Abstract
24
Biological aging is marked by a decline in resilience at the cellular and systemic levels, driving an 25
exponential increase in mortality risk. Here, we evaluate several clinical and epigenetic clocks for their 26
ability to predict mortality, demonstrating that clocks trained on survival and functional aging 27
outperform those trained on chronological age. We present an enhanced clinical clock that predicts 28
mortality more accurately and provides actionable insights for guiding personalized interventions. 29
These findings highlight the potential of mortality-predicting clocks to inform clinical decision-making 30
and promote strategies for healthy longevity. 31
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3
Main 32
Biological aging is characterized by the progressive decline in intrinsic biological resilience that is 33
associated with an exponential increase in mortality, expressed in the demographic “Gompertz 34
mortality law”1. Not all humans age at the same rate since genetics, lifestyle and stochastic factors 35
can affect future mortality and morbidity trajectories. Consequently, individual true biological age (BA) 36
is not identical to calendar or chronological age (CA). The true BA of an individual can be uniquely 37
defined as the age at which subjects of a reference cohort have the same risk of age-dependent 38
disease and all-cause mortality as the subject in question. Tools to accurately track changes in true 39
BA are essential for the development and validation of novel life- and healthspan-optimizing diet, 40
lifestyle, supplement and drug interventions. 41
42
Biological aging “clocks” are computational tools that estimate individual true BA based on 43
demographic, clinical, and/or molecular data. CA itself is widely used for both clinical prognostication 44
and decision-making, and can be viewed as a first order approximation of true BA. The ideal BA clock 45
should predict individual Gompertz mortality risk with higher accuracy than CA. Some aging clocks, 46
including most clinical clocks, explicitly include CA as a covariate, using biological features to estimate 47
a correction factor aimed at providing a better estimate of true BA. CA in this case is used as a proxy 48
for effects and mechanisms, such as entropic damage, not captured by the clock itself. Of course, the 49
ideal clock would include all relevant processes, wherein the model would assign zero or negligible 50
weight to CA. 51
52
Aging clocks are generalizations of current clinical risk markers that predict disease-specific morbidity 53
and, in some cases, mortality. Aging clocks should similarly enable early detection of hidden or 54
subclinical diseases, surpassing the capabilities of diagnostics by identifying disease processes years 55
or decades before overt disease is present. Secondly, to inform risk-to-benefit estimates (clinical 56
equipoise), aging clocks should capture all-cause mortality holistically, providing value beyond organ 57
or disease-specific risks. Thirdly, aging clocks must be sensitive to individual variations in biological 58
resilience. Finally, aging clocks should provide tools for mechanistic interpretation and provide 59
actionable insights, facilitating targeted interventions. To date, none of the existing clocks meet all 60
these criteria. 61
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4
62
To evaluate the performance of aging clocks, we can compare them to a hypothetical “ideal” clock, 63
which we term “CrystalAge”. This optimal clock would predict disease-specific and all-cause mortality 64
at the individual level with near-perfect accuracy, essentially forecasting an individual’s date of death 65
(Fig. 1a and d). While practically impossible, in retrospective studies, we can determine the 66
theoretically optimal performance of CrystalAge and use it as a benchmark to evaluate the 67
performance of existing aging clocks. 68
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69
Fig. 1: LinAge2 predicts 20-year all-cause mortality and tracks with healthspan markers. a-c, 70
Kaplan-Meier survival curves showing 20-year survival in the 65-74 CA bin ( n=631). For each clock, 71
subjects were stratified by selecting the lowest (best, solid line) and highest (worst, dotted line) 25% 72
quartiles for BA. Clocks within the same quartile were compared using log-rank tests with Benjamini-73
Hochberg correction. Areas shaded indicate 95% error bands for lines of the same color. b, 74
Compared to ChronAge, use of LinAge2 BA results in a significant survival difference for the lowest 75
