{"paper_id":"26e16776-979b-4aa6-b327-686bc53af84d","body_text":"Metabolomic Age (MileAge) predicts health and lifespan: a 1 \ncomparison of multiple machine learning algorithms 2 \n 3 \nShort title: Metabolomic MileAge UK Biobank 4 \n 5 \nAuthors: Julian Mutz1*, Raquel Iniesta2 and Cathryn M Lewis1,3 6 \n 7 \nAffiliations: 8 \n1. Social, Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, 9 \nPsychology & Neuroscience, King’s College London, London, United Kingdom. 10 \n2. Department of Biostatistics and Health Informatics, King’s College London, London, 11 \nUnited Kingdom. 12 \n3. Department of Medical and Molecular Genetics, Faculty of Life Sciences & 13 \nMedicine, King’s College London, London, United Kingdom. 14 \n 15 \n*Corresponding author: 16 \nJulian Mutz, PhD; Social, Genetic and Developmental Psychiatry Centre, Institute of 17 \nPsychiatry, Psychology & Neuroscience, King’s College London, Memory Lane, London, 18 \nSE5 8AF, United Kingdom. Email: julian.mutz@gmail.com.   19 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 2 \nAbstract 20 \nBackground: Molecular ageing clocks estimate an individual’s biological age. Our aim was 21 \nto compare multiple machine learning algorithms for developing ageing clocks from nuclear 22 \nmagnetic resonance (NMR) spectroscopy metabolomics data. To validate how well each 23 \nageing clock predicted age-related morbidity and lifespan, we assessed their associations with 24 \nmultiple health indicators (e.g., telomere length and frailty) and all-cause mortality. 25 \nMethods: The UK Biobank is a multicentre observational health study of middle-aged and 26 \nolder adults. The Nightingale Health platform was used to quantify 168 circulating plasma 27 \nmetabolites at the baseline assessment from 2006 to 2010. We trained and internally 28 \nvalidated 17 machine learning algorithms including regularised regression, kernel-based 29 \nmethods and ensembles. Metabolomic age (MileAge) delta was defined as the difference 30 \nbetween predicted and chronological age. 31 \nResults: The sample included 101,359 participants (mean age = 56.53 years, SD = 8.10). 32 \nMost metabolite levels varied by chronological age. The nested cross-validation mean 33 \nabsolute error (MAE) ranged from 5.31 to 6.36 years. 31.76% of participants had an age-bias 34 \nadjusted MileAge more than one standard deviation (3.75 years) above or below the mean. A 35 \nCubist rule-based regression model overall performed best at predicting health outcomes. The 36 \nall-cause mortality hazard ratio (HR) comparing individuals with a MileAge delta more than 37 \none standard deviation above and below the mean was HR = 1.52 (95% CI 1.41-1.64, p < 38 \n0.001) over a median follow-up of 13.87 years. Individuals with an older MileAge were 39 \nfrailer, had shorter telomeres, were more likely to have a chronic illness and rated their health 40 \nworse. 41 \nConclusions: Metabolomic ageing clocks derived from multiple machine learning algorithms 42 \nwere robustly associated with health indicators and mortality. Our metabolomic ageing clock 43 \n(MileAge) derived from a Cubist rule-based regression model can be incorporated in 44 \nresearch, and may find applications in health assessments, risk stratification and proactive 45 \nhealth tracking. 46 \n 47 \nKeywords: ageing clocks; biological age; biomarkers; machine learning; metabolomics 48 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 3 \nIntroduction 49 \nChronological age, the time elapsed since birth, is a powerful predictor of health and disease 50 \n(Mutz, Roscoe, & Lewis, 2021). However, there is considerable heterogeneity in health 51 \nstatus, lifestyle and the physical signs of ageing between individuals of the same 52 \nchronological age. This variability may partly reflect individual differences in biological 53 \nageing, which is the process of accumulating molecular and cellular damage that results in a 54 \nprogressive decline in physiological functioning (Moqri et al., 2023). While our 55 \nchronological age cannot be altered, biological ageing trajectories in humans may be 56 \nmodifiable, or even reversible. Therefore, developing reliable measures of biological age is 57 \nan important priority in biomedical research and population health. 58 \n 59 \nAlthough there is no single biological marker of biological ageing, several hallmarks such as 60 \ntelomere length shortening have been identified (López-Otín, Blasco, Partridge, Serrano, & 61 \nKroemer, 2023). Clinical and population studies of age-related biological changes have also 62 \nexamined physiological measures of grip strength and cardiovascular function (Mutz, 63 \nHoppen, Fabbri, & Lewis, 2022; Mutz & Lewis, 2021; Mutz, Young, & Lewis, 2022), blood-64 \nbased biomarkers (Nakamura, Miyao, & Ozeki, 1988), inflammatory markers (Franceschi, 65 \nGaragnani, Parini, Giuliani, & Santoro, 2018) and frailty (Hoogendijk et al., 2019). 66 \n 67 \nMolecular “omics” and neuroimaging data such as DNA methylation (Hannum et al., 2013; 68 \nHorvath & Raj, 2018; Lu et al., 2019) and structural magnetic resonance imaging (Cole & 69 \nFranke, 2017) have facilitated the development of biological ageing clocks (Rutledge, Oh, & 70 \nWyss-Coray, 2022; Solovev, Shaposhnikov, & Moskalev, 2020). Ageing clocks are usually 71 \ndeveloped using machine learning algorithms that identify relationships between 72 \nchronological age and molecular data. The difference between predicted age, which 73 \napproximates biological age, and chronological age is associated with health outcomes 74 \n(Macdonald-Dunlop et al., 2022). Ageing clocks provide a more holistic picture of a person’s 75 \nhealth and are conceptually easier to understand than most individual molecular markers as 76 \nthey are expressed in unit of years. 77 \n 78 \nPopulation-scale metabolomics, the study of small molecules, i.e., metabolites, within cells, 79 \ntissues or organisms, is increasingly incorporated into biological ageing research (Panyard, 80 \nYu, & Snyder, 2022). Metabolites are the products of metabolism, for example when food is 81 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 4 \nconverted to energy. While many initial metabolomics studies were limited to few 82 \nmetabolites and small samples, technological advancements have enabled the population-83 \nscale profiling of multiple molecular pathways (Soininen, Kangas, Würtz, Suna, & Ala-84 \nKorpela, 2015). Simultaneously quantifying hundreds or thousands of metabolites can 85 \nprovide unprecedented snapshots of an individual’s physiological state. Metabolomic profiles 86 \npredict many common incident diseases (Buergel et al., 2022) and mortality risk (Deelen et 87 \nal., 2019). Over the past decade, studies have characterised associations between 88 \nchronological age and metabolomic biomarkers (Lawton et al., 2008; Menni et al., 2013; Yu 89 \net al., 2012). The first study to develop a “metabolite-derived age variable” showed that a 90 \npanel of 22 metabolites explained 59% of the variance in chronological age. A linear 91 \ncombination of these metabolites was correlated with age-related clinical measures 92 \nindependent of chronological age (Menni et al., 2013). The first study to develop a biological 93 \nageing clock from metabolomics data showed that the difference between predicted and 94 \nchronological age, metabolomic age delta, was associated with a higher disease burden and 95 \nhigher mortality (Hertel et al., 2016). Analyses in other samples, for example the Airwave 96 \nHealth Monitoring Study in the UK (Robinson et al., 2020) and the Dutch BBMRI-NL 97 \nconsortium (van den Akker et al., 2020), have since replicated some of these findings. 98 \nMetabolomics is amongst the most powerful omics data for biological age estimation 99 \n(Solovev et al., 2020) and prediction of disease (Macdonald-Dunlop et al., 2022). 100 \n 101 \nThe aim of this study was to compare multiple machine learning algorithms for developing 102 \nageing clocks from nuclear magnetic resonance (NMR) spectroscopy metabolomics data in 103 \nmore than 100,000 participants in the UK Biobank (Bycroft et al., 2018). These data provide 104 \nan unprecedented resource to develop ageing clocks and represent one of the largest single 105 \nNMR metabolomics databases to date. To validate how well each ageing clock predicted age-106 \nrelated morbidity and lifespan, and captured biological signal beyond that approximated by 107 \nchronological age (Hertel et al., 2019), we assessed their associations with multiple health 108 \nindicators (e.g., telomere length and frailty) and all-cause mortality.  