Research Paper Volume 12, Issue 7 pp 5920—5947

Genetics of physiological dysregulation: findings from the long life family study using joint models

Konstantin G. Arbeev1, , Olivia Bagley1, , Svetlana V. Ukraintseva1, , Deqing Wu1, , Hongzhe Duan1, , Alexander M. Kulminski1, , Eric Stallard1, , Kaare Christensen2, , Joseph H. Lee3,4,5, , Bharat Thyagarajan6, , Joseph M. Zmuda7, , Anatoliy I. Yashin1, ,

  • 1 Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham NC, 27708, USA
  • 2 Danish Aging Research Center, Department of Public Health, University of Southern Denmark 5000, Odense C, Denmark
  • 3 Taub Institute for Research on Alzheimer's Disease and the Aging Brain, Columbia University, New York, NY 10032, USA
  • 4 G. H. Sergievsky Center, Columbia University, New York, NY 10032, USA
  • 5 Departments of Epidemiology and Neurology, Columbia University Medical Center, New York, NY 10032, USA
  • 6 Department of Laboratory Medicine and Pathology, University of Minnesota, Minneapolis, MN 55455, USA
  • 7 Department of Epidemiology, University of Pittsburgh, Pittsburgh, PA 15261, USA

Received: October 11, 2019       Accepted: March 24, 2020       Published: April 1, 2020
How to Cite

Copyright © 2020 Arbeev et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY 3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Recently, Mahalanobis distance (DM) was suggested as a statistical measure of physiological dysregulation in aging individuals. We constructed DM variants using sets of biomarkers collected at the two visits of the Long Life Family Study (LLFS) and performed joint analyses of longitudinal observations of DM and follow-up mortality in LLFS using joint models. We found that DM is significantly associated with mortality (hazard ratio per standard deviation: 1.31 [1.16, 1.48] to 2.22 [1.84, 2.67]) after controlling for age and other covariates. GWAS of random intercepts and slopes of DM estimated from joint models found a genome-wide significant SNP (rs12652543, p=7.2×10-9) in the TRIO gene associated with the slope of DM constructed from biomarkers declining in late life. Review of biological effects of genes corresponding to top SNPs from GWAS of DM slopes revealed that these genes are broadly involved in cancer prognosis and axon guidance/synapse function. Although axon growth is mainly observed during early development, the axon guidance genes can function in adults and contribute to maintenance of neural circuits and synaptic plasticity. Our results indicate that decline in axons’ ability to maintain complex regulatory networks may potentially play an important role in the increase in physiological dysregulation during aging.


Aging is a complex process that involves multiple systems, leading to physiological dysregulation, health deterioration, and eventually death. Changes that occur at the molecular and cellular levels as individuals grow older propagate to changes detectable in laboratory tests of blood or other tissues and observable in measurements of various physiological variables in an individual at different ages. Cross-sectional measurements of such biomarkers correspond to the instantaneous profile of the current physiological state of an organism which provides valuable information about the current aging status of the body. Numerous studies show that such biomarkers are associated with risks of death and aging-related diseases (see, e.g., reviews in [13]). However, such “snapshots” of the physiological state do not help in understanding how exactly the organism arrived at this particular state. For example, if a person at some age has values of biomarkers that are associated with higher survival chances or reduced risks of diseases (e.g., lower values), it is unclear from the cross-sectional information alone if such outcome is due to lower values of respective biomarkers early in life, or due to their slower change with age, or both. Different studies have shown that dynamic characteristics of individual trajectories of biomarkers are associated with mortality risk and other aging-related traits [4]. To investigate such associations, one needs repeated measurements of biomarkers along with relevant time-to-event outcomes (e.g., mortality, onset of diseases) and other relevant health-related outcomes. Such information is routinely collected in contemporary longitudinal studies on humans and many of those, in addition, contain extensive genetic (and, most recently, various omics) data providing opportunities to explore this additional dimension in relation to aging, health, and longevity.

Analyses of longitudinal studies of aging present special methodological challenges due to inherent complexities that need to be taken into account to avoid biased inference. An essential assumption of such analyses is that the longitudinal outcomes (e.g., biomarkers) can be related to the risk of death so that the probability of having a missing value because of death depends on an unobserved value, which is missing not at random (MNAR) [5]. This means that standard methods such as mixed-effects models [6] or generalized estimating equations [7] are not appropriate in such applications because they assume the data are missing (completely) at random. Ignoring this can lead to severe bias, as is well-known in the statistical literature [8]. Furthermore, biomarkers are subject to measurement error and random biological variability; they can be collected at intermittent sparse examination visits, and typically they are not observed at event times. Ignoring measurement errors or biological variation and using the observed “raw” values of such variables as time-dependent covariates in the Cox regression model may lead to biased estimates and incorrect inferences [9, 10], especially when biomarkers are measured at sparse examinations or with a long time interval before an outcome event. Despite such evidence and well recognized needs for using appropriate methods in analyses of longitudinal data on aging [1114], the adoption of such methods is slow.

