (Figures S62 and 4h; Table S17). 453 454 Comparison with other ageing markers 455 A comparison of the all-cause mortality hazard associated with MileAge delta (adj.) and 456 other ageing marker subgroups defined by the standard deviation from the mean showed that 457 the largest hazard ratio (HR = 2.90) was observed for the frailty index (Figure 5a). The 458 smallest hazard ratio was observed for telomere length (HR = 1.31) (Table S18), with 459 MileAge delta (adj.) (HR = 1.52) and grip strength (HR = 1.90) in-between. Adding each 460 ageing marker individually as a continuous variable to a base model that included 461 chronological age and sex improved prediction of all-cause mortality, with the best prediction 462 observed for the frailty index (C-index 0.737, 95% CI 0.732 to 0.742 vs C-index 0.716, 95% 463 CI 0.711 to 0.722 for the base model) (Figure 5b and Table S19). Modelling the mortality 464 hazard as a spline function of the ageing markers, to identify potential non-linear effects, 465 suggested that the all-cause mortality hazard was considerably higher in individuals with an 466 older predicted than chronological age. For example, compared to the sample median 467 MileAge delta (adj.), which was equivalent to no difference between predicted and 468 chronological age, a MileAge delta (adj.) of 10 was associated with a HR of about 2.7, i.e., a 469 170% higher morality hazard (Figure 5c). 470 . 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471 In 101,359 UK Biobank participants with Nightingale Health metabolomics data, we 472 observed that most metabolite levels varied by chronological age, with considerable evidence 473 of non-linear associations. Across the machine learning algorithms employed to develop 474 ageing clocks from circulating plasma metabolites, the nested cross-validation mean absolute 475 error between predicted age (MileAge) and chronological age ranged from 5.31 to 6.36 years 476 (R2 between 0.13 and 0.35). All models overestimated age in young individuals and 477 underestimated age in older individuals. After applying a statistical correction to remove this 478 age bias, 31.76% of participants had adjusted MileAge delta values of at least 3.75 years, 479 highlighting the potential of metabolomic ageing clocks to differentiate between individuals 480 of the same chronological age (Hertel et al., 2019). While there was a high degree of 481 consistency across the top performing models such as support vector regression, tree-based 482 and rule-based ensembles, the ageing clock derived from a Cubist rule-based regression 483 model (MAE = 5.42) was most strongly associated with most health indicators. We observed 484 across most models that individuals with an older predicted than chronological age, 485 indicating accelerated biological ageing, were frailer, had shorter telomeres, were more likely 486 to have a chronic illness, rated their health worse and had a higher mortality risk. 487 488 Multiple studies have developed biological ageing clocks trained on chronological age from 489 metabolomics data. The seminal study by Menni et al. (2013) derived a metabolite age score 490 as a linear combination of 22 plasma metabolites that were correlated with chronological age 491 in 6055 twins, achieving an R2 of 59% and a hazard ratio for all-cause mortality of HR = 1.08 492 per year. Hertel et al. (2016) tested a multivariable linear regression and a fractional 493 polynomial model in 3611 participants, with the latter achieving a correlation between 494 predicted and chronological age of r = 0.53 (RMSE = 11.19) in men and r = 0.61 (RMSE = 495 10.37) in women. Their metabolomic ageing clock included 59 urinary metabolites and was 496 predictive of all-cause mortality (HR = 1.24 per SD). Robinson et al. (2020) developed 497 several ageing clocks using elastic net models in 2238 participants, with correlations between 498 predicted and chronological age of r = 0.45 (MAE = 4.17) to r = 0.83 (MAE = 6.49). Akker 499 et al. (2020) developed an ageing clock, MetaboAge, from 56 metabolites in 18,716 500 participants from 24 community and hospital-based cohorts using a linear regression model, 501 achieving a correlation of r = 0.65 and a median absolute error of 7.3. An independent 502 