109 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 5 \nMethods 110 \nStudy population 111 \nThe UK Biobank is a prospective health study of over 500,000 UK residents aged 37–73 who 112 \nwere recruited between 2006 and 2010. Individuals registered with the UK National Health 113 \nService (NHS) and living within a 25-mile (~40 km) radius of one of 22 assessment centres 114 \nwere invited to participate (Bycroft et al., 2018). Participants provided data on their 115 \nsociodemographic characteristics, health behaviours and medical history, underwent physical 116 \nexamination and had blood and urine samples taken. There is extensive record linkage, for 117 \nexample with national death registries, hospital inpatient records and primary care data. 118 \n 119 \nMetabolomic biomarker quantification 120 \nNuclear magnetic resonance (NMR) spectroscopy metabolomic biomarkers were quantified 121 \nin non-fasting blood plasma samples taken at the baseline assessment. The Nightingale 122 \nHealth platform ascertains 168 circulating metabolites using a high-throughput standardized 123 \nprotocol for sample quality control, preparation, data storage and automated analyses (Würtz 124 \net al., 2017). The metabolites span multiple pathways, including lipoprotein lipids in 14 125 \nsubclasses, circulating fatty acids and fatty acid compositions, as well as low-molecular 126 \nweight metabolites, such as amino acids, ketone bodies and glycolysis metabolites. Most 127 \nmeasures are highly correlated (r > 0.9) with routine clinical chemistry assays (Würtz et al., 128 \n2017). For further details on sample preparation and quality control procedures, see 129 \nhttps://biobank.ndph.ox.ac.uk/ukb/ukb/docs/nmrm_companion_doc.pdf. We used the first 130 \nrelease of metabolomics data (March 2021) on a random subset of 118,019 participants. 131 \n 132 \nMachine learning 133 \nWe evaluated 17 machine learning algorithms, including regularised linear regression, latent 134 \nvariable modelling, instance-based learning, non-parametric regression, kernel-based 135 \nmethods, tree-based models, rule-based models and ensemble methods (Panel 1). To 136 \ninternally validate each algorithm in predicting chronological age from plasma metabolites, 137 \nwe implemented 10×5 nested cross-validation (Figure 1a). Nested cross-validation is 138 \npreferred for internal validation over other existing approaches as it provides more accurate 139 \nerror estimation (Bates, Hastie, & Tibshirani). We split the data into 10 folds of equal size, to 140 \nwhich individuals were allocated at random while preserving the chronological age 141 \ndistribution of the full analytical sample (Figure 1b).  142 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 6 \nPanel 1. Overview of the machine learning algorithms used in this study. 143 \n 144 \nRidge regression: linear regression model with a penalty term (L2 regularization) to shrink the 145 \nmagnitude of coefficient estimates towards zero (Hoerl & Kennard, 1970). 146 \n 147 \nLeast Absolute Shrinkage and Selection Operator (LASSO): linear regression model with a 148 \npenalty term (L1 regularization) to shrink the magnitude of coefficient estimates towards 149 \nzero. This technique can result in sparse models as variable selection is performed by 150 \nreducing some coefficient estimates exactly equal to zero (Tibshirani, 1996). 151 \n 152 \nElastic net: linear regression model that combines the L1 and L2 penalty terms of LASSO and 153 \nRidge regression. This technique reduces the magnitude of some coefficient estimates 154 \ntowards zero and can perform variable selection by reducing some coefficient estimates 155 \nexactly equal to zero (Zou & Hastie, 2005). 156 \n 157 \nPartial least squares regression (PLSR): latent variable model that extracts a set of latent 158 \nfactors that best explain the covariance between the predictors and outcome. These factors 159 \nare then used as predictors in a linear regression model (Wold, Sjöström, & Eriksson, 2001). 160 \n 161 \nK-nearest neighbors (KNN): instance-based learning model which uses the weighted average 162 \noutcome of the k nearest data points to make predictions. In this context, “nearest” is usually 163 \ndetermined by a distance metric such as the Minkowski distance (Cover & Hart, 1967). 164 \n 165 \nMultivariate adaptive regression splines (MARS): non-parametric regression model that 166 \ncreates piecewise linear approximations of the relationship between the predictors and 167 \noutcome. This technique can model non-linear associations and interactions between the 168 \npredictors (J. Friedman, H., 1991). 169 \n 170 \nMARS ensemble: ensemble method that combines the predictions of multiple MARS models 171 \nto improve the predictive accuracy and stability of the model (Kuhn & Johnson, 2013a). 172 \n 173 \nSupport vector regression (SVR): kernel-based method that seeks to identify a hyperplane 174 \nthat best models the relationships between the predictors and outcome. This variation of the 175 \nsupport vector machine algorithm (Boser, Guyon, & Vapnik, 1992) was adapted for 176 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 7 \nregression and can employ a range of kernels to transform the data to a higher-dimensional 177 \nspace, allowing for complex non-linear associations (Drucker, Burges, Kaufman, Smola, & 178 \nVapnik, 1996). We tested linear, polynomial and radial basis function kernels. 179 \n 180 \nRegression tree: technique that models the relationship between the predictors and outcome 181 \nby creating a tree-like structure of decision rules based on values of the predictors. Decision 182 \ntrees are interpretable and can incorporate non-linear relationships and higher-order 183 \ninteractions in the data (Breiman, Friedman, Olshen, & Stone, 1984). 184 \n 185 \nBagging: ensemble method that combines the predictions of multiple regression trees. 186 \nBootstrapped aggregating (“bagging”) involves training regression trees on multiple, 187 \nrandomly selected (“bootstrapped”) samples of the data. Bagging can improve the stability 188 \nand accuracy of decision tree models (Breiman, 1996). 189 \n 190 \nRandom forest: ensemble method that combines predictions of multiple regression trees. 191 \nEach tree is trained on a random subset of the data and, at each split, a subset of predictors, 192 \nreducing the correlation between decision trees in the ensemble (Breiman, 2001). 193 \n 194 \nExtreme gradient boosting (XGBoost): ensemble method that builds decision trees 195 \nsequentially by implementing a gradient descent algorithm that seeks to minimize errors from 196 \nprevious models while increasing the influence (“boosting”) of highly predictive models. 197 \nMore complex models are penalised through L1 and L2 regularization to avoid overfitting (T. 198 \nChen & Guestrin, 2016). 199 \n 200 \nBayesian additive regression trees (BART): ensemble method that uses Bayesian techniques 201 \nto iteratively construct and update multiple decision trees. Regularization priors force each 202 \ntree to explain only a subset of the relationship between the predictors and outcome, thereby 203 \npreventing overfitting (Chipman, George, & McCulloch, 2010). 204 \n 205 \nCubist rule-based regression: ensemble model that that derives rules from decision trees and 206 \nfits linear regression models for the subset of the data defined by each rule. The model 207 \nincorporates boosting techniques and may adjust predictions based on k-nearest neighbors 208 \n(Kuhn & Johnson, 2013b; Quinlan, 1992). 209 \n 210 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 8 \nRuleFit ensemble: ensemble method that uses a tree-based model (XGBoost) to predict an 211 \noutcome and subsequently derives rules. LASSO is then used to select the most predictive 212 \nrules, resulting in a sparse linear model (J. H. Friedman & Popescu, 2008). 