In this paper, we apply one such method developed for dealing with MNAR situations, joint models (JM) [15, 16], to data on mortality and available longitudinal measurements of multiple biomarkers from two visits in the Long Life Family Study (LLFS). We apply the statistical (Mahalanobis) distance measure (denoted as DM) [17] to reduce a high-dimensional biomarker space into a single measure that summarizes information about deviations of biomarkers from an optimal “baseline” state defined in a “reference population” and that is interpreted as the measure of physiological dysregulation [17]. DM trajectories were shown to be good predictors of mortality, frailty, and chronic diseases in different studies [1821] (with higher DM values associated with higher mortality risk, etc.). The dynamic characteristics of DM trajectories are related to different hidden mechanisms of aging-related changes that produce an increase in the risk of death with age [22], onset of unhealthy lifespan, and survival following the onset of unhealthy lifespan [23]. The LLFS collected follow-up data on mortality and measurements of multiple biomarkers in two visits as well as extensive data on common single nucleotide polymorphisms (SNPs) for genotyped participants. Such information allows one to construct DM using biomarker data from both visits, to explore its dynamics in relation to mortality, and to perform genome-wide association studies (GWAS) to investigate genetic factors associated with such dynamics. However, the methodological complexities indicated above are applicable to this analysis. First, DM is constructed from biomarkers that can have measurement errors and random biological variability and thus appropriate modelling (e.g., joint models [15, 16]) should be used rather than analyses using the observed “raw” values of DM as time-dependent covariates in the Cox model [9, 10]. Second, the LLFS currently has only two visits (at which the biomarkers were collected) and many individuals died before visit 2; thus they will have DM measured only at visit 1. DM is known to be strongly associated with the risk of death [17, 18, 20, 22, 23]. Hence, individuals with adverse dynamics of DM should tend to drop-out earlier due to death (see hypothetical illustration in Figure 1), i.e., the probability of drop-out can depend on missing (unobserved) values of DM. Also, a single observation at visit 1 does not provide information on the future dynamics of DM. However, information on time to death combined with available observations of DM can still be used to infer the dynamics of DM (if modeled appropriately). Here we illustrate this using such modelling (joint models) and show how the estimates from joint models can be used to perform GWAS to infer associations of SNPs with static and dynamic characteristics of the measure of physiological dysregulation (DM).

Hypothetical dynamics of the measure of physiological dysregulation (DM) in LLFS among those who survived beyond visit 2 and those who died before visit 2.

Figure 1. Hypothetical dynamics of the measure of physiological dysregulation (DM) in LLFS among those who survived beyond visit 2 and those who died before visit 2.


Empirical analyses and applications of joint models

Table 1 shows the characteristics of the LLFS sample (for the probands’ and offspring generations and the total sample) including information on variables used in fitting the joint models (see section Specification of joint models). Information on time-dependent variables is presented for each visit. Information on time-independent variables is given for each individual participating in the study (whether he/she was enrolled at baseline or at follow-up visit). See Notes under the table for the number of missing values for each variable.

Table 1. Characteristics of the LLFS Probands and Offspring generations and the total sample.

ProbandsOffspringTotal Sample
Number of participants at in-person visit 1167332264899
Number of visit 1 participants who died before in-person visit 210501891239
Number of visit 1 participants who returned for in-person visit 255426233177
Number of new participants enrolled for in-person visit 214123137
Number of participants (returning and new) at in-person visit 256827463314
Number of participants who died after in-person visit 217343216
Total number of participants in the study168733495036
Number of deaths during the entire follow-up12232321455
Years from visit 1 to visit 2 (mean ± SD [range]) (for those with both visits)7.13 ± 1.02 [5–11]8.03 ± 1.1 [5–11]7.88 ± 1.13 [5–11]
Age at visit 1 (mean ± SD [range])89.57 ± 6.81 [49–110]60.65 ± 8.37 [24–88]70.53 ± 15.81 [24–110]
Age at visit 2 (mean ± SD [range])92.93 ± 6.82 [56–110]68.4 ± 7.84 [40–95]72.39 ± 11.88 [40–110]
Females (%)55.7855.0355.28
Participants from US field centers (%)84.7770.0274.96
Low educated participants (below high school) (%)24.726.4212.55
Smokers (smoked >100 cigarettes in lifetime) (%)37.745.642.95
Medication use at visit 1: anti-diabetic (%)7.114.685.51
Medication use at visit 1: anti-hypertensive (%)67.5431.4343.76
Medication use at visit 1: lipid-lowering (%)31.6825.3327.5
Medication use at visit 2: anti-diabetic (%)
Medication use at visit 2: anti-hypertensive (%)54.5835.438.68
Medication use at visit 2: lipid-lowering (%)33.2729.5330.18
Fasting (>=8 hrs.) at visit 1 (%)88.1189.7789.2
Fasting (>=8 hrs.) at visit 2 (%)54.0574.2570.79
Follow-up period (mean ± SD [range])5.66 ± 2.97 [0–11.9]8.36 ± 2.49 [0–12]7.46 ± 2.95 [0–12]
Prevalence of cancer, number (%)588 (34.85)621 (18.54)1209 (24.01)
Prevalence of CVD, number (%)461 (27.33)206 (6.15)667 (13.24)
Prevalence of AD or dementia, number (%)119 (7.05)8 (0.24)127 (2.52)
Prevalence of diabetes, number (%)162 (9.60)212 (6.33)374 (7.43)
Incidence of cancer, number (%)183 (10.85)339 (10.12)522 (10.37)
Incidence of CVD, number (%)341 (20.21)188 (5.61)529 (10.50)
Incidence of AD or dementia, number (%)119 (7.05)27 (0.81)146 (2.90)
Incidence of diabetes, number (%)23 (1.36)112 (3.34)135 (2.68)
Note: Number of missing data (Probands, Offspring, Total Sample): indicator of death/lifespan - (0, 0, 0); age at visit 1 - (0, 0, 0); age at visit 2 - (100, 338, 438); sex - (0, 0, 0); country - (0, 0, 0); education - (8, 3, 11); smoking - (6, 14, 20); anti-diabetic drugs at visit 1 - (62, 424, 486); anti-diabetic drugs at visit 2 - (123, 529, 652); anti-hypertensive drugs at visit 1 - (62, 424, 486); anti-hypertensive drugs at visit 2 - (123, 529, 652); lipid-lowering drugs at visit 1 - (62, 424, 486); lipid-lowering drugs at visit 2 - (123, 529, 652); fasting at visit 1 - (3, 16, 19); fasting at visit 2 - (0, 0, 0); follow-up period - (0, 0, 0); cancer - (1, 3, 4); CVD - (1, 3, 4); AD - (5, 3, 8); diabetes - (4, 5, 9)