external validation of this clock observed a notably lower correlation of r = 0.21 (Macdonald-503 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 19 Dunlop et al., 2022). The same study also developed a clock from NMR metabolomics data 504 (81/86 metabolites selected) in 1643 individuals, which achieved a correlation of r = 0.74 but 505 failed to replicate in a validation cohort, and another clock from mass spectrometry 506 metabolomics (181/682 metabolites selected) in 861 individuals, which achieved a 507 correlation of r = 0.81 (Macdonald-Dunlop et al., 2022). An updated ageing clock, 508 MetaboAge 2.0, in the BBMRI-nl data that included 65 metabolites achieved an R2 of 0.451 509 and 0.449 for a linear regression and elastic net model, respectively (Bizzarri et al., 2023). 510 511 Metabolomic ageing clocks trained on chronological age are generally less accurate than 512 ageing clocks derived from other types of omics data (Rutledge et al., 2022). Nevertheless, 513 our most predictive model (MAE = 5.31 years) had a similar accuracy as a deep learning 514 ageing clock (MAE = 5.68) derived from blood markers, biometrics and sex in the China 515 Health and Retirement Longitudinal Study. An elastic net model in the same data achieved a 516 MAE = 6.19 years (Galkin et al., 2022), while the elastic net model in our study had a lower 517 MAE = 5.70, likely due to the larger sample size. While a discussion of how well different 518 ageing clocks predict health outcomes is beyond the scope of this study, the most widely 519 tested epigenetic ageing clocks that were trained on chronological age are weak predictors of 520 mortality (B. H. Chen et al., 2016; Fransquet, Wrigglesworth, Woods, Ernst, & Ryan, 2019). 521 Second-generation ageing clocks are more predictive of mortality. For example, a one-year 522 increase in PhenoAge, which was trained on physiological dysregulation, was associated with 523 a 9% increase in mortality risk. Its epigenetic derivation, DNAm PhenoAge, was associated 524 with a 4.5% increase in all-cause mortality (Levine et al., 2018). GrimAge, another popular 525 mortality risk predictor that incorporates chronological age, sex and eight DNA methylation 526 surrogate markers (seven for plasma proteins and one for smoking pack-years) strongly 527 predicts mortality and age-related diseases (Lu et al., 2019). A recent clock developed from 528 circulating biomarkers and trained to predict mortality in the UK Biobank (n = 307,000) 529 using an elastic net Cox model (Bortz et al., 2023) yielded a 9.2% relative increase in 530 prediction compared to the PhenoAge model. However, the improvement in prediction over a 531 model that included chronological age and sex was modest (C-index 0.715 vs 0.762, 532 compared to 0.716 vs 0.719 in our study; though note that our clock was not trained to predict 533 mortality). These findings suggest that certain omics clocks capture physiologically relevant 534 signals more, while first-generation epigenetic clocks are specifically good at predicting 535 chronological time (Rutledge et al., 2022). 536 537 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 20 Although chronological age prediction is valuable in fields such as forensics (Vidaki et al., 538 2017), it is of limited use in population health and geroscience, given that chronological age 539 is non-modifiable (Robinson & Lau, 2020). A perfect prediction model would merely tell us 540 about chronological, not biological, age (Nakamura et al., 1988). It is the difference between 541 predicted and chronological age (MileAge delta) that serves as an indicator of accelerated or 542 decelerated ageing. A less accurate chronological age prediction does not necessarily indicate 543 a worse biological age model (Hertel et al., 2019), hence we also tested algorithms that were 544 expected to perform less well at predicting chronological age (e.g., bagging). Prior studies 545 suggested that biological age estimates derived from physical activity (Pyrkov et al., 2018) or 546 epigenetic data (Zhang et al., 2019) with higher predictive accuracy of chronological age 547 were less predictive of all-cause mortality. Our study showed that the models that were most 548 predictive of chronological age were generally also more strongly associated with health and 549 mortality, though we note that the pattern of predictive accuracy largely inverted after we 550 applied the age bias correction. 