213 \n 214 \nFor each iteration of the outer loop of the nested cross-validation, 9/10 folds combined served 215 \nas the training set and the tenth fold served as the test set. The 90% training sets were further 216 \ndivided into five equal size sets, and we performed 5-fold cross validation to empirically 217 \nidentify, for each algorithm, the hyperparameter combination that resulted in the lowest 218 \ncross-validation mean absolute error (MAE). Tuning grids were set up using a maximum 219 \nentropy space-filling design. The size of each tuning grid was determined by the number of 220 \navailable hyperparameters, type of hyperparameter (continuous, discrete or categorical) and 221 \ncomputational constraints. We tested up to ten values for each hyperparameter, resulting in 222 \ntuning grid sizes between ten (for Ridge regression) and 3125 (for XGBoost). Further details, 223 \nincluding pre-processing requirements, are available in Table S1. The model specifications 224 \nwith the lowest 5-fold cross-validation MAE were subsequently fit in the 90% training sets, 225 \nand performance was assessed by calculating the MAE, root-mean-square error (RMSE), 226 \nPearson correlation coefficient (r) and the coefficient of determination (R2) in the 10% test 227 \nsets. We also examined the average magnitude of discrepancy in predictive performance 228 \nbetween the training and test sets, extrapolation beyond the chronological age range in the 229 \ndata and the computing hours required for hyperparameter tuning for each model. 230 \n 231 \nMetabolomic ageing clocks 232 \nIndividual-level age predictions for all participants were obtained by aggregating the 233 \npredictions of the ten test sets of the outer loop of the nested cross-validation. Metabolomic 234 \nage delta (MileAge delta) was calculated as the difference between predicted and 235 \nchronological age, with positive values representing an older predicted than chronological 236 \nage and negative values representing a younger predicted than chronological age. Given that 237 \nageing clocks overestimate age in young individuals and underestimate age in older 238 \nindividuals, we regressed predicted age (MileAge) on chronological age and used the 239 \nresulting intercept (β ) and slope coefficient (α ) estimates to apply a statistical correction to 240 \nthe 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 \nLange & Cole, 2020).  242 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 9 \nHealth indicators and mortality 243 \nWe tested associations between MileAge delta (adj.) and multiple health indicators: having a 244 \nlong-standing illness, disability or infirmity (yes/no), self-rated health (“poor”, “fair”, “good” 245 \nor “excellent”) and overall health status (unhealthy/healthy) derived from 81 cancer and 443 246 \nnon-cancer illnesses (Mutz & Lewis, 2022; Mutz et al., 2021). Next we examined 247 \nassociations with the frailty phenotype and frailty index (Mutz, Choudhury, Zhao, & Dregan, 248 \n2022). The frailty phenotype summarises data on weight loss, exhaustion, physical activity, 249 \nwalking speed and hand-grip strength. The frailty index was derived from 49 variables 250 \nobtained at the baseline assessment, including cardiometabolic, cranial, immunological, 251 \nmusculoskeletal, respiratory and sensory traits, well-being, infirmity, cancer and pain. We 252 \nalso tested associations between MileAge delta (adj.) and telomere length, measured using a 253 \nvalidated quantitative polymerase chain reaction assay that expresses telomere length as the 254 \nratio of the telomere repeat copy number (T) relative to a single-copy gene (S) that encodes 255 \nhaemoglobin subunit beta. T/S ratio is proportional to an individual’s average telomere length 256 \n(Lai, Wright, & Shay, 2018). Finally, we examined prospective associations with all-cause 257 \nmortality. The date of death was obtained through linkage with national death registries, NHS 258 \nDigital (England and Wales) and the NHS Central Register (Scotland). The censoring date 259 \nwas 30 November 2022. 260 \n 261 \nExclusion criteria 262 \nWomen who were pregnant or unsure that they were pregnant at the time of assessment were 263 \nexcluded from the analysis given that their metabolite profiles likely changed during 264 \npregnancy. Participants for whom their genetic and self-reported sex did not match were also 265 \nexcluded as this may indicate poor data quality. We also excluded individuals with missing 266 \nmetabolite data or potential outlier metabolite values, defined as values 4× the interquartile 267 \nrange (IQR) above or below the median. 268 \n 269 \nStatistical analyses 270 \nAll data processing and analyses were performed in R (version 4.2). 271 \n 272 \nSample characteristics were summarised using means and standard deviations or counts and 273 \npercentages. Generalised additive models were used to explore the relationship between 274 \nchronological age and metabolite levels. We further conducted metabolome-wide association 275 \nanalyses of chronological age and all-cause mortality to identify metabolites that were 276 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 10\nstatistically significantly associated with chronological age and mortality (at P < 0.05/168). 277 \nCorrelations between the predicted age derived from each machine learning model were 278 \nestimated using Pearson’s correlation coefficient. 279 \n 280 \nCross-sectional associations between MileAge delta (adj.) and the frailty index and telomere 281 \nlength were estimated using ordinary least squares regression. Associations between MileAge 282 \ndelta and having a long-standing illness and overall health status were estimated using 283 \nlogistic regression. Association between MileAge delta and the frailty phenotype and self-284 \nrated health were estimated using ordinal logistic regression. For each health indicator, higher 285 \nvalues corresponded to worse health. For the health association analyses, we fitted minimally 286 \nadjusted models that included chronological age and sex as covariates. For the prospective 287 \nanalyses of all-cause mortality, we calculated person-years of follow-up and the median 288 \nduration of follow-up of censored individuals. Survival probabilities by MileAge delta were 289 \nestimated using the Kaplan-Meier (KM) method (Kaplan & Meier, 1958) and we calculated 290 \nlog-rank p-values. Hazard ratios (HRs) and 95% confidence intervals were estimated using 291 \nCox proportional hazards models (Cox, 1972). Age in years was used as the underlying time 292 \naxis, with age 40 as the start of follow-up. Across both cross-sectional and prospective 293 \nanalyses, we defined MileAge delta subgroups by standard deviation from the mean. 294 \nIndividuals with a MileAge delta equal to or smaller than one standard deviation below the 295 \nmean were the reference group. To discern how this analytical decision might impact results, 296 \nand to enable comparability with other studies, we also report associations with all-cause 297 \nmortality for all models with subgroups defined by the bottom and top 10% of the 298 \ndistribution as well as negative and positive values. Finally, we used generalised additive 299 \nmodels and spline functions to explore the relationship between MileAge delta as a 300 \ncontinuous variable and health indicators and all-cause mortality, respectively. 301 \n 302 \nFor the Cubist rule-based regression model, which across most analyses performed best at 303 \npredicting health outcomes, we performed additional analyses. We calculated variable 304 \nimportance scores to identify metabolites that strongly contributed to MileAge. We explored 305 \nassociations between MileAge delta and all-cause mortality stratified by sex, self-rated health 306 \nand chronological age group (39-49, 50-59 and 60-71 years). Finally, we assessed the 307 \nperformance of our ageing clock by benchmarking it against other ageing markers: (a) we 308 \nestimated the hazard ratio for all-cause mortality by MileAge delta and other ageing marker 309 \n(grip strength, telomere length and the frailty index) subgroups defined by standard deviation 310 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 11\nfrom the mean, adjusted for chronological age and sex; (b) we calculated the C-index and 311 \n95% confidence intervals for chronological age + sex (as the base model) and for each ageing 312 \nmarker added separately to the model, with time (in days) since the baseline assessment as 313 \nthe underlying time axis.  314 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 12\nResults 315 \nSample characteristics 316 \nOf the 118,019 participants with metabolomics data, 110,730 had complete information on all 317 \nmetabolites (Figure S1). After removing individuals with potential outlier metabolite values, 318 \ninconsistencies between self-reported and genetic sex or possible pregnancies, the analytical 319 \nsample included 101,359 participants (Table 1). The mean chronological age was 56.44 years 320 \n(SD = 8.12), with the most common age being 61 years (Figure 1b). Most metabolite levels 321 \nvaried by chronological age (Figure 1c), showing considerable evidence of non-linear 322 \nrelationships (Figures S2-S33). 