Table 1 also includes information on prevalent (existing before the baseline visit) and incident (new cases reported after the baseline visit) cases of major aging-related diseases in the LLFS. It shows that participants from the probands’ generation had higher prevalence of major diseases compared to the younger (offspring) generation, as expected. However, for incidence the pattern is not uniform: the proportions of new cancer cases are almost the same in two generations and the proportions of new diabetes cases tended to be higher in the offspring generation. We note also that verified information on causes of deaths of LLFS participants was not available for this study. Therefore, the numbers and proportions of individuals dying from different causes were not determined in this sample.

We constructed the measure of physiological dysregulation (denoted as DM1) from a set of biomarkers moderately correlated with age as described in Methods and separate measures based on subsets of respective biomarkers negatively and positively correlated with age (DM1 and DM1+), as well as the “age-dependent” DM variants (denoted, accordingly, DMa1, DMa1, and DMa1+) that considered deviations of biomarker values from those typical of age peers rather than those of younger individuals as in the original measures (DM1, DM1, and DM1+) (see Methods). Table 2 lists the biomarkers used in these computations along with respective numbers of observations in each LLFS visit and the total number of observations.

Table 2. Biomarkers used in construction of statistical distance measures (DM).

Name (Unit of Measurement)Number of Observations Visit 1Number of Observations Visit 2Number of Observations Total
Absolute monocyte count (10e9/L)4,4952,2526,747
Creatinine (mg/dL)4,6582,6157,273
Diastolic blood pressure (mmHg)4,7572,7777,534
Forced vital capacity (mL)4,3992,3536,752
Grip strength (kg)4,7312,7147,445
Hematocrit (%)4,5222,5717,093
Glycosylated hemoglobin (%)4,6262,5967,222
Mean corpuscular volume (fl)4,5192,5697,088
Pulse pressure (mmHg)4,7572,7777,534
Red cell distribution width (%)4,5062,5697,075
Total cholesterol (mg/dL)4,6582,6137,271
White blood cell count (10e9/L)4,5212,5557,076
Note: Biomarkers included in DM1 (and its “age-dependent” variant DMa1) are highlighted in bold. Other (not highlighted) biomarkers are included in DM1+ and DMa1+. All biomarkers indicated in the table are included in DM1 and DMa1. See explanations about DM variants in the text.

We compared the average values of DM at visit 1 between (1) those who died between visit 1 and visit 2 and (2) those who survived beyond visit 2. The average values of DM at visit 1 for those who died were significantly higher than those for the second group (see Table 3). Similar patterns were observed when stratified by sex, with larger and more significant differences for the “original” DM variants. These analyses indicate that the situation depicted in Figure 1 is likely to be happening here, i.e., participants with higher values of DM and/or higher rates of change tend to die earlier thus creating the paradigm for application of appropriate statistical techniques for joint analyses of longitudinal observations of DM and time-to-event data on mortality.

Table 3. Average values of DM at visit 1 among those who died between visit 1 and visit 2 and those who survived beyond visit 2 (standard deviations in parentheses).