551 552 We report several additional analyses, including variable importance scores and 553 benchmarking against other ageing markers, for the ageing clock derived from the Cubist 554 rule-based regression model, which was most strongly associated with most health indicators. 555 There are, however, several conclusions that can be drawn across most of the machine 556 learning algorithms tested. First, the wide range of the MileAge delta values quantifies the 557 latent patterns in the metabolomics data not captured by chronological age and suggests that 558 our ageing clocks approximate (past) rate of biological ageing for people of the same 559 chronological age. Second, the associations between most ageing clocks, health and mortality 560 demonstrate that these clocks capture biologically relevant information, which may find 561 applications in health tracking, nutrition or in clinical trials (e.g., sample stratification). A key 562 finding across most ageing clock models tested here was that associations with health and 563 mortality were stronger in individuals with an older predicted than chronological age and less 564 so in individuals with a younger predicted than chronological age. 565 566 Several of the algorithms included in our comparison, including those that were most 567 predictive of chronological age, mortality and health, allowed for non-linear relationships in 568 the data, which were often not considered in previous studies (Panyard et al., 2022). A recent 569 review found that most molecular ageing clocks were developed using linear models with 570 regularization, whereas few used non-linear models (Xia, Wang, Yu, Chen, & Han, 2021). 571 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 21 Although it has been asserted that age-related physiological markers are linearly associated 572 with age (Pyrkov et al., 2018), we have shown here and in previous studies (Mutz, Hoppen, et 573 al., 2022; Mutz & Lewis, 2021; Mutz, Young, et al., 2022) that this does not apply to many 574 biological markers. To enable comparability between studies, we provide a comprehensive 575 set of statistical estimates and developed our ageing clock using metabolites measured in 576 absolute concentrations instead of relative to other measures. Although it may be argued that 577 quantification of a smaller number of metabolites would in principle be more feasible and 578 convenient in clinical practice, all metabolites included in our model can be quantified from a 579 single assay with minimal sample preparation required (Würtz et al., 2017). 580 581

and future directions 582 Our study had certain limitations. Some algorithms that have previously been used to develop 583 biological ageing clocks, for example deep learning (Zhavoronkov, Li, Ma, & Mamoshina, 584 2019), or approaches combining HSIC LASSO feature selection with non-linear support 585 vector regression (Takahashi et al., 2020) were not tested, and could be explored in future 586 studies. Our ageing clock provides a “systems level” indicator of age-related changes in 587 metabolites; future clocks may be developed at the tissue or cellular level. Plasma samples 588 may differ from other body fluids, e.g., serum, urine or cerebrospinal fluid. The metabolite 589 coverage of the Nightingale Health platform is lipid focussed and mostly covers larger 590 molecules, while there are potentially over 217,000 endogenous and exogenous molecules 591 (Wishart et al., 2021). Nevertheless, this platform enables robust assessment of these 592 metabolites in a single experiment (Würtz et al., 2017). Although more complex ageing 593 clocks could be developed using technologies with wider metabolite coverage, prior analyses 594 suggested that a majority of metabolites associated with age were related to lipid and amino 595 acid pathways, both of which were included here (Menni et al., 2013). As in previous studies, 596 we observed a systematic overestimation of age in young individuals and underestimation of 597 age in older individuals (Nakamura et al., 1988). This bias is neither