323 \n 324 \nTable 1. Sample characteristics \n  MileAge delta (adj.) \n Full sample \n(N=101359) \n≤  1SD below \nthe mean \n(n=16204) \nMiddle \n(n=69166) \n≥  1SD above \nthe mean \n(n=15989) \nAge; mean (SD) 56.44 (8.12) 55.85 (8.33) 56.75 (8.08) 55.69 (8.00) \nSex     \nFemale 54484 (53.8%) 8062 (49.8%) 37002 (53.5%)  9420 (58.9%) \nMale 46875 (46.2%)  8142 (50.2%) 32164 (46.5%)  6569 (41.1%) \nEthnicity     \nWhite 95672 (94.4%)  15163 (93.6%) 65486 (94.7%) 15023 (94.0%) \nMixed-race 574 (0.6%) 103 (0.6%) 386 (0.6%) 85 (0.5%) \nBlack 1529 (1.5%) 233 (1.4%) 975 (1.4%) 321 (2.0%) \nAsian 1953 (1.9%) 375 (2.3%) 1265 (1.8%) 313 (2.0%) \nChinese 291 (0.3%) 77 (0.5%) 184 (0.3%) 30 (0.2%) \nOther 880 (0.9%) 173 (1.1%) 564 (0.8%) 143 (0.9%) \nMissing1 460 (0.5%) 80 (0.5%) 306 (0.4%) 74 (0.5%) \nHighest qualification     \nNone 17084 (16.9%) 2551 (15.7%) 11868 (17.2%)  2665 (16.7%) \nO levels/GCSEs/CSEs 27008 (26.6%)  4237 (26.1%) 18435 (26.7%)  4336 (27.1%) \nA levels/NVQ/HND/HNC2 23235 (22.9%)  3637 (22.4%) 15961 (23.1%)  3637 (22.7%) \nDegree 32826 (32.4%)  5577 (34.4%) 22091 (31.9%)  5158 (32.3%) \nMissing1 1206 (1.2%) 202 (1.2%) 811 (1.2%) 193 (1.2%) \nHousehold income3     \nVery low 19422 (19.2%)  2863 (17.7%) 13265 (19.2%)  3294 (20.6%) \nLow 22159 (21.9%)  3487 (21.5%) 15137 (21.9%)  3535 (22.1%) \nMedium 22634 (22.3%)  3831 (23.6%) 15417 (22.3%)  3386 (21.2%) \nHigh 17767 (17.5%)  3095 (19.1%) 12027 (17.4%)  2645 (16.5%) \nVery high 4725 (4.7%) 819 (5.1%) 3188 (4.6%) 718 (4.5%) \nMissing1 14652 (14.5%) 2109 (13.0%) 10132 (14.6%)  2411 (15.1%) \nCohabitation     \nWith partner 73896 (72.9%)  12054 (74.4%) 50748 (73.4%) 11094 (69.4%) \nSingle 8341 (8.2%) 1418 (8.8%) 5467 (7.9%) 1456 (9.1%) \nMissing1 19122 (18.9%) 2732 (16.9%) 12951 (18.7%)  3439 (21.5%) \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 13\nSmoking status     \nNever 55643 (54.9%)  9149 (56.5%) 37876 (54.8%)  8618 (53.9%) \nFormer 34805 (34.3%)  5342 (33.0%) 23838 (34.5%)  5625 (35.2%) \nCurrent 10416 (10.3%)  1634 (10.1%) 7119 (10.3%) 1663 (10.4%) \nMissing1 495 (0.5%) 79 (0.5%) 333 (0.5%) 83 (0.5%) \nMenopause4     \nNo 12986 (12.8%)  2887 (17.8%) 8096 (11.7%) 2003 (12.5%) \nYes 32745 (32.3%)  4046 (25.0%) 23034 (33.3%)  5665 (35.4%) \nMissing1 55628 (54.9%) 9271 (57.2%) 38036 (55.0%)  8321 (52.0%) \nMorbidity count     \nNone 23788 (23.5%)  4459 (27.5%) 16311 (23.6%)  3018 (18.9%) \nOne 26923 (26.6%)  4581 (28.3%) 18615 (26.9%)  3727 (23.3%) \nTwo 20535 (20.3%)  3195 (19.7%) 14011 (20.3%)  3329 (20.8%) \nThree 13157 (13.0%)  1857 (11.5%) 9001 (13.0%) 2299 (14.4%) \nFour 7553 (7.5%) 989 (6.1%) 5077 (7.3%) 1487 (9.3%) \nFive+ 9387 (9.3%) 1119 (6.9%) 6141 (8.9%) 2127 (13.3%) \nMissing1 16 (0.0%) 4 (0.0%) 10 (0.0%) 2 (0.0%) \nFasting time5; mean (SD) 3.75 (2.40) 3.74 (2.47) 3.74 (2.39) 3.79 (2.38) \nBody mass index6; mean (SD) 27.43 (4.73) 26.17 (4.07) 27.41 (4.57) 28.80 (5.59) \nNote: GCSEs = general certificate of secondary education; CSE = certificate of secondary \neducation; NVQ = national vocational qualification; HND = higher national diploma; HNC = \nhigher national certificate. MileAge delta (adj.) derived from the Cubist rule-based regression \nmodel. 1Missing data may also include “do not know”, “prefer not to answer”, “not applicable” \nor related responses. 2Also includes 'other professional qualifications'. 3Annual household \nincome groups: very low (<£18,000), low (£18,000–£30,999), middle (£31,000–£51,999), high \n(£52,000–£100,000) and very high (>£100,000). \n4n = 59519 females. 5n = 3 missing. 6n = 345 \nmissing. \n 325 \nMetabolite-wide associations 326 \n165/168 metabolites were associated with chronological age (p < 0.05/168). While most 327 \nmetabolite levels were elevated in older individuals (e.g., Omega 3, citrate and glucose), 328 \nseven, including albumin, glycine and histidine, were negatively associated with 329 \nchronological age (Figure S34; Additional file 1). Amongst the 119 metabolites associated 330 \nwith all-cause mortality, GlycA was most strongly associated with a higher mortality hazard 331 \n(HR = 1.22, 95% CI 1.20-1.25, p < 0.001), whereas the degree of unsaturation, 332 \ndocosahexaenoic acid (DHA) and Omega 3 were strongly associated with a lower mortality 333 \nhazard (Figure S35; Additional file 2). Notably, 116 metabolites associated with 334 \nchronological age also predicted mortality, with GlycA, Omega 3 and DHA amongst the 335 \nmost strongly associated metabolites of both age and mortality (Figure 1d). Between 87% 336 \nand 95% of the metabolites that were statistically significantly associated with other health 337 \nindicators (e.g., frailty and health status) were associated with chronological age (Figure 338 \nS36). The exception was telomere length for which only 53% of statistically significant 339 \nmetabolites were shared with chronological age. 340 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 14\n 341 \nPredictive model performance 342 \nPredictive performance estimates in the 90% training (n = 91,222 to 91,226) and 10% test 343 \nsets are shown in Table S3. The nested cross-validation mean absolute error (MAE) in the 344 \ntest sets (n = 10,133 to 10,137) ranged from 5.31 to 6.36 years, with the support vector 345 \nregression with a radial basis function (SVM radial) performing best and the MARS 346 \nensemble performing worst. The root-mean-square error (RMSE) ranged from 6.60 to 7.58 347 \nyears. Correlation coefficients between predicted and chronological age ranged from 0.36 to 348 \n0.59, with R2 values between 0.13 and 0.35. The difference in predictive performance 349 \nbetween the training and test sets, i.e., the model’s optimism which may indicate poor 350 \ngeneralization to unseen data, was generally low (e.g., MAEdifference < 0.15 for 10/17 models). 351 \nHowever, certain tree-based models (bagging, random forest and XGBoost) and the k-nearest 352 \nneighbors model overfit the training data (MAEdifference = -1.51 to -5.83), with correlation 353 \ncoefficients between predicted and chronological age of r > 0.8 in the training sets (Figure 354 \nS40). Figure 2a shows the nested cross-validation MAEs for all models. For comparison, 355 \ndrawing random samples from a uniform distribution between the sample’s minimum and 356 \nmaximum chronological age, i.e., a random prediction model, resulted in a MAE = 9.79. 357 \nPredicting the sample mean, i.e., a null model, resulted in a MAE = 6.96. Additional plots 358 \nshowing other performance measures (MAE, RMSE, r and R2) in the training and test sets are 359 \npresented in the supplement (Figures S37-S43). There were moderate to high correlations 360 \nbetween the predicted age values of the various models (r = 0.48 to > 0.99) (Figure 2b). High 361 \ncorrelations (r > 0.87) amongst the most accurate models suggest they capture similar 362 \npatterns in the data. Omega 3, albumin and citrate were amongst the most important 363 \ncontributors to predictive accuracy (Figure S44). 364 \n 365 \nAge bias correction 366 \nAll models overestimated the age of young individuals and underestimated the age of older 367 \nindividuals (Figure S44). Applying a statistical correction (see Methods) to the predicted age 368 \nvalues removed this bias (Figures 2c-e and S45). The predicted age values were originally 369 \nwithin the chronological age range (39 to 70 years) of the sample for most individuals. 370 \nAcross all models, 0.23% (n = 238) and 0.96% (n = 976) of predictions were below or above 371 \nthe minimum and maximum age, respectively (Table S4). More predicted age values were 372 \noutside the chronological age range (up to 8.27%, n = 8382 for a single model) after the age 373 \nbias correction. Re-calculating the predictive performance estimates after the age bias 374 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 15\ncorrection suggested higher accuracy (MAE = 2.12 to 3.40; Figure 2f). The overall 375 \nperformance rankings across the models inverted, with the models that originally predicted 376 \nchronological age best showing reduced accuracy (Figures S46-S48). The age bias adjusted 377 \nMileAge delta ranged from -18.94 years younger to 16.05 years older for the Cubist rule-378 \nbased regression model, with 15.99% (n = 16,204) and 15.77% (n = 15,989) of the sample 379 \nhaving a MileAge delta (adj.) of at least 3.75 years below or above the mean (Figure 2g; 380 \nTable S5). 