DMTotal SampleFemalesMales
Died before Visit 2Alive at Visit 2P-valueDied before Visit 2Alive at Visit 2P-valueDied before Visit 2Alive at Visit 2P-value
DM11.58 (0.42)0.90 (0.48)2.1×10-2541.55 (0.42)0.89 (0.47)2.3×10-1161.62 (0.42)0.91 (0.50)5.1×10-138
DM1+1.34 (0.40)0.97 (0.41)1.7×10-1251.38 (0.38)0.98 (0.41)8.3×10-801.31 (0.42)0.97 (0.40)3.1×10-51
DM11.51 (0.21)1.15 (0.25)3.4×10-2571.51 (0.21)1.15 (0.25)1.6×10-1331.50 (0.22)1.16 (0.25)4.1×10-124
DMa10.87 (0.49)0.81 (0.47)4.8×10-40.87 (0.50)0.82 (0.47)0.0840.88 (0.47)0.79 (0.47)8.5×10-4
DMa1+0.92 (0.41)0.85 (0.37)5.7×10-60.93 (0.40)0.85 (0.38)4.6×10-50.90 (0.41)0.86 (0.37)0.018
DMa11.14 (0.24)1.09 (0.23)3.2×10-81.15 (0.24)1.09 (0.24)1.4×10-51.14 (0.24)1.09 (0.22)4.5×10-4

Table 4 shows the results of application of the joint models to DM variants DM1, DM1+, and DM1 and mortality data in LLFS. The “Longitudinal” values represent estimates (coefficients, 95% confidence intervals [CI], and p-values for the null hypotheses of zero coefficients) from the fixed effects parts of joint models. Positive (and highly significant) values of the coefficient for age at visit 1 and follow-up period since visit 1 indicate that the trajectories of DM increase with age for all variants, similar to other studies, e.g., [23]. The estimates for sex and country indicator varied in direction and significance showing that the levels of physiological dysregulation represented by the DM variants constructed from different sets of biomarkers can be different in females and males and can have geographical/country-specific variation. Smoking and low education have consistent negative impacts on all DM variants (i.e., smoking and low education are associated with an increase in the level of physiological dysregulation represented by the respective DM variants). Use of medication for diabetes and hypertension, but not lipid-lowering medications also consistently showed negative impacts on the level of physiological dysregulation. The observations for anti-diabetic and anti-hypertensive drugs may reflect the destabilizing role of underlying disease in the physiological regulation since such drugs are typically prescribed after respective diagnoses. On the contrary, lipid-lowering drugs are commonly prescribed for prevention, often without clinical manifestation of a pathology (e.g., cardiovascular disease), which might contribute to their weaker association with physiological dysregulation. The fasting variable consistently reduced the values of DM, but it reached significance only for DM1. The “Survival” values represent estimates (coefficients, hazard ratios (HR) along with their 95% CI and p-values) from the survival parts of joint models. The results indicate that DM (current value estimated continuously through time using the joint model) is associated with mortality (HR per standard deviation (SD) ranging from 1.66 for DM1+ to 2.22 for DM1) even after controlling for age and the other covariates indicated in the table (see Methods), all of which increase the risk of death with varying magnitude and significance levels.

Table 4. Results of the joint models applied to DM variants DM1, DM1+, and DM1.

DM1Coef.95% CIP-valueCoef.HR95 % CIP-value
DM1.3802.10[1.718, 2.577]6.6×10-13
AgeV10.023[0.022, 0.024]00.0961.10[1.089, 1.112]6.7×10-77
SexM0.071[0.047, 0.095]7.9×10-90.2391.27[1.110, 1.453]5.0×10-4
IsDK-0.117[-0.147, -0.088]8.9×10-150.4861.63[1.352, 1.954]2.3×10-7
LowEduc0.063[0.021, 0.105]0.0030.0051.01[0.851, 1.186]0.955
Smoke1000.026[0.002, 0.050]0.0360.1341.14[1.001, 1.305]0.048
DrugDiab0.144[0.097, 0.191]2.4×10-9
DrugHtn0.033[0.009, 0.058]0.008
DrugLipid0.0003[-0.025, 0.026]0.983
Fasting-0.026[-0.065, 0.012]0.183
TimeV10.017[0.014, 0.020]2.8×10-35
DM1.1901.66[1.420, 1.937]1.7×10-10
AgeV10.011[0.011, 0.012]6×10-1770.1091.12[1.107, 1.123]4.6×10-200
SexM-0.013[-0.034, 0.008]0.2210.3851.47[1.303, 1.658]3.5×10-10
IsDK0.008[-0.018, 0.034]0.540.3071.36[1.159, 1.593]1.6×10-4
LowEduc0.039[0.003, 0.074]0.0340.0241.02[0.881, 1.192]0.75
Smoke1000.026[0.005, 0.047]0.0170.1101.12[0.989, 1.259]0.075
DrugDiab0.303[0.262, 0.344]3.6×10-47
DrugHtn0.068[0.046, 0.089]8.2×10-10
DrugLipid-0.018[-0.040, 0.004]0.116
Fasting-0.023[-0.057, 0.011]0.182
TimeV10.019[0.016, 0.021]4.5×10-57
DM2.8832.22[1.841, 2.673]5.8×10-17
AgeV10.011[0.011, 0.012]00.0901.09[1.084, 1.105]2.4×10-80
SexM0.018[0.006, 0.031]0.0050.3171.37[1.203, 1.568]2.7×10-6
IsDK-0.027[-0.042, -0.011]6.2×10-40.3731.45[1.212, 1.739]5.1×10-5
LowEduc0.042[0.021, 0.064]1.3×10-40.0281.03[0.870, 1.217]0.741
Smoke1000.018[0.005, 0.031]0.0050.0771.08[0.945, 1.235]0.257
DrugDiab0.160[0.136, 0.185]3.4×10-37
DrugHtn0.038[0.025, 0.051]7.1×10-9
DrugLipid-0.001[-0.014, 0.012]0.922
Fasting-0.025[-0.045, -0.005]0.016
TimeV10.014[0.012, 0.015]7.9×10-81
Notes: 1.Variables: AgeV1: Age at visit 1, SexM: Sex (1 – male, 0 – female), IsDK: Participant is from Denmark (1) or USA (0), LowEduc: Low education (1 – below high school, 0 – otherwise), Smoke100: Smoker (1 – smoked >100 cigarettes in lifetime, 0 – otherwise), DrugDiab: Takes (1) or does not take (0) anti-diabetic drugs, DrugHtn: Takes (1) or does not take (0) anti-hypertensive drugs, DrugLipid: Takes (1) or does not take (0) lipid-lowering drugs, Fasting: Fasting (1 – >=8 hrs., 0 – otherwise), TimeV1: Follow-up period since visit 1.
2.Hazard ratios (HR) of all-cause mortality risk for DM variables are per standard deviation: DM1: 0.539, DM1+: 0.425, DM1: 0.276; HR for other variables are per a unit change.