data nor method specific 598 and may be explained by regression to the mean (Liang, Zhang, & Niu, 2019) of the training 599 data (Jones, Lee, & Topol, 2022). To account for this bias, we have adjusted the predicted 600 age and included chronological age as a covariate in the health association analyses (Xia et 601 al., 2021). Longitudinal ageing metrics may be more robustly associated with certain health 602 outcomes than cross-sectional ageing metrics, e.g., with physical and cognitive decline but 603 not, for example, multimorbidity (Kuo et al., 2022). Future research should develop 604 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 22 metabolomic ageing clocks from longitudinal data. Finally, the lack of independent data for 605 external validation is a limitation. 606 607

608 Metabolomic ageing clocks derived from multiple machine learning algorithms were robustly 609 associated with health indicators and mortality. We found that our ageing clock (MileAge) 610 derived from a Cubist rule-based regression model was overall most strongly associated with 611 health indicators. Individuals with MileAge values greater than their chronological age, 612 indicating accelerated biological ageing, were frailer, had shorter telomeres, were more likely 613 to have a chronic illness, rated their health worse and had a higher mortality risk. 614 Metabolomic ageing clocks hold significant promise for research on lifespan and healthspan 615 extension, as they provide a proxy of biological ageing that is potentially modifiable. These 616 clocks may also help identify health risks before clinical symptoms emerge. As such, 617 biological ageing clocks may contribute to health risk assessments, complementing clinical 618 biomarkers. However, the utility of ageing clocks is not limited to risk stratification, but also 619 in providing an intuitive, year-based metric for health tracking that may help individuals 620 proactively engage with their health. 621 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 23 Acknowledgments 622 This research is funded by the National Institute for Health and Care Research (NIHR) 623 Maudsley Biomedical Research Centre at South London and Maudsley NHS Foundation 624 Trust and King’s College London. The views expressed are those of the authors and not 625 necessarily those of the NHS, the NIHR or the Department of Health and Social Care. 626 Computational analyses were supported by: King's College London. (2023). King's 627 Computational Research, Engineering and Technology Environment (CREATE). Retrieved 628 May 24, 2023, from https://doi.org/10.18742/rnvf-m076. This research has been conducted 629 using data from UK Biobank, a major biomedical database. Data access permission has been 630 granted under UK Biobank application 45514. 631 632 Financial disclosures 633 CML is a member of the scientific advisory board of Myriad Neuroscience, has received 634 speaker fees from SYNLAB and received consultancy fees from UCB. JM and RI declare no 635 financial conflict of interest. 636 637 Authorship contributions 638 JM conceived the idea of the study, acquired the data, carried out the analysis, interpreted the 639 findings and wrote the manuscript. CML and RI interpreted the findings and reviewed the 640 manuscript. All authors read and approved the final manuscript. 641 642 Ethics 643 Ethical approval for the UK Biobank study has been granted by the National Information 644 Governance Board for Health and Social Care and the NHS North West Multicentre Research 645 Ethics Committee (11/NW/0382). No project-specific ethical approval is needed. 646 647 Data sharing statement 648 The data used are available to all bona fide researchers for health-related research that is in 649 the public interest, subject to an application process and approval criteria. Study materials are 650 publicly available online at http://www.ukbiobank.ac.uk. 651 652 Supplementary material 653 Supplementary information is available online. 654 . CC-BY 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint 24