381 \n 382 \nAssociations with health indicators 383 \nDescriptive statistics for the health indicators are shown in Table S6. Having an older 384 \npredicted than chronological age was associated with higher frailty index scores across all 385 \nmodels (Table S7). This extended to the frailty phenotype for all models when comparing 386 \nindividuals with a MileAge delta (adj.) more than one standard deviation above and below 387 \nthe mean, and for 12/17 models when comparing the middle of the distribution to individuals 388 \nwith MileAge delta (adj.) values more than one standard deviation below the mean (Table 389 \nS8). For telomere length, we observed a group difference for 12/17 models when comparing 390 \nthe tails of the distribution, and for 9/17 models when comparing the middle of the 391 \ndistribution to the reference group (Table S9). Having an older predicted than chronological 392 \nage was generally associated with chronic illness and poor self-rated health (Tables S10- 393 \nS12). An exception to this pattern were the MARS models, for which an older predicted than 394 \nchronological age was associated with longer telomeres, and for which there was little 395 \nevidence of statistically significant differences in health between individuals with MileAge 396 \ndelta (adj.) values in the middle of the distribution and the reference group. 397 \n 398 \nMileAge delta (adj.) derived from the Cubist rule-based regression model was most strongly 399 \nassociated with most health indicators (Figure 3a). Individuals with a MileAge delta (adj.) 400 \ngreater than one standard deviation above the mean had higher frailty index scores than 401 \nindividuals with a MileAge delta (adj.) smaller than one standard deviation below the mean 402 \n(β  = 0.023, 95% CI 0.021–0.024, p < 0.001). This group difference was approximately 403 \nequivalent to an 18.3-year chronological age difference in frailty index scores (β  = 0.023 404 \ndivided by β  = 0.001255 derived from a linear model, y frailty index ~ x chronological age). 405 \nIndividuals with an older predicted than chronological age were also more likely to be 406 \nphysically frail (OR = 1.29, 95% CI 1.23–1.35, p < 0.001) and had shorter telomeres (β  = 407 \n0.052, 95% CI 0.030 to 0.073, p < 0.001) equivalent to a 2.2-year chronological age 408 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 16\ndifference in telomere length. Such individuals were also more likely to have a long-standing 409 \nillness (OR = 1.82, 95% CI 1.73–1.91, p < 0.001), poorer health status (OR = 1.85, 95% CI 410 \n1.76–1.94, p < 0.001) and worse self-rated health (OR = 1.72, 95% CI 1.65–1.80, p < 0.001). 411 \nGeneralised additive models showed that positive MileAge delta (adj.) values, indicating 412 \naccelerated biological ageing, were robustly associated with unfavourable health (Figure 3b), 413 \nwhereas negative MileAge delta (adj.) values were only weakly associated with favourable 414 \nhealth, a pattern that was consistent across most models (Figures S49-S54). 415 \n 416 \nPredicting mortality 417 \nThe median duration of follow-up of censored individuals was 13.87 years (IQR = 1.37 418 \nyears), with 1,361,970 person-years of follow-up. There were 8113 deaths amongst 101,274 419 \nparticipants (n = 85 missing). MileAge (adj.) was strongly associated with all-cause 420 \nmortality, comparable to chronological age (Figures 4a-e). In the prospective analyses we 421 \nexamined the age bias adjusted MileAge delta and models were adjusted for chronological 422 \nage and sex, with age (in years) as the underlying time axis (Figure S55 and Table S13). 423 \n 424 \nFor the Cubist rule-based regression model, the hazard ratio (HR) comparing individuals with 425 \na MileAge delta (adj.) greater than one standard deviation above and below the mean was HR 426 \n= 1.52 (95% CI 1.41-1.64, p < 0.001). Individuals with a MileAge delta (adj.) between one 427 \nstandard deviation above and below the mean had a statistically significantly higher mortality 428 \nrisk for 14/17 models (p between 0.03 and < 0.001) (Table S14). Comparing the bottom and 429 \ntop 10% of the MileAge delta (adj.) distribution, instead of one standard deviation above and 430 \nbelow the mean, resulted in greater differences (e.g., HR = 1.63, 95% CI 1.48-1.79, p < 0.001 431 \nfor the Cubist model). Individuals in between the tails of the distribution had a higher 432 \nmortality risk compared to the bottom 10% for 14/17 models (Figure S56 and Table S15). 433 \nWhen comparing individuals with a positive and negative MileAge delta (adj.), we found that 434 \nindividuals with an older predicted than chronological age had a higher mortality risk for all 435 \nmodels except the MARS models (Figure S57 and Table S16). Modelling the mortality 436 \nhazard as a spline function of MileAge delta (adj.) suggested that positive values were 437 \nstrongly associated with a higher mortality hazard, while there was little evidence that 438 \nnegative values were associated with a lower mortality hazard (Figure S58). 439 \n 440 \nF\nemales had slightly higher MileAge delta (adj.) values than males (Figure 4f), a pattern 441 \nwhich we observed across all models (Figure S59). The mortality hazard of individuals with a 442 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 17\nMileAge delta (adj.) greater than one standard deviation above the mean was elevated in both 443 \nfemales (HR = 1.26, 95% CI 1.11-1.43, p < 0.001) and males (HR = 1.73, 95% CI 1.57-1.91, 444 \np < 0.001) (Figures S60-S61; Table S17). The difference in mortality between individuals 445 \nwith a MileAge delta (adj.) in the middle of the distribution and the reference group was only 446 \nstatistically significant in males (HR = 1.14, 95% CI 1.05-1.23, p = 0.002). Stratifying the 447 \nsample by self-rated health, the mortality hazard of individuals with a MileAge delta (adj.) 448 \ngreater than one standard deviation above the mean was higher in all strata (e.g., HR = 1.41, 449 \n95% CI 1.11-1.78, p < 0.001 for poor self-rated health) except for individuals with excellent 450 \nhealth (Figure 4g and Table S17). The mortality hazard of individuals with a MileAge delta 451 \n(adj.) greater than one standard deviation above the mean was higher in the age groups above 452 \n50 years (Figures S62 and 4h; Table S17). 453 \n 454 \nComparison with other ageing markers 455 \nA comparison of the all-cause mortality hazard associated with MileAge delta (adj.) and 456 \nother ageing marker subgroups defined by the standard deviation from the mean showed that 457 \nthe largest hazard ratio (HR = 2.90) was observed for the frailty index (Figure 5a). The 458 \nsmallest hazard ratio was observed for telomere length (HR = 1.31) (Table S18), with 459 \nMileAge delta (adj.) (HR = 1.52) and grip strength (HR = 1.90) in-between. Adding each 460 \nageing marker individually as a continuous variable to a base model that included 461 \nchronological age and sex improved prediction of all-cause mortality, with the best prediction 462 \nobserved for the frailty index (C-index 0.737, 95% CI 0.732 to 0.742 vs C-index 0.716, 95% 463 \nCI 0.711 to 0.722 for the base model) (Figure 5b and Table S19). Modelling the mortality 464 \nhazard as a spline function of the ageing markers, to identify potential non-linear effects, 465 \nsuggested that the all-cause mortality hazard was considerably higher in individuals with an 466 \nolder predicted than chronological age. For example, compared to the sample median 467 \nMileAge delta (adj.), which was equivalent to no difference between predicted and 468 \nchronological age, a MileAge delta (adj.) of 10 was associated with a HR of about 2.7, i.e., a 469 \n170% higher morality hazard (Figure 5c).  