25% BA quartile ( P=6.16E-04), but not for the highest 25% quartile ( P=0.07). PhenoAge Clinical did 76
not significantly outperform ChronAge in predicting survival in this age bin. c, LinAge2 significantly 77
outperformed DunedinPoAm (P=1.09E-02) and PhenoAge DNAm (P=1.37E-03) in the lowest 25% BA 78
quartile, but not GrimAge2 ( P=0.22). In the highest 25% quartile, while LinAge2 significantly 79
outperformed PhenoAge DNAm ( P=0.03), the differences between LinAge2 and DunedinPoAm 80
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6
(P=0.11) and GrimAge2 (P=0.58) did not reach statistical significance. e, ROC analysis revealed that 81
LinAge2 (area under the curve (AUC)=0.8684) was significantly more informative than PhenoAge 82
Clinical (AUC=0.8479, P=6.35E-05) and ChronAge (AUC=0.8288, P=3.16E-10) in predicting future 83
mortality ( n=2,036). LinAge2 performed similarly to LinAge (AUC=0.8647). f, LinAge2 also 84
outperformed PhenoAge DNAm (AUC=0.7859, P=4.44E-07) and GrimAge2 (AUC=0.8233, P=0.02) in 85
predicting 20-year mortality ( n=1,065). Although GrimAge2 outperformed ChronAge (AUC=0.7933, 86
P=2.74E-03) in predicting 20-year mortality, PhenoAge DNAm did not ( P=0.47). a,d, HorvathAge, 87
HannumAge, and ChronAge did not significantly differ in predicting mortality risk (AUCs=0.7776, 88
0.7978 and 0.7933, respectively, n=1,065). ROC curves were compared using DeLong’s test. 89
a,b,d,e,f, CrystalAge, a theoretical perfect clock shown for reference, accurately identifies individuals 90
at risk of dying (AUC=1), whereas RandomAge adds random gaussian noise of +10 years to CA. g-k, 91
Violin plots for each clock categorized into low (biologically younger/best 25% quartile) and high 92
(biologically older/worst 25% quartile) groups plotted against healthspan markers: cognitive scores 93
(digit symbol substitution test), gait speed, ability to work, and ability to perform all instrumental and 94
basic activities of daily living (iADLs and bADLs). Groups (BA high versus low) were compared using 95
two-sided t-tests. Median value, lower (25 th) and upper (75 th) percentiles are indicated. Lines extend 96
to +1.5 times interquartile range, with points outside this range drawn individually. The violin shape 97
indicates the probability density function. yo, years old. HA, HorvathAge. LA2, LinAge2. GA2, 98
GrimAge2. DPA, DunedinPoAm. 99
100
Taking inspiration from Levine’s PhenoAge clinical clock2, we recently developed and validated clinical 101
aging clocks (PCAge, LinAge) based on linear dimensionality reduction by matrix factorization 102
(singular value decomposition) and demonstrated them to be highly predictive in terms of future 103
disease-specific and all-cause mortality3. These clocks have since been applied in a range of clinical 104
settings and, taking advantage of user feedback, we have implemented several improvements, 105
creating an updated version of these clocks (LinAge2). Like LinAge, we trained LinAge2 in the 106
National Health and Nutrition Examination Survey (NHANES) IV 1999-2000 wave before testing it in 107
the 2001-2002 wave. LinAge2 further reduces the number of rarely measured parameters and 108
emphasizes interpretability. For a detailed description of LinAge2's features and construction, refer to 109
Methods. 110
111
Many aging clocks have been developed, with epigenetic or DNA methylation (DNAm) clocks most 112
widely recognized and well-established. Several epigenetic clocks have been commercially licensed 113
for applications, including estimating CA (HorvathAge 4, HannumAge 5), optimizing life insurance 114
policies (PhenoAge DNAm6, GrimAge7), and monitoring the rate of aging (DunedinPoAm8)9. Recently, 115
a dataset of pre-calculated epigenetic clock ages has been published for the NHANES 1999-2002 116
waves, permitting direct comparison of the predictive power of CA, the original LinAge, LinAge2 and 117
PhenoAge clinical clocks, and the HorvathAge, HannumAge, PhenoAge DNAm, GrimAge2 10 and 118
DunedinPoAm epigenetic clocks. 119
120
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To compare efficacy in predicting mortality, we performed survival and receiver operating 121
characteristic (ROC) analyses on 20- and 10-year mortality in the NHANES 2001-2002 test cohort. 122
Compared to CA, LinAge2 demonstrated significant survival differences across all age bins, whereas 123
PhenoAge Clinical did not (Fig. 1b, Extended Data Fig. 1b and e). LinAge2 performed similarly to 124
LinAge and demonstrated superior predictive power for future mortality compared to PhenoAge 125
Clinical and CA (Fig. 1e and Extended Data Fig. 2b). Surprisingly, LinAge2 also outperformed 126
PhenoAge DNAm and DunedinPoAm in predicting age-specific survival differences (Fig. 1c, Extended 127
Data Fig. 1c and f) and future mortality (Fig. 1f and Extended Data Fig. 2c). In contrast, PhenoAge 128
DNAm, HorvathAge, and HannumAge did not significantly differ from CA in predicting future mortality 129
(Fig. 1a, d and f, Extended Data Fig. 1a and d, and Extended Data Fig. 2a and c). LinAge2 and 130
GrimAge2 performed similarly in predicting future mortality (Fig. 1f and Extended Data Fig. 2c) and 131
survival across all age bins (Fig. 1c, Extended Data Fig. 1c and f). 132
133
While mortality prediction is an important function of aging clocks, it is important to evaluate if clock 134
ages are similarly predictive of functional status and healthspan. We tested this for the same clinical 135
and epigenetic clocks by comparing markers of functional and health status in individuals selected by 136
each clock to be in the lowest 25% BA quartile (biologically younger, low) with those in the highest 137
25% quartile (biologically older, high). Our analysis revealed that LinAge2 low was associated with 138
superior healthspan markers, including higher cognitive scores, faster gait speed, ability to work, and 139
performance of all instrumental and basic activities of daily living (iADLs and bADLs) (Fig. 1g-k). 140
Conversely, individuals in the LinAge2 high group had poorer healthspan, with statistically significant 141
differences between the two groups across all markers (Fig. 1g-k). Similar trends were observed for 142
GrimAge2 and DunedinPoAm, with statistically significant differences between the low and high 143
groups across most healthspan markers, except for the ability to perform all bADLs (Fig. 1g-k and 144
Extended Data Fig. 3). In contrast, no statistically significant differences were found between 145
HorvathAge low and HorvathAge high across healthspan markers (Fig. 1g-k). Our findings on 146
healthspan markers and mortality, for HorvathAge, HannumAge, PhenoAge DNAm and GrimAge2, 147
corroborate similar findings for 10-year survival in 490 subjects of the Irish Longitudinal Study on 148
Aging11. 149
150
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A significant drawback of many existing aging clocks is that they lack interpretability and actionable 151
insights, making it challenging to develop targeted interventions. However, one key benefit of clinical 152
clocks is that they are built from parameters directly related to the underlying disease mechanisms, 153
enabling easier interpretation of clock residuals and providing actionable insights into disease 154
pathophysiology. Individual age-associated principal components (PCs) identify clusters of features 155
that change in a coordinated manner during aging. Analyzing individual PCs can provide valuable 156
insights into the underlying patterns and trajectories of aging-related changes. Using heatmaps, we 157
visualized the predictive power of individual PCs relative to clinical outcomes, including sex-specific 158
causes of death and chronic diseases (Fig. 2). Supplementary Table 5 provides detailed insights into 159
the interpretation of each PC, including associations with causes of death, chronic diseases, lifestyle 160
factors, and potential aging mechanisms, as well as suggested interventions to optimize each PC and 161
lower BA. 162
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163
Fig. 2: Heatmaps illustrating the associations between clinical outcomes and PCs analyzed 164
using multivariate logistic regression. Associations of PCs with specific causes of death at a-b, 10-165
20 year and c-d, 0-5 year follow-up for male and females, respectively. Strength of association (odds 166
ratio) is represented using a red color scale. PCs that are strongly positively associated with a specific 167
cause of death are bright red. For cause of death, negative associations were truncated by setting 168
their values to zero (i.e. no harm). e-f, Association of PCs with specific chronic diseases, and 169
measures of lifestyle and socioeconomic status. Strength of association is represented using a blue-170
red scale ranging from -1 (blue, negative association) to 2 (red, positive association). PCs that are 171
strongly positively associated (positive risk ratios) with a specific disease are bright red, whereas PCs 172
that are strongly negatively associated (negative risk ratios) with a specific disease are bright blue. 173
174
Accurately predicting patient outcomes and allocating healthcare resources is a significant challenge 175