For comparison, the results of application of the Cox model to the same data (with the respective DM variant included as a time-dependent covariate carried forward from visit 1 and updated if there is a visit 2) are presented in Table 5. This table shows that the HRs for DM from joint models were 1.3 to 1.4 times larger than the estimates from the Cox model.

Table 5. Results of the Cox model with DM as a time-dependent covariate.

DMVariableCoef.HR95 % CIP-value
DM0.8771.60[1.460, 1.764]1.0×10-22
AgeV10.1051.11[1.103, 1.120]3.6×10-162
SexM0.2751.32[1.159, 1.494]2.2×10-5
IsDK0.3661.44[1.219, 1.705]1.9×10-5
LowEduc0.0511.05[0.901, 1.230]0.517
Smoke1000.1311.14[1.005, 1.293]0.041
DM0.4781.23[1.147, 1.309]1.8×10-9
AgeV10.1211.13[1.121, 1.136]5.7×10-296
SexM0.3861.47[1.309, 1.655]9.6×10-11
IsDK0.3241.38[1.184, 1.615]4.2×10-5
LowEduc0.0361.04[0.897, 1.199]0.626
Smoke1000.1331.14[1.016, 1.285]0.026
DM1.6661.58[1.442, 1.740]7.4×10-22
AgeV10.1081.11[1.106, 1.123]2.7×10-175
SexM0.3641.44[1.269, 1.634]1.7×10-8
IsDK0.3601.43[1.211, 1.698]2.9×10-5
LowEduc0.0551.06[0.904, 1.236]0.489
Smoke1000.1051.11[0.978, 1.261]0.106
Notes: Variables: AgeV1: Age at visit 1, SexM: Sex (1 – male, 0 – female), IsDK: Participant is from Denmark (1) or USA (0), LowEduc: Low education (1 – below high school, 0 – otherwise), Smoke100: Smoker (1 – smoked >100 cigarettes in lifetime, 0 – otherwise).
Hazard ratios (HR) of all-cause mortality risk for DM variables are per standard deviation: DM1: 0.539, DM1+: 0.425, DM1: 0.276; HR for other variables are per a unit change.

The results for the “age-dependent” DM variants (DMa1, DMa1+, DMa1) are shown in Tables 6 (joint models) and 7 (Cox model). In contrast to the “original” DM variants (DM1, DM1+, DM1), AgeV1, and TimeV1 have little influence on these measures (p=0.04 for DMa1+, AgeV1; p=0.03 for DMa1, TimeV1; non-significant for the other cases; see Table 6, “Longitudinal”) reflecting the way such measures were constructed. Other variables in the “Longitudinal” part of Table 6 show varying significance and direction of impact on DM. The “Survival” part of Table 6 reveals that the “age-dependent” variants still have strong associations with mortality after controlling for age and the other covariates indicated in the table (see Methods) which showed significance levels similar to the original DM variants. However, the effect size for “age-dependent” DM variants diminished compared to the original DM variants (HR per SD ranging from 1.31 for DMa1 to 1.7 for DMa1). Table 7 shows that the HRs from joint models are also larger (1.1 to 1.4 times) than the HRs from the Cox model, similar to the original DM variants.

Table 6. Results of the joint models applied to age-dependent DM variants DMa1, DMa1+, and DMa1.