470 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 18\nDiscussion 471 \nIn 101,359 UK Biobank participants with Nightingale Health metabolomics data, we 472 \nobserved that most metabolite levels varied by chronological age, with considerable evidence 473 \nof non-linear associations. Across the machine learning algorithms employed to develop 474 \nageing clocks from circulating plasma metabolites, the nested cross-validation mean absolute 475 \nerror between predicted age (MileAge) and chronological age ranged from 5.31 to 6.36 years 476 \n(R2 between 0.13 and 0.35). All models overestimated age in young individuals and 477 \nunderestimated age in older individuals. After applying a statistical correction to remove this 478 \nage bias, 31.76% of participants had adjusted MileAge delta values of at least 3.75 years, 479 \nhighlighting the potential of metabolomic ageing clocks to differentiate between individuals 480 \nof the same chronological age (Hertel et al., 2019). While there was a high degree of 481 \nconsistency across the top performing models such as support vector regression, tree-based 482 \nand rule-based ensembles, the ageing clock derived from a Cubist rule-based regression 483 \nmodel (MAE = 5.42) was most strongly associated with most health indicators. We observed 484 \nacross most models that individuals with an older predicted than chronological age, 485 \nindicating accelerated biological ageing, were frailer, had shorter telomeres, were more likely 486 \nto have a chronic illness, rated their health worse and had a higher mortality risk. 487 \n 488 \nMultiple studies have developed biological ageing clocks trained on chronological age from 489 \nmetabolomics data. The seminal study by Menni et al. (2013) derived a metabolite age score 490 \nas a linear combination of 22 plasma metabolites that were correlated with chronological age 491 \nin 6055 twins, achieving an R2 of 59% and a hazard ratio for all-cause mortality of HR = 1.08 492 \nper year. Hertel et al. (2016) tested a multivariable linear regression and a fractional 493 \npolynomial model in 3611 participants, with the latter achieving a correlation between 494 \npredicted and chronological age of r = 0.53 (RMSE = 11.19) in men and r = 0.61 (RMSE = 495 \n10.37) in women. Their metabolomic ageing clock included 59 urinary metabolites and was 496 \npredictive of all-cause mortality (HR = 1.24 per SD). Robinson et al. (2020) developed 497 \nseveral ageing clocks using elastic net models in 2238 participants, with correlations between 498 \npredicted and chronological age of r = 0.45 (MAE = 4.17) to r = 0.83 (MAE = 6.49). Akker 499 \net al. (2020) developed an ageing clock, MetaboAge, from 56 metabolites in 18,716 500 \nparticipants from 24 community and hospital-based cohorts using a linear regression model, 501 \nachieving a correlation of r = 0.65 and a median absolute error of 7.3. An independent 502 \nexternal validation of this clock observed a notably lower correlation of r = 0.21 (Macdonald-503 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 19\nDunlop et al., 2022). The same study also developed a clock from NMR metabolomics data 504 \n(81/86 metabolites selected) in 1643 individuals, which achieved a correlation of r = 0.74 but 505 \nfailed to replicate in a validation cohort, and another clock from mass spectrometry 506 \nmetabolomics (181/682 metabolites selected) in 861 individuals, which achieved a 507 \ncorrelation of r = 0.81 (Macdonald-Dunlop et al., 2022). An updated ageing clock, 508 \nMetaboAge 2.0, in the BBMRI-nl data that included 65 metabolites achieved an R2 of 0.451 509 \nand 0.449 for a linear regression and elastic net model, respectively (Bizzarri et al., 2023). 510 \n 511 \nMetabolomic ageing clocks trained on chronological age are generally less accurate than 512 \nageing clocks derived from other types of omics data (Rutledge et al., 2022). Nevertheless, 513 \nour most predictive model (MAE = 5.31 years) had a similar accuracy as a deep learning 514 \nageing clock (MAE = 5.68) derived from blood markers, biometrics and sex in the China 515 \nHealth and Retirement Longitudinal Study. An elastic net model in the same data achieved a 516 \nMAE = 6.19 years (Galkin et al., 2022), while the elastic net model in our study had a lower 517 \nMAE = 5.70, likely due to the larger sample size. While a discussion of how well different 518 \nageing clocks predict health outcomes is beyond the scope of this study, the most widely 519 \ntested epigenetic ageing clocks that were trained on chronological age are weak predictors of 520 \nmortality (B. H. Chen et al., 2016; Fransquet, Wrigglesworth, Woods, Ernst, & Ryan, 2019). 521 \nSecond-generation ageing clocks are more predictive of mortality. For example, a one-year 522 \nincrease in PhenoAge, which was trained on physiological dysregulation, was associated with 523 \na 9% increase in mortality risk. Its epigenetic derivation, DNAm PhenoAge, was associated 524 \nwith a 4.5% increase in all-cause mortality (Levine et al., 2018). GrimAge, another popular 525 \nmortality risk predictor that incorporates chronological age, sex and eight DNA methylation 526 \nsurrogate markers (seven for plasma proteins and one for smoking pack-years) strongly 527 \npredicts mortality and age-related diseases (Lu et al., 2019). A recent clock developed from 528 \ncirculating biomarkers and trained to predict mortality in the UK Biobank (n = 307,000) 529 \nusing an elastic net Cox model (Bortz et al., 2023) yielded a 9.2% relative increase in 530 \nprediction compared to the PhenoAge model. However, the improvement in prediction over a 531 \nmodel that included chronological age and sex was modest (C-index 0.715 vs 0.762, 532 \ncompared to 0.716 vs 0.719 in our study; though note that our clock was not trained to predict 533 \nmortality). These findings suggest that certain omics clocks capture physiologically relevant 534 \nsignals more, while first-generation epigenetic clocks are specifically good at predicting 535 \nchronological time (Rutledge et al., 2022). 536 \n 537 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 20\nAlthough chronological age prediction is valuable in fields such as forensics (Vidaki et al., 538 \n2017), it is of limited use in population health and geroscience, given that chronological age 539 \nis non-modifiable (Robinson & Lau, 2020). A perfect prediction model would merely tell us 540 \nabout chronological, not biological, age (Nakamura et al., 1988). It is the difference between 541 \npredicted and chronological age (MileAge delta) that serves as an indicator of accelerated or 542 \ndecelerated ageing. A less accurate chronological age prediction does not necessarily indicate 543 \na worse biological age model (Hertel et al., 2019), hence we also tested algorithms that were 544 \nexpected to perform less well at predicting chronological age (e.g., bagging). Prior studies 545 \nsuggested that biological age estimates derived from physical activity (Pyrkov et al., 2018) or 546 \nepigenetic data (Zhang et al., 2019) with higher predictive accuracy of chronological age 547 \nwere less predictive of all-cause mortality. Our study showed that the models that were most 548 \npredictive of chronological age were generally also more strongly associated with health and 549 \nmortality, though we note that the pattern of predictive accuracy largely inverted after we 550 \napplied the age bias correction. 551 \n 552 \nWe report several additional analyses, including variable importance scores and 553 \nbenchmarking against other ageing markers, for the ageing clock derived from the Cubist 554 \nrule-based regression model, which was most strongly associated with most health indicators. 555 \nThere are, however, several conclusions that can be drawn across most of the machine 556 \nlearning algorithms tested. First, the wide range of the MileAge delta values quantifies the 557 \nlatent patterns in the metabolomics data not captured by chronological age and suggests that 558 \nour ageing clocks approximate (past) rate of biological ageing for people of the same 559 \nchronological age. Second, the associations between most ageing clocks, health and mortality 560 \ndemonstrate that these clocks capture biologically relevant information, which may find 561 \napplications in health tracking, nutrition or in clinical trials (e.g., sample stratification). A key 562 \nfinding across most ageing clock models tested here was that associations with health and 563 \nmortality were stronger in individuals with an older predicted than chronological age and less 564 \nso in individuals with a younger predicted than chronological age. 565 \n 566 \nSeveral of the algorithms included in our comparison, including those that were most 567 \npredictive of chronological age, mortality and health, allowed for non-linear relationships in 568 \nthe data, which were often not considered in previous studies (Panyard et al., 2022). A recent 569 \nreview found that most molecular ageing clocks were developed using linear models with 570 \nregularization, whereas few used non-linear models (Xia, Wang, Yu, Chen, & Han, 2021). 