in clinical practice12. Currently, clinicians rely heavily on CA to make these decisions. However, here 176
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10
we show that mortality-predicting clocks, such as LinAge2 and GrimAge2, outperform CA in predicting 177
mortality risk across timeframes, ranging from 2-20 years (Fig. 1, Extended Data Fig. 4). Moreover, 178
clinical clocks can also predict specific causes of death within a 5-year window (Fig. 2c and d). This 179
illustrates that clock-based BAs are more accurate and informative estimates of true BA than CA itself. 180
By providing a more precise metric of biological status than CA alone, BA can enable clinicians to 181
better support patients and their caregivers in navigating healthcare choices, including end-of-life 182
care. 183
184
Overall, our analysis reveals that, regardless of feature space (methylation or clinical), aging clocks 185
trained to predict mortality or functional aging outcomes provide more predictive value in terms of 186
clinical decision-making. Surprisingly, clinical aging clocks still outperform several prominent mortality-187
predicting and functional epigenetic clocks, including PhenoAge DNAm and DunedinPoAm, in 188
predicting future mortality. A key advantage of LinAge2 lies in its interpretability. Because principal 189
component analysis is a linear matrix factorization technique, the resulting model is easier to interpret 190
than nonlinear alternatives 13. Latent variables based on linear dimensionality reduction (PCs), 191
especially those based on clinical parameters, are comparatively easy to understand and interpret, 192
making them more actionable. This enables clinical aging clocks like LinAge2 to detect hidden or 193
subclinical diseases and inform primordial prevention strategies. By identifying individuals at high risk 194
of developing specific diseases, healthcare providers can implement targeted interventions early and 195
proactively. By casting specific risk in terms of BA acceleration, aging clocks can significantly increase 196
compliance and adherence with specific health recommendations14. For example, male smokers with 197
high PC5M values in LinAge2 are at increased risk of death from chronic lung disease and should be 198
screened and advised to quit smoking (Fig. 2 and Supplementary Table 5). 199
200
All current aging clocks, regardless of feature space (e.g. clinical, methylation, proteomics, etc.) and 201
target (mortality, functional outcomes, disease, or CA) share significant limitations. Most importantly, 202
many current clocks employ linear techniques (e.g. principal component analysis/singular value 203
decomposition, regression-based predictions), which limit their ability to distinguish between aging 204
signatures and those of age-dependent diseases, and to learn U-shape response patterns. Current 205
clocks therefore inherently conflate intrinsic biological aging with disease-specific signatures (hidden 206
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sickness, primordial disease signatures). Nonlinear approaches including generative artificial 207
intelligence and artificial neural networks are being investigated and could offer improved models, but 208
their increased complexity pose a significant challenge for interpretation 15,16. Next generation clocks 209
will need to differentiate between disease signatures and intrinsic aging, and quantify intrinsic 210
biological resilience. Further theoretical work will be required to deconvolute these disease-centric 211
signatures from determinants of intrinsic resilience and entropic aging17-19. Advancing next generation 212
clocks is crucial to equip healthcare providers with the essential tools needed to make informed 213
decisions regarding targeted interventions that support healthy longevity in populations where 214
healthcare needs are increasingly dominated by aging. 215
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Methods
216
Motivation for enhancing LinAge2 217
The original PCAge and LinAge 3 both utilized some parameters that are not routinely collected. 218
LinAge has been utilized by several clinics worldwide, and we have received informal feedback 219
regarding its use. Common suggestions for enhancing the clock include: (i) improving handling of 220
outliers and threshold effects, (ii) further refining the clinical parameters, especially removing serum 221
fibrinogen due to the need for a specialized sodium citrate tube, (iii) providing additional tools to 222
improve the interpretability of PCs, and (iv) providing specific strategies to optimize each PC to lower 223