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(which was not certified by peer review) The copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint MAERMSE R2 r Training set (90%)Test setFold 1Fold 2Fold 3Fold 4Fold 5Fold 1Fold 2Fold 3Fold 4Fold 5Fold 1Fold 2Fold 3Fold 4Fold 5Fold 1Fold 2Fold 3Fold 4Fold 5Fold 1Fold 2Fold 3Fold 4Fold 5 Split 1Split 2Split 3Split 4Split 5 Full analytical sample (N = 101,359)Training (80%)Validation Test setEvaluate model with hyperparameter combination that resulted in lowest cross-validation MAE Maximum entropy gridHyperparameter 2Hyperparameter 115#!"#$MAEMAE 1MAE 2MAE 3MAE 4MAE 5Cross-validation for each hyperparameter combinationPerformance Preserve the age distribution across foldsFold1Fold2Fold3Fold4Fold5Fold6Fold8Fold7Fold10Fold9Fold1Fold2Fold3Fold4Fold5Fold6Fold8Fold7Fold10Fold910-fold Outer loop5-fold Inner loop Figure 1. a, Overview of the nested cross-validation approach. MAE = mean absolute error; RMSE = root-mean-square error. b, Histogram of the chronological age distribution of the full analytical sample. The statistical mode (age = 61 years) is shown in red. c, Distribution of metabolite levels by chronological age, showing scatter plots of all observations and smooth curves (note the difference in y-axis scale). The smooth curves were estimated using generalised additive models, with shaded areas corresponding to 95% confidence intervals. GlycA = glycoprotein acetyls. d, Scatter plot showing the hazard ratio (HR) for all-cause mortality and the beta for chronological age associated with a one standard deviation (SD) difference in metabolite levels. Metabolites that had statistically significant associations with both chronological age and all-cause mortality are shown in purple. 0 1000 2000 3000 4000 5000 40506070Chronological age Count Age distribution a b Acetoacetate Albumin bOHbutyrate CholinesClinical_LDL_C DHA Glucose GlycA HDL_P HDL_PLHis IDL_CIDL_CE IDL_TG L_LDL_C L_LDL_CEL_LDL_FC L_LDL_L L_LDL_TGLactate LDL_C LDL_FC LDL_size LDL_TG Leu M_HDL_PL M_LDL_TG Omega_3PhosphatidylcPhosphoglycPUFA S_HDL_FC S_HDL_TG S_LDL_FC S_VLDL_L Total_CTotal_CE Total_FA Total_FCTotal_P Total_PL Unsaturation XS_VLDL_FC XS_VLDL_P XS_VLDL_TG XXL_VLDL_FCXXL_VLDL_L XXL_VLDL_PXXL_VLDL_PL XXL_VLDL_TG 0.8 0.9 1.0 1.1 1.2 −1.0−0.50.00.51.01.52.0Beta (per 1SD) Age HR (per 1SD) Mortality Metabolites × (Age and Mortality) c d 5.42 5.70 6.30 5.70 6.346.36 6.19 5.91 5.525.65 5.355.31 6.26 5.94 5.625.59 5.92 5.0 5.5 6.0 6.5 7.0 RidgeLASSOElastic netPLSRKNNMARS MARS ensembleSVM linearSVM polynomialSVM radialRegression tree BaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble Mean absolute error (years) MeanNested CV 9393 99 88 78 78 57 55 55 53 68 62 62 69 49 68 61 61 72 48 87 96 98 98 80 56 64 63 83 87 87 70 61 63 62 87 81 86 86 68 61 61 60 85 98 60 56 56 60 52 64 65 57 61 60 77 73 73 74 68 75 76 74 80 79 81 77 74 74 74 69 74 74 75 81 80 79 98 83 81 81 73 66 66 66 82 90 89 68 88 89 86 85 85 75 64 67 66 86 90 89 65 85 86 93 87 94 94 74 61 65 65 92 93 93 63 82 82 87 89 84 89 89 70 60 62 62 88 91 90 62 81 82 89 90 920.48 0.53 0.58 0.64 0.69 0.74 0.79 0.84 0.9 0.95 1LASSOElastic netPLSRKNNMARSMARS ensembleSVM linearSVM polynomialSVM radialRegression treeBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensembleRidge LASSO Elastic net PLSR KNN MARS MARS ensemble SVM linear SVM polynomial SVM radial Regression tree Bagging Random forest XGBoost BART Cubist rules a b 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) Ridge 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) LASSO 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) Elastic net 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) PLSR 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) KNN 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) MARS 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) MARS ensemble 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) SVM linear 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) SVM polynomial 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) SVM radial 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) Regression tree 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) Bagging 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) Random forest 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) XGBoost 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) BART 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) Cubist rules 30 40 50 60 70 80 40506070Age (years) Predicted age (adj.) RuleFit ensemble 30 40 50 60 70 80 40506070Age (years) Predicted age Ridge 30 40 50 60 70 80 40506070Age (years) Predicted age LASSO 30 40 50 60 70 80 40506070Age (years) Predicted age Elastic net 30 40 50 60 70 80 40506070Age (years) Predicted age PLSR 30 40 50 60 70 80 40506070Age (years) Predicted age KNN 30 40 50 60 70 80 40506070Age (years) Predicted age MARS 30 40 50 60 70 80 40506070Age (years) Predicted age MARS ensemble 30 40 50 60 70 80 40506070Age (years) Predicted age SVM linear 30 40 50 60 70 80 40506070Age (years) Predicted age SVM polynomial 30 40 50 60 70 80 40506070Age (years) Predicted age SVM radial 30 40 50 60 70 80 40506070Age (years) Predicted age Regression tree 30 40 50 60 70 80 40506070Age (years) Predicted age Bagging 30 40 50 60 70 80 40506070Age (years) Predicted age Random forest 30 40 50 60 70 80 40506070Age (years) Predicted age XGBoost 30 40 50 60 70 80 40506070Age (years) Predicted age BART 30 40 50 60 70 80 40506070Age (years) Predicted age Cubist rules 30 40 50 60 70 80 40506070Age (years) Predicted age RuleFit ensemble Mean =56.44 30 40 50 60 70 80 40506070Age (years) Predicted age ModelRidgeLASSOElastic netPLSRKNNMARSMARS ensembleSVM linearSVM polynomialSVM radialRegression treeBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble Age bias correction c d e 0.00 0.05 0.10 0.15 −20−1001020MileAge delta (adj.) Density ModelRidgeLASSOElastic netPLSRKNNMARSMARS ensembleSVM linearSVM polynomialSVM radialRegression treeBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble MileAge delta (adj.) 2.52 2.842.84 2.382.492.162.12 3.12 3.303.40 2.79 2.362.32 2.912.893.013.08 2.0 2.5 3.0 3.5 RidgeLASSOElastic netPLSRKNNMARS MARS ensembleSVM linearSVM polynomialSVM radialRegression tree BaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble Mean absolute error (years) f g Figure 2. a, Nested cross-validation mean absolute error (MAE) for all models with tuned hyperparameter values in the 10% hold-out test sets. CV = cross-validation. b, Heatmap of Pearson’s correlation coefficient (r) between the predicted age values for all models. Estimates shown were multiplied by 100. c, Line plot showing the correlation between predicted age and chronological age for all models before (solid lines) and after (dotted lines) applying a statistical correction to the predicted age to remove the age bias (i.e., the systematic overestimation of age in young individuals and underestimation of age in older individuals). d, e, 2D density plots showing the correlation between predicted age derived from the Cubist rule-based regression model and chronological age before and after age bias correction. Observations beyond y-axis limits of 30 to 80 not shown. f, Mean absolute error for all models with tuned hyperparameter values calculated in the full sample after age bias correction. g, Density plot showing the distribution of MileAge delta (adj.) for all models. See Panel 1 for model abbreviations. Figure 3. a, Associations between MileAge delta (adj.) and health indicators for all models. Models were adjusted for chronological age and sex. Reference group: individuals with a MileAge delta (adj.) smaller than one standard deviation below the mean. See Panel 1 for model abbreviations. b, Partial effect plots of generalised additive models of the association between health indicators and MileAge delta (adj.). Models were adjusted for chronological age and sex. The shaded areas correspond to 95% confidence intervals. 0.00 0.01 0.02Beta Frailty index 1.00 1.10 1.20 1.30 1.40Odds ratio Frailty phenotype -0.04 -0.02 0.00 0.02 0.04 0.06 0.08Beta Telomere length 1.00 1.25 1.50 1.75 SVM radial SVM polynomial Cubist rules RuleFit ensemble XGBoostBART SVM linearElastic netLASSORidge Random forest BaggingPLSR Regression tree KNNMARS MARS ensemble Odds ratio Long-standing illness 1.00 1.25 1.50 1.75 SVM radial SVM polynomial Cubist rules RuleFit ensemble XGBoostBART SVM linearElastic netLASSORidge Random forest BaggingPLSR Regression tree KNNMARS MARS ensemble Odds ratio Health status 1.00 1.25 1.50 1.75 SVM radial SVM polynomial Cubist rules RuleFit ensemble XGBoostBART SVM linearElastic netLASSORidge Random forest BaggingPLSR Regression tree KNNMARS MARS ensemble Odds ratio Self-rated health MileAgedelta (adj.)