571 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 21\nAlthough it has been asserted that age-related physiological markers are linearly associated 572 \nwith age (Pyrkov et al., 2018), we have shown here and in previous studies (Mutz, Hoppen, et 573 \nal., 2022; Mutz & Lewis, 2021; Mutz, Young, et al., 2022) that this does not apply to many 574 \nbiological markers. To enable comparability between studies, we provide a comprehensive 575 \nset of statistical estimates and developed our ageing clock using metabolites measured in 576 \nabsolute concentrations instead of relative to other measures. Although it may be argued that 577 \nquantification of a smaller number of metabolites would in principle be more feasible and 578 \nconvenient in clinical practice, all metabolites included in our model can be quantified from a 579 \nsingle assay with minimal sample preparation required (Würtz et al., 2017). 580 \n 581 \nLimitations and future directions 582 \nOur study had certain limitations. Some algorithms that have previously been used to develop 583 \nbiological ageing clocks, for example deep learning (Zhavoronkov, Li, Ma, & Mamoshina, 584 \n2019), or approaches combining HSIC LASSO feature selection with non-linear support 585 \nvector regression (Takahashi et al., 2020) were not tested, and could be explored in future 586 \nstudies. Our ageing clock provides a “systems level” indicator of age-related changes in 587 \nmetabolites; future clocks may be developed at the tissue or cellular level. Plasma samples 588 \nmay differ from other body fluids, e.g., serum, urine or cerebrospinal fluid. The metabolite 589 \ncoverage of the Nightingale Health platform is lipid focussed and mostly covers larger 590 \nmolecules, while there are potentially over 217,000 endogenous and exogenous molecules 591 \n(Wishart et al., 2021). Nevertheless, this platform enables robust assessment of these 592 \nmetabolites in a single experiment (Würtz et al., 2017). Although more complex ageing 593 \nclocks could be developed using technologies with wider metabolite coverage, prior analyses 594 \nsuggested that a majority of metabolites associated with age were related to lipid and amino 595 \nacid pathways, both of which were included here (Menni et al., 2013). As in previous studies, 596 \nwe observed a systematic overestimation of age in young individuals and underestimation of 597 \nage in older individuals (Nakamura et al., 1988). This bias is neither data nor method specific 598 \nand may be explained by regression to the mean (Liang, Zhang, & Niu, 2019) of the training 599 \ndata (Jones, Lee, & Topol, 2022). To account for this bias, we have adjusted the predicted 600 \nage and included chronological age as a covariate in the health association analyses (Xia et 601 \nal., 2021). Longitudinal ageing metrics may be more robustly associated with certain health 602 \noutcomes than cross-sectional ageing metrics, e.g., with physical and cognitive decline but 603 \nnot, for example, multimorbidity (Kuo et al., 2022). Future research should develop 604 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 22\nmetabolomic ageing clocks from longitudinal data. Finally, the lack of independent data for 605 \nexternal validation is a limitation. 606 \n 607 \nConclusions 608 \nMetabolomic ageing clocks derived from multiple machine learning algorithms were robustly 609 \nassociated with health indicators and mortality. We found that our ageing clock (MileAge) 610 \nderived from a Cubist rule-based regression model was overall most strongly associated with 611 \nhealth indicators. Individuals with MileAge values greater than their chronological age, 612 \nindicating accelerated biological ageing, were frailer, had shorter telomeres, were more likely 613 \nto have a chronic illness, rated their health worse and had a higher mortality risk. 614 \nMetabolomic ageing clocks hold significant promise for research on lifespan and healthspan 615 \nextension, as they provide a proxy of biological ageing that is potentially modifiable. These 616 \nclocks may also help identify health risks before clinical symptoms emerge. As such, 617 \nbiological ageing clocks may contribute to health risk assessments, complementing clinical 618 \nbiomarkers. However, the utility of ageing clocks is not limited to risk stratification, but also 619 \nin providing an intuitive, year-based metric for health tracking that may help individuals 620 \nproactively engage with their health.  621 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 23\nAcknowledgments 622 \nThis research is funded by the National Institute for Health and Care Research (NIHR) 623 \nMaudsley Biomedical Research Centre at South London and Maudsley NHS Foundation 624 \nTrust and King’s College London. The views expressed are those of the authors and not 625 \nnecessarily those of the NHS, the NIHR or the Department of Health and Social Care. 626 \nComputational analyses were supported by: King's College London. (2023). King's 627 \nComputational Research, Engineering and Technology Environment (CREATE). Retrieved 628 \nMay 24, 2023, from https://doi.org/10.18742/rnvf-m076. This research has been conducted 629 \nusing data from UK Biobank, a major biomedical database. Data access permission has been 630 \ngranted under UK Biobank application 45514. 631 \n 632 \nFinancial disclosures 633 \nCML is a member of the scientific advisory board of Myriad Neuroscience, has received 634 \nspeaker fees from SYNLAB and received consultancy fees from UCB. JM and RI declare no 635 \nfinancial conflict of interest. 636 \n 637 \nAuthorship contributions 638 \nJM conceived the idea of the study, acquired the data, carried out the analysis, interpreted the 639 \nfindings and wrote the manuscript. CML and RI interpreted the findings and reviewed the 640 \nmanuscript. All authors read and approved the final manuscript. 641 \n 642 \nEthics 643 \nEthical approval for the UK Biobank study has been granted by the National Information 644 \nGovernance Board for Health and Social Care and the NHS North West Multicentre Research 645 \nEthics Committee (11/NW/0382). 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DNA methylation-based forensic age prediction using artificial neural 846 \nnetworks and next generation sequencing. Forensic Science International: Genetics, 847 \n28, 225-236. doi:10.1016/j.fsigen.2017.02.009 848 \nWishart, D. S., Guo, A., Oler, E., Wang, F., Anjum, A., Peters, H., . . . Gautam, V. (2021). 849 \nHMDB 5.0: the Human Metabolome Database for 2022. Nucleic Acids Research, 850 \n50(D1), D622-D631. doi:10.1093/nar/gkab1062 851 \nWold, S., Sjöström, M., & Eriksson, L. (2001). PLS-regression: a basic tool of chemometrics. 852 \nChemometrics and Intelligent Laboratory Systems, 58(2), 109-130. 853 \ndoi:https://doi.org/10.1016/S0169-7439(01)00155-1 854 \nWürtz, P., Kangas, A. J., Soininen, P., Lawlor, D. A., Davey Smith, G., & Ala-Korpela, M. 855 \n(2017). Quantitative Serum Nuclear Magnetic Resonance Metabolomics in Large-856 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\n 30\nScale Epidemiology: A Primer on -Omic Technologies. American Journal of 857 \nEpidemiology, 186(9), 1084-1096. doi:10.1093/aje/kwx016 858 \nXia, X., Wang, Y., Yu, Z., Chen, J., & Han, J.-D. J. (2021). Assessing the rate of aging to 859 \nmonitor aging itself. Ageing Research Reviews, 69, 101350. 860 \ndoi:https://doi.org/10.1016/j.arr.2021.101350 861 \nYu, Z., Zhai, G., Singmann, P., He, Y., Xu, T., Prehn, C., . . . Wang-Sattler, R. (2012). 862 \nHuman serum metabolic profiles are age dependent. Aging Cell, 11(6), 960-967. 863 \ndoi:https://doi.org/10.1111/j.1474-9726.2012.00865.x 864 \nZhang, Q., Vallerga, C. L., Walker, R. M., Lin, T., Henders, A. K., Montgomery, G. W., . . . 865 \nVisscher, P. M. (2019). Improved precision of epigenetic clock estimates across 866 \ntissues and its implication for biological ageing. Genome Medicine, 11(1), 54. 867 \ndoi:10.1186/s13073-019-0667-1 868 \nZhavoronkov, A., Li, R., Ma, C., & Mamoshina, P. (2019). Deep biomarkers of aging and 869 \nlongevity: from research to applications. Aging (Albany NY), 11(22), 10771-10780. 870 \ndoi:10.18632/aging.102475 871 \nZou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. 872 \nJournal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 873 \n301-320. doi:https://doi.org/10.1111/j.1467-9868.2005.00503.x 874 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted February 11, 2024. ; https://doi.org/10.1101/2024.02.10.24302617doi: medRxiv preprint \n\nMAERMSE R2 r\nTraining 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\nSplit 1Split 2Split 3Split 4Split 5\nFull analytical sample (N = 101,359)Training (80%)Validation\nTest setEvaluate model with hyperparameter combination that resulted in lowest cross-validation MAE\nMaximum entropy gridHyperparameter 2Hyperparameter 115#!\"#$MAEMAE 1MAE 2MAE 3MAE 4MAE 5Cross-validation for each hyperparameter combinationPerformance\nPreserve the age distribution across foldsFold1Fold2Fold3Fold4Fold5Fold6Fold8Fold7Fold10Fold9Fold1Fold2Fold3Fold4Fold5Fold6Fold8Fold7Fold10Fold910-fold Outer loop5-fold Inner loop\nFigure 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.\n0\n1000\n2000\n3000\n4000\n5000\n40506070Chronological age\nCount\nAge distribution\na b\nAcetoacetate\nAlbumin\nbOHbutyrate\nCholinesClinical_LDL_C\nDHA\nGlucose\nGlycA\nHDL_P\nHDL_PLHis\nIDL_CIDL_CE\nIDL_TG\nL_LDL_C\nL_LDL_CEL_LDL_FC\nL_LDL_L\nL_LDL_TGLactate\nLDL_C\nLDL_FC\nLDL_size\nLDL_TG\nLeu M_HDL_PL\nM_LDL_TG\nOmega_3PhosphatidylcPhosphoglycPUFA\nS_HDL_FC\nS_HDL_TG\nS_LDL_FC\nS_VLDL_L\nTotal_CTotal_CE\nTotal_FA\nTotal_FCTotal_P\nTotal_PL\nUnsaturation\nXS_VLDL_FC\nXS_VLDL_P\nXS_VLDL_TG\nXXL_VLDL_FCXXL_VLDL_L\nXXL_VLDL_PXXL_VLDL_PL\nXXL_VLDL_TG\n0.8\n0.9\n1.0\n1.1\n1.2\n−1.0−0.50.00.51.01.52.0Beta (per 1SD) Age\nHR (per 1SD) Mortality\nMetabolites × (Age and Mortality)\nc d\n\n5.42\n5.70\n6.30\n5.70\n6.346.36\n6.19\n5.91\n5.525.65\n5.355.31\n6.26\n5.94\n5.625.59\n5.92\n5.0\n5.5\n6.0\n6.5\n7.0\nRidgeLASSOElastic netPLSRKNNMARS\nMARS ensembleSVM linearSVM polynomialSVM radialRegression tree\nBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble\nMean absolute error (years)\nMeanNested CV\n9393\n99\n88\n78\n78\n57\n55\n55\n53\n68\n62\n62\n69\n49\n68\n61\n61\n72\n48\n87\n96\n98\n98\n80\n56\n64\n63\n83\n87\n87\n70\n61\n63\n62\n87\n81\n86\n86\n68\n61\n61\n60\n85\n98\n60\n56\n56\n60\n52\n64\n65\n57\n61\n60\n77\n73\n73\n74\n68\n75\n76\n74\n80\n79\n81\n77\n74\n74\n74\n69\n74\n74\n75\n81\n80\n79\n98\n83\n81\n81\n73\n66\n66\n66\n82\n90\n89\n68\n88\n89\n86\n85\n85\n75\n64\n67\n66\n86\n90\n89\n65\n85\n86\n93\n87\n94\n94\n74\n61\n65\n65\n92\n93\n93\n63\n82\n82\n87\n89\n84\n89\n89\n70\n60\n62\n62\n88\n91\n90\n62\n81\n82\n89\n90\n920.48\n0.53\n0.58\n0.64\n0.69\n0.74\n0.79\n0.84\n0.9\n0.95\n1LASSOElastic netPLSRKNNMARSMARS ensembleSVM linearSVM polynomialSVM radialRegression treeBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensembleRidge\nLASSO\nElastic net\nPLSR\nKNN\nMARS\nMARS ensemble\nSVM linear\nSVM polynomial\nSVM radial\nRegression tree\nBagging\nRandom forest\nXGBoost\nBART\nCubist rules\na b\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nRidge\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nLASSO\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nElastic net\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nPLSR\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nKNN\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nMARS\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nMARS ensemble\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nSVM linear\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nSVM polynomial\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nSVM radial\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nRegression tree\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nBagging\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nRandom forest\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nXGBoost\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nBART\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nCubist rules\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age (adj.)\nRuleFit ensemble\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nRidge\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nLASSO\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nElastic net\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nPLSR\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nKNN\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nMARS\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nMARS ensemble\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nSVM linear\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nSVM polynomial\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nSVM radial\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nRegression tree\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nBagging\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nRandom forest\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nXGBoost\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nBART\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nCubist rules\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nRuleFit ensemble\nMean =56.44\n30\n40\n50\n60\n70\n80\n40506070Age (years)\nPredicted age\nModelRidgeLASSOElastic netPLSRKNNMARSMARS ensembleSVM linearSVM polynomialSVM radialRegression treeBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble\nAge bias correction\nc d e\n0.00\n0.05\n0.10\n0.15\n−20−1001020MileAge delta (adj.)\nDensity\nModelRidgeLASSOElastic netPLSRKNNMARSMARS ensembleSVM linearSVM polynomialSVM radialRegression treeBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble\nMileAge delta (adj.)\n2.52\n2.842.84\n2.382.492.162.12\n3.12\n3.303.40\n2.79\n2.362.32\n2.912.893.013.08\n2.0\n2.5\n3.0\n3.5\nRidgeLASSOElastic netPLSRKNNMARS\nMARS ensembleSVM linearSVM polynomialSVM radialRegression tree\nBaggingRandom forestXGBoostBARTCubist rulesRuleFit ensemble\nMean absolute error (years)\nf g\nFigure 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.\n\nFigure 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.\n0.00\n0.01\n0.02Beta\nFrailty index\n1.00\n1.10\n1.20\n1.30\n1.40Odds ratio\nFrailty phenotype\n-0.04\n-0.02\n0.00\n0.02\n0.04\n0.06\n0.08Beta\nTelomere length\n1.00\n1.25\n1.50\n1.75\nSVM radial\nSVM polynomial\nCubist rules\nRuleFit ensemble\nXGBoostBART\nSVM linearElastic netLASSORidge\nRandom forest\nBaggingPLSR\nRegression tree\nKNNMARS\nMARS ensemble\nOdds ratio\nLong-standing illness\n1.00\n1.25\n1.50\n1.75\nSVM radial\nSVM polynomial\nCubist rules\nRuleFit ensemble\nXGBoostBART\nSVM linearElastic netLASSORidge\nRandom forest\nBaggingPLSR\nRegression tree\nKNNMARS\nMARS ensemble\nOdds ratio\nHealth status\n1.00\n1.25\n1.50\n1.75\nSVM radial\nSVM polynomial\nCubist rules\nRuleFit ensemble\nXGBoostBART\nSVM linearElastic netLASSORidge\nRandom forest\nBaggingPLSR\nRegression tree\nKNNMARS\nMARS ensemble\nOdds ratio\nSelf-rated health\nMileAgedelta (adj.)≤X̄-1SD Middle≥X̄+1SD\n0.00\n0.03\n0.06\n0.09\n0.12\n−20−1001020MileAge delta (adj.)\nPartial effect\nFrailty index\n−0.5\n0.0\n0.5\n1.0\n1.5\n−20−1001020MileAge delta (adj.)\nPartial effect\nFrailty phenotype\n−0.3−0.2−0.10.00.10.20.30.4\n−20−1001020MileAge delta (adj.)\nPartial effect\nTelomere length\n−1.0−0.50.00.51.01.52.02.53.0\n−20−1001020MileAge delta (adj.)\nPartial effect\nLong−standing illness\n−1.0−0.50.00.51.01.52.02.53.0\n−20−1001020MileAge delta (adj.)\nPartial effect\nHealth status\n−0.50.00.51.01.52.02.5\n−20−1001020MileAge delta (adj.)\nPartial effect\nSelf−rated health\na\nb\n\n0\n2000\n4000\n6000\n−20−1001020MileAge delta (adj.)\nCount\nSexFemaleMale\nCubist rules\n1.00\n1.25\n1.50\n1.75\nPoorFairGoodExcellent\nHazard ratio\nMileAgedelta (adj.)≤X̄-1SDMiddle≥X̄+1SD\nSelf-rated health\n1.00\n1.25\n1.50\nSVM radialSVM polynomialCubist rulesRuleFit ensemble\nXGBoostBARTSVM linearElastic netLASSORidge\nRandom forest\nBaggingPLSR\nRegression tree\nKNNMARS\nMARS ensemble\nHazard ratio\nMileAgedelta (adj.)≤X̄-1SDMiddle≥X̄+1SD\na b\nMiddle\nBiologically younger≤X̄-1SD Biologically older≥X̄+1SD\n0.00\n0.05\n0.10\n-20 -10 0 10MileAge delta (adj.)\nDensity\nCubist rules\nMean\n0.07\n0.09\n0.11\n0255075100MileAge delta (adj.) percentile\nEvent rate\nAll−cause mortality\n0.0\n0.1\n0.2\n0255075100Percentile\nEvent rate\nAgeMileAge (adj.)ChronAge\nAll−cause mortalityc d e\nFigure 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.\n0.8\n1.2\n1.6\n2.0\n39-4950-5960-71\nHazard ratio\nMileAgedelta (adj.)≤X̄-1SDMiddle≥X̄+1SD\nChronological age groupf g h\n\n1.0\n1.5\n2.0\n2.5\n3.0\nMileAge delta (adj.)\nFrailty indexGrip strengthTe lo m e re  le n g th\nHazard ratio\nDistribution≤X̄-1SDMiddle≥X̄+1SD\n+ Frailty index\n+ Grip strength\n+ MileAge delta (adj.)\n+ Telomere length\nAge+Sex\n0.710.720.730.74C−index\nModel\nAll−cause mortality\na b\n0\n1\n2\n3\n−10010MileAge delta (adj.)\nLog(HR) mortality\nMileAge delta\n0\n1\n2\n0.00.20.4Frailty index\nLog(HR) mortality\nFrailty\n−1.5\n−1.0\n−0.5\n0.0\n0.5\n1.0\n020406080Kilogram−force\nLog(HR) mortality\nGrip strength\n−4\n−2\n0\n2\n4\n−10−50510T/S ratio (log z adjusted)\nLog(HR) mortality\nTelomere length\nc\nFigure 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.","source_license":"CC-BY-4.0","license_restricted":false}