BA. PCs can also be sensitive to outliers, thresholding and batch effects. We developed LinAge2 in 224
response to these concerns. 225
226
We followed the same workflow, as previously described 3, to construct LinAge2 but with several 227
modifications. To enhance LinAge2, we refined the clinical parameters by reducing the total number to 228
60, removing serum fibrinogen (Supplementary Table 2). We also addressed outliers and thresholding 229
by capping outliers at six standard deviations and log-transforming additional parameters 230
(Supplementary Table 2). Batch effects were mitigated through z-score normalization by median and 231
median absolute deviation to a younger, generally healthy cohort (age 40-50 years), separately for 232
males and females (Supplementary Table 2), generating sex-specific PCs. The loadings for male and 233
female PCs are provided in Supplementary Table 3, and sex-specific weights of the Cox proportional 234
hazards models are listed in Supplementary Table 4. 235
236
A parametrized version of LinAge2 is provided as previously described3 (Supplementary Table 2). The 237
baseline characteristics of the study participants are listed in Supplementary Table 1. 238
239
PhenoAge Clinical and epigenetic clocks 240
PhenoAge Clinical was implemented using the equation from the original publication. The dataset of 241
pre-calculated epigenetic clock ages published for the NHANES 1999-2002 waves were obtained 242
from https://wwwn.cdc.gov/nchs/nhanes/dnam/ and analyzed. 243
244
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13
Construction of healthspan markers 245
The digit symbol substitution test score (NHANES variable ‘CFDRIGHT’) was used as a cognitive 246
measure. Gait speeds were obtained by taking the total distance walked (20 feet or 6.096 meters) 247
divided by the time taken (NHANES variable ‘MSXWTIME’). Differences in cognitive scores and gait 248
speeds were calculated as the percent difference between a control group (middle 50% of all 249
subjects), for younger (best 25% quartile) and older (worst 25% quartile) groups. The ability to work 250
was established using the NHANES variable ‘PFQ048’. The ability to perform all instrumental 251
activities of daily living (iADLs) was a combination of the NHANES variables ‘PFQ060A’, ‘PFQ060F’, 252
‘PFQ060G’, ‘PFQ060Q’, PFQ060R’ and ‘PFQ060S’, while the ability to perform all basic activities of 253
daily living (bADLs) was a combination of the NHANES variables ‘PFQ060B’, ‘PFQ060C’, ‘PFQ060H’, 254
‘PFQ060I’, ‘PFQ060J’, ‘PFQ060K’ and ‘PFQ060L’. Participants had to have either no difficulty or 255
some difficulty in all the variables to be deemed able to perform all iADLs or all bADLs. 256
257
Heatmap analysis 258
Using the ‘nnet’ 20 (version 7.3-19) R package, heatmaps were generated to evaluate the predictive 259
values for PCs included in LinAge2. For each parameter, we attempted to predict status 260
(diseased/compromised or not) using multivariate logistic regression with the clock PCs as covariates. 261
PCs that received a statistically insignificant ( P>0.05) weight in the logistic regression model were 262
assigned zero weights (white). The remaining PCs ( P<0.05) were assigned color values according to 263
their weight in the model (see Fig. 2f legend for color mapping). 264
265
Statistics and reproducibility 266
For the NHANES IV 1999-2002 waves, we excluded: participants top-coded at age 85 years, as we 267
could not ascertain the exact CAs of these adults, and participants who died from accidental deaths, 268
as these were deemed to be not age-related. 269
270
Survival analyses were performed using log-rank tests with Benjamini-Hochberg correction. ROC 271
curves were compared using DeLong’s test. For healthspan markers, two-sided t-tests were used to 272
compare between the low and high clock groups. All statistical analyses were performed using R 273
version 4.2.0 (https://www.R-project.org/). 274
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275
Data availability 276
All datasets used are publicly available online at https://wwwn.cdc.gov/nchs/nhanes/Default.aspx. 277
There were no restrictions on data availability. This study was reported according to STROBE 278
guidelines for cohort studies. 279
280
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Acknowledgements
335
We thank the National Health and Nutrition Examination Survey participants and staff who made this 336
study possible. We thank C. Chen for her careful reading of this manuscript. This research was 337
funded by the Ministry of Education in Singapore, grant numbers IG21-SG007 and A-0007215-00-00, 338
to J.G. S.F. is supported by the Research Training Fellowship (MOH-001294-00) from the National 339
Medical Research Council Singapore. This work was supported by the Lien Foundation. 340
341
Author contributions 342
S.F., B.K.K. and J.G. conceived, conceptualized and designed the study. S.F., K.A.D. and J.G. 343
analyzed and interpreted the data. S.F., B.K.K. and J.G. wrote the first draft of the paper. 344
345
Competing interests 346
The authors declare no competing interests. 347
. CC-BY-NC-ND 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)preprint
The copyright holder for thisthis version posted December 26, 2024. ; https://doi.org/10.1101/2024.12.23.24319587doi: medRxiv preprint
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Additional information 348
349
Extended Data Fig. 1: LinAge2 predicts survival in chronologically 55-64 and 75-84 year old 350
individuals. Kaplan-Meier survival curves showing 20-year survival in the a-c, 55-64 CA bin (n=657) 351
and d-f, 75-84 CA bin ( n=348) in the test cohort. a,d, HannumAge, HorvathAge, and ChronAge 352
showed no statistically significant differences in survival. b, LinAge2 demonstrated significant survival 353
differences compared to ChronAge in both the best 25% ( P=2.01E-03) and worst 25% ( P=0.03) 354
quartiles. In contrast, PhenoAge Clinical showed a significant difference only in the best 25% quartile 355
(P=3.80E-02). c,f, In the best 25% quartile, LinAge2 outperformed DunedinPoAm ( P=6.45E-03 and 356
P=1.39E-02 in the 55-64 and 75-84 CA bins, respectively) and PhenoAge DNAm ( P=8.90E-03 and 357
P=1.73E-02 in the 55-64 and 75-84 CA bins, respectively). LinAge2 and GrimAge2 performed 358
similarly with no significant differences between them. In the worst 25% quartile, no significant 359
differences in survival were found between LinAge2, DunedinPoAm, PhenoAge DNAm, and 360
GrimAge2. e, Compared to ChronAge, both LinAge2 (P=4.56E-03) and PhenoAge Clinical (P=3.16E-361
02) showed significant survival differences in the best 25% quartile, but not in the worst 25% quartile. 362
Clocks were compared using log-rank tests with Benjamini-Hochberg correction. Areas shaded 363
indicate 95% error bands for lines of the same color. yo, years old. 364
365
366
Extended Data Fig. 2: ROC curves for 10-year all-cause mortality in the test cohort. a, There 367
were no significant differences in the AUCs between HorvathAge (AUC=0.7425), HannumAge 368
(AUC=0.7612), and ChronAge (AUC=0.7501) ( n=1,065). b, LinAge2 (AUC=0.8468) was significantly 369
more informative than PhenoAge Clinical (AUC=0.8203, P=6.91E-05) and ChronAge (AUC=0.7946, 370
P=2.65E-09) in predicting future mortality ( n=2,036). LinAge2 performed similarly to LinAge 371
(AUC=0.8383). c, Compared to LinAge2 (AUC=0.8144), PhenoAge DNAm (AUC=0.7390, P=2.84E-372
. CC-BY-NC-ND 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)preprint
The copyright holder for thisthis version posted December 26, 2024. ; https://doi.org/10.1101/2024.12.23.24319587doi: medRxiv preprint
17
06) and GrimAge2 (AUC=0.7801, P =1.81E-03) were significantly less predictive of 10-year follow-up 373
(n=1,065). Although GrimAge2 outperformed ChronAge (AUC=0.7501, P =0.01) in predicting 10-year 374
mortality, PhenoAge DNAm did not (P=0.39). ROC curves were compared using DeLong’s test. 375
376
377
Extended Data Fig. 3: DunedinPoAm tracks with healthspan markers. Differences between 378
DunedinPoAm low (slow aging) and DunedinPoAm high (fast aging) were significant for: a, ability to 379
work; b, ability to perform instrumental activities of daily living (iADLs); but not for c, ability to perform 380
basic activities of daily living (bADLs). Median value, lower (25 th) and upper (75 th) percentiles are 381
indicated. Lines extend to + 1.5 times interquartile range, with points outside this range drawn 382
individually. The violin shape indicates the probability density function. 383
384
385
Extended Data Fig. 4: Clinical clocks are better predictors of 2-year mortality than CA. ROC 386
curves for 2-year all-cause mortality in the test cohort. LinAge2 (AUC=0.8294, P =4.02E-06), LinAge 387
(AUC=0.8003, P=3.91E-04) and PhenoAge Clinical (AUC=0.7870, P=3.24E-03) were significantly 388
more predictive of 2-year follow-up than ChronAge (AUC=0.7120) ( n=2,036). ROC curves were 389
compared using DeLong’s test. 390
. CC-BY-NC-ND 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)preprint
The copyright holder for thisthis version posted December 26, 2024. ; https://doi.org/10.1101/2024.12.23.24319587doi: medRxiv preprint