≤X̄-1SD Middle≥X̄+1SD 0.00 0.03 0.06 0.09 0.12 −20−1001020MileAge delta (adj.) Partial effect Frailty index −0.5 0.0 0.5 1.0 1.5 −20−1001020MileAge delta (adj.) Partial effect Frailty phenotype −0.3−0.2−0.10.00.10.20.30.4 −20−1001020MileAge delta (adj.) Partial effect Telomere length −1.0−0.50.00.51.01.52.02.53.0 −20−1001020MileAge delta (adj.) Partial effect Long−standing illness −1.0−0.50.00.51.01.52.02.53.0 −20−1001020MileAge delta (adj.) Partial effect Health status −0.50.00.51.01.52.02.5 −20−1001020MileAge delta (adj.) Partial effect Self−rated health a b 0 2000 4000 6000 −20−1001020MileAge delta (adj.) Count SexFemaleMale Cubist rules 1.00 1.25 1.50 1.75 PoorFairGoodExcellent Hazard ratio MileAgedelta (adj.)≤X̄-1SDMiddle≥X̄+1SD Self-rated health 1.00 1.25 1.50 SVM radialSVM polynomialCubist rulesRuleFit ensemble XGBoostBARTSVM linearElastic netLASSORidge Random forest BaggingPLSR Regression tree KNNMARS MARS ensemble Hazard ratio MileAgedelta (adj.)≤X̄-1SDMiddle≥X̄+1SD a b Middle Biologically younger≤X̄-1SD Biologically older≥X̄+1SD 0.00 0.05 0.10 -20 -10 0 10MileAge delta (adj.) Density Cubist rules Mean 0.07 0.09 0.11 0255075100MileAge delta (adj.) percentile Event rate All−cause mortality 0.0 0.1 0.2 0255075100Percentile Event rate AgeMileAge (adj.)ChronAge All−cause mortalityc d e Figure 4. a, Kaplan-Meier plot showing survival probabilities for all-cause mortality by MileAge delta (adj.) derived from the Cubist rule-based regression model. Log-rank test p-value < 0.001. b, Hazard ratios and 95% confidence intervals from Cox proportional hazards models by MileAge delta (adj.) for all models. Models were adjusted for chronological age and sex. Age (in years) was used as the underlying time axis. Reference group: individuals with a MileAge delta (adj.) smaller than one standard deviation below the mean. See Panel 1 for model abbreviations. c, Density plot showing the distribution of MileAge delta (adj.) derived from the Cubist rule-based regression model. d, e, All-cause mortality rate by percentile of chronological age, MileAge (adj.) and MileAge delta (adj.) derived from the Cubist rule-based regression model. f, Histogram showing the distribution of MileAge delta (adj.) derived from the Cubist rule-based regression model, stratified by sex. g, h, Hazard ratios and 95% confidence intervals from Cox proportional hazards models for all-cause mortality by MileAge delta (adj.) derived from the Cubist rule-based regression model, stratified by self-rated health and chronological age group. 0.8 1.2 1.6 2.0 39-4950-5960-71 Hazard ratio MileAgedelta (adj.)≤X̄-1SDMiddle≥X̄+1SD Chronological age groupf g h 1.0 1.5 2.0 2.5 3.0 MileAge delta (adj.) Frailty indexGrip strengthTe lo m e re le n g th Hazard ratio Distribution≤X̄-1SDMiddle≥X̄+1SD + Frailty index + Grip strength + MileAge delta (adj.) + Telomere length Age+Sex 0.710.720.730.74C−index Model All−cause mortality a b 0 1 2 3 −10010MileAge delta (adj.) Log(HR) mortality MileAge delta 0 1 2 0.00.20.4Frailty index Log(HR) mortality Frailty −1.5 −1.0 −0.5 0.0 0.5 1.0 020406080Kilogram−force Log(HR) mortality Grip strength −4 −2 0 2 4 −10−50510T/S ratio (log z adjusted) Log(HR) mortality Telomere length c Figure 5. a, Hazard ratios (HR) and 95% confidence intervals from Cox proportional hazards models for all-cause mortality by MileAge delta (adj.), the frailty index, grip strength and telomere length. Models were adjusted for chronological age and sex. Age (in years) was used as the underlying time axis. Reference group: individuals with a score smaller than one standard deviation below the mean. b, C-index and 95% confidence intervals from Cox proportional hazards models for all-cause mortality for chronological age + sex (the base model) and for each ageing marker added separately to the base model. Time (in days) was used as the underlying time axis. c, Log(HRs) and 95% confidence intervals from Cox proportional hazards models for all-cause mortality. Models were adjusted for chronological age and sex. Age (in years) was used as the underlying time axis. Vertical lines indicate the median of the distribution which represents the reference for interpreting the estimates shown.