DMa1Coef.95% CIP-valueCoef.HR95 % CIP-value
DM0.5621.31[1.155, 1.476]2.1×10-5
AgeV10.00006[-0.001, 0.001]0.9040.1251.13[1.125, 1.140]9.1×10-300
SexM0.003[-0.024, 0.030]0.8210.3641.44[1.268, 1.634]1.9×10-8
IsDK0.045[0.012, 0.079]0.0080.2551.29[1.089, 1.530]0.003
LowEduc0.030[-0.018, 0.077]0.2210.0661.07[0.912, 1.251]0.413
Smoke1000.037[0.010, 0.065]0.0070.1291.14[1.000, 1.292]0.049
DrugDiab0.100[0.046, 0.154]2.7×10-8
DrugHtn0.011[-0.017, 0.04]0.427
DrugLipid0.017[-0.012, 0.046]0.247
Fasting-0.011[-0.055, 0.033]0.623
TimeV1-0.003[-0.006, -0.0003]0.032
DM1.3321.67[1.419, 1.965]6.6×10-10
AgeV1-0.0008[-0.001, -0.0004]0.0400.1271.14[1.129, 1.143]0
SexM-0.0008[-0.021, 0.020]0.9390.3761.46[1.290, 1.644]1.3×10-9
IsDK0.013[-0.013, 0.038]0.3250.2821.33[1.129, 1.556]5.7×10-4
LowEduc0.041[0.006, 0.077]0.022-0.001.998[0.856, 1.165]0.986
Smoke1000.024[0.003, 0.045]0.0240.1121.12[0.989, 1.263]0.074
DrugDiab0.288[0.247, 0.330]8.1×10-43
DrugHtn0.037[0.016, 0.059]7.3×10-4
DrugLipid-0.033[-0.055, -0.010]0.004
Fasting-0.029[-0.063, 0.005]0.098
TimeV1-0.001[-0.004, 0.001]0.321
DM2.2461.70[1.445, 2.005]1.9×10-10
AgeV1-0.0002[-0.0007, 0.0003]0.4200.1281.14[1.129, 1.145]4.2×10-279
SexM0.003[-0.011, 0.016]0.6830.3831.47[1.286, 1.674]1.2×10-8
IsDK0.010[-0.006, 0.027]0.2230.2791.32[1.109, 1.576]0.002
LowEduc0.030[0.006, 0.054]0.0130.0231.02[0.866, 1.209]0.791
Smoke1000.023[0.01, 0.037]7.3×10-40.0881.09[0.956, 1.247]0.196
DrugDiab0.157[0.130, 0.184]1.0×10-29
DrugHtn0.016[0.002, 0.030]0.024
DrugLipid-0.012[-0.026, 0.003]0.114
Fasting-0.019[-0.042, 0.004]0.103
TimeV1-0.001[-0.003, 0.001]0.198
Notes: Variables: AgeV1: Age at visit 1, SexM: Sex (1 – male, 0 – female), IsDK: Participant is from Denmark (1) or USA (0), LowEduc: Low education (1 – below high school, 0 – otherwise), Smoke100: Smoker (1 – smoked >100 cigarettes in lifetime, 0 – otherwise), DrugDiab: Takes (1) or does not take (0) anti-diabetic drugs, DrugHtn: Takes (1) or does not take (0) anti-hypertensive drugs, DrugLipid: Takes (1) or does not take (0) lipid-lowering drugs, Fasting: Fasting (1 – >=8 hrs., 0 – otherwise), TimeV1: Follow-up period since visit 1.

Table 7. Results of the Cox model with age-dependent DM as a time-dependent covariate.

DMVariableCoef.HR95 % CIP-value
DM0.2841.14[1.077, 1.216]1.2×10-5
AgeV10.1261.13[1.127, 1.142]0.4×10-309
SexM0.3751.46[1.284, 1.650]4.7×10-9
IsDK0.2741.32[1.112, 1.556]0.001
LowEduc0.0751.08[0.922, 1.259]0.348
Smoke1000.1311.14[1.004, 1.293]0.043
DM0.5031.21[1.148, 1.283]8.7×10-12
AgeV10.1281.14[1.129, 1.143]0
SexM0.3761.46[1.296, 1.637]3.1×10-10
IsDK0.3011.35[1.158, 1.578]1.4×10-4
LowEduc0.0241.02[0.885, 1.185]0.748
Smoke1000.1241.13[1.006, 1.273]0.04
DM0.9381.25[1.173, 1.329]3.1×10-12
AgeV10.1281.14[1.129, 1.144]0.6×10-309
SexM0.3951.48[1.307, 1.685]1.1×10-9
IsDK0.2841.33[1.123, 1.572]9.2×10-4
LowEduc0.0671.07[0.914, 1.252]0.402
Smoke1000.1001.11[0.973, 1.255]0.124
Notes: Variables: AgeV1: Age at visit 1, SexM: Sex (1 – male, 0 – female), IsDK: Participant is from Denmark (1) or USA (0), LowEduc: Low education (1 – below high school, 0 – otherwise), Smoke100: Smoker (1 – smoked >100 cigarettes in lifetime, 0 – otherwise). Hazard ratios (HR) of all-cause mortality risk for DM variables are per standard deviation: DMa1: 0.474, DMa1+: 0.385, DMa1: 0.237; HR for other variables are per a unit change.

Genetic analyses of DM-related traits

The R-package JM provides estimates of two types of random effects (random intercept, DM-RI, and random slope, DM-RS) for each individual in the analytic sample; these random effects are the traits used in the genetic analyses (see Methods). Figure 2 presents the results of the GWAS of DM-RS for the "age-dependent" DM variants. We found two genome-wide significant variants on chromosome 5 in the TRIO gene (rs12652543, p=7.2×10-9, and rs16903264, p=1.2×10-8, which are in linkage disequilibrium (LD) [r2 ~ 0.95] in whites, according to the NIH-supported online tool LDlink, that are associated with DM-RS for DMa1. Biological interpretations of these findings are provided in Discussion. Several SNPs from this region and some others showed suggestive associations (p < 10-5) with DM-RI for DMa1 (Supplementary Figure 1). Analyses of other DM variants (Figure 2: DM-RS for DMa1+ and DMa1; Supplementary Figure 2: DM-RS for DM1, DM1+, and DM1; Supplementary Figure 3: DM-RI for DM1, DM1+, and DM1) did not yield any genome-wide significant signals, but there were several suggestive signals on different chromosomes.

Results of genome-wide association study of random slopes of DM (DM-RS) for “age-dependent” DM variants (DMa1−, DMa1+, DMa1; see Methods).

Figure 2. Results of genome-wide association study of random slopes of DM (DM-RS) for “age-dependent” DM variants (DMa1, DMa1+, DMa1; see Methods).

The DM variants were constructed using several biomarkers (see Methods). To check whether the signals observed in the analyses of DM-RS for DMa1 are due to associations of the genetic variants with some particular biomarker (or a subset of biomarkers) used in the construction of DMa1, we performed GWAS of DM constructed from individual biomarkers following the same procedures as for DM based on several biomarkers. The results are shown in Supplementary Figure 4. As one can see from this figure, there were no signals on chromosome 5 for any of the biomarkers constituting DMa1. However, the GWAS of DM-RS for grip strength revealed a genome-wide significant signal (see description of sensitivity analyses below) on chromosome 7 (rs10231286, p=4.6×10-8; this SNP is located near GRM3, a glutamate receptor gene involved in brain functioning). Supplementary Table 1 shows top SNPs from this analysis.

We also performed sensitivity analyses running the models with different numbers of principal components (PCs: 1, 2, 5, 10). The top two signals for DM-RS of DMa1 shown in Figure 2 remained genome-wide significant in all cases (p-values for the top SNP rs12652543 varied from p = 2.1 ×10-8 to p=9.7×10-9; p-values for the second-ranked SNP rs16903264 varied from p=3.3×10-8 to p=1.4×10-8). However, the genome-wide significant signal for grip strength found in the analyses with 20 PCs Hazard ratios (HR) of all-cause mortality risk for DM variables are per standard deviation: DMa1: 0.474, DMa1+: 0.385, DMa1: 0.237; HR for other variables are per a unit change.

(Supplementary Figure 4) did not reach the genome-wide significant level in some models with different numbers of PCs (e.g., p=8.8×10-8 for the model with 2 PCs). In addition, we performed analyses of DM variants constructed using different sets of biomarkers selected according to other thresholds for correlation with age (absolute value of the correlation ≥ 0.1 and ≥ 0.2) which did not produce any genome-wide significant signals. We also ran the model with time-interaction terms for all covariates (except age) in the fixed effects part of the longitudinal sub-model in JM. All interactions were non-significant except that for country (estimate: -0.008; p = 0.03). The GWAS results for DM-RS of DMa1 constructed from this model were similar to those shown in Figure 2 (the top two SNPs remained genome-wide significant: p = 4.3×10-9 for rs12652543 and p = 7.4×10-9 for rs16903264).


Applications of joint models to composite measures of physiological dysregulation (DM) and genetic analyses of individual characteristics of DM, in the context of research on aging

In this work, we constructed the statistical (Mahalanobis) distance measure (DM) using multiple biomarkers collected at two visits in the LLFS using the original approach from [17] and its “age-dependent” modification that considers deviations of biomarker values from those typical of age peers rather than those of younger individuals. Analyses of longitudinal trajectories of such measures present methodological challenges (see Introduction) that require applying appropriate statistical methodology for correct inference. Here we applied one such method, joint models, for joint analyses of longitudinal observations of DM and follow-up data on mortality for LLFS participants. Applications confirmed that, as in other studies [17, 18, 20, 22, 23], the association of DM with mortality in LLFS is significant and effect sizes are substantial (with larger HRs for the “original” DM variants). Comparisons of joint models with the Cox regression model with DM considered as a time-dependent covariate indicated that the values of the association parameter for DM in the hazard are underestimated in the Cox model, as expected [9, 10, 15]. Even though both models reveal the same direction of the influence and the result remains highly significant so that one may argue that the interpretation of the results in this case is the same in these two approaches, application of an inappropriate approach can still have substantial consequences if, for example, one needs to build a predictive model based on these results. As shown in many studies [4], including our applications to LLFS [24] and other data [23], inclusion of composite measures improves the predictive accuracy of the models for mortality and other health-related outcomes. Therefore, such predictive models should be based on an appropriate statistical approach such as joint models, which effectively account for informative missingness (death), and thus are able to correct for that type of bias.

Joint models is an active area of research in statistics with numerous extensions of the basic model (analyzed in this paper) suggested in the literature that cover a wide range of research applications such as latent classes, competing risks, multivariate models, non-linear models, dynamic predictions, stochastic processes, etc. (see books [15, 16] and recent review papers and tutorials [2533]). Such extended models can be applied to analyze dynamic characteristics of composite measures such as DM with various outcomes in more comprehensive ways.

One particular approach for joint analyses of longitudinal and time-to-event outcomes, the stochastic process model, SPM (see non-technical introduction in [4] and technical reviews in [34, 35]), is especially relevant in the context of research on aging as the model has components that permit clear biological interpretation in terms of fundamental features of aging-related changes in an organism. Our recent applications [22, 23] of SPM to DM confirmed its significant association with mortality and proxy measures of physiological robustness and resilience, and revealed significant relationships of physiological dysregulation with other hidden aging-related characteristics, such as decline in stress resistance and adaptive capacity which typically are not observed in the data and thus can be analyzed only indirectly through such an analytic approach. The availability of genetic data in longitudinal studies makes it possible to explore genetic determinants of biological aging of individuals based on the dynamics of such composite measures as DM. However, this is still a largely unexplored area. The “genetic” SPM [3638] allows investigation of genetic determinants of such aging-related characteristics in applications to longitudinal observations of composite biomarkers (such as DM). In particular, recent developments in the SPM methodology [39] have considerably enhanced the computational speed (which was a critical barrier in implementing this approach to large-scale genetic analyses) and opened new avenues for applying this model to GWAS, with far reaching implications for significantly improving our understanding of the genetic underpinnings of complex aging-related traits.

Interpretation of genetic associations with DM: Biological and health effects of genes associated with the increase in physiological dysregulation with age

Table 8 shows the five genes (TRIO, FNBP1, PLXNA4, CADM1, and UBE2E2) corresponding to the top SNPs found in the association analysis of the random slope of DM (for the “age-dependent” DM constructed from biomarkers that decline in late life), including the SNP rs12652543 that reached genome-wide level of significance (other three genes shown in Table 8 will be discussed later). Note that multiple SNPs in these five genes were associated with slopes of DM, many of which were in LD with each other (according to LDlink, We eliminated the redundant SNPs (r2>0.8), so the SNPs shown in Table 8 represent not only themselves but also LD blocks (r2>0.8) of other (not shown) SNPs associated with DM slopes. We then performed in depth review of scientific literature and information provided by the NCBI Gene (, and found that four of the above five genes have been implemented in cancer, especially in its progression/prognosis. Three of these genes (TRIO, PLXNA4 [Plexin A4] and CADM1 [TSLC1, SynCAM1]) are also involved in axon guidance and growth (Table 8, last column) [4046].

Table 8. Top-ranked SNPs from GWAS of the random slope of DM, and respective genes (explanation in Discussion).

SNPChrPositionA1A2MAFP-valueRegionGeneGene/protein is involved in
rs12652543514177235AG0.187.2×10-9intronTRIOcancer cells migration, invasion, prognosis, axon guidance,
rs32573514172108GA0.203.0×10-7intronTRIOsynapse function, neurite outgrowth, neurotransmission,
rs151473514123313TC0.161.6×10-620kb 5'TRIOcognition, intellectual disability
rs727572299132653055GA0.048.9×10-7intronFNBP1high expression in cancer
rs794342687131853832AG0.079.8×10-6intronPLXNA4 (Plexin A4)axon guidance, Parkinson's, AD, tau, cancer progression
rs189277311115122626CA0.219.6×10-6intronCADM1 (TSLC1)synaptic cell adhesion, axon guidance, cancer prognosis
rs14363513104617973GT0.255.1×10-55' ofALCAM (CD166)cell adhesion, migration, cancer, axon growth, immunoglobulins
rs1309732931320815AG0.455.9×10-5intronCNTN6cell adhesion, axon connections, intellectual disability
rs1444261255354466CT0.081.9×10-5intronRTN4 (Reticulon4)nerve growth inhibitor, blocks regeneration
Notes: SNP – rs-number; Chr – chromosome number; Position – SNP position on chromosome; A1 – minor allele; A2 – major allele; MAF – minor allele frequency; P-value – p-value after GC; Region – SNP location in gene, or distance to closest gene; Gene – GENCODE gene name of closest gene; Gene/protein is involved in – cell process, biological function, or health disorder associated with this gene/gene product (based on the NCBI Gene resource [] and the up-to-date literature).

For a broader functional analysis, we selected 36 genes corresponding to the top 100 SNPs (all with p-value < 10-4) from GWAS of the DM-RS for the "age-dependent" DM (Supplementary Table 2). We performed the pathway/process enrichment analyses for these 36 genes using several online tools available through Enrichr ( [47]) and MetaScape ( portals that exploit traditional ontologies and pathway sources, such as Gene Ontology [GO] processes, KEGG, BioCarta and Reactome pathway collections, among other. We also run the enrichment analysis using a commercial MetaCore platform for the functional analyses, by Clarivate Analytics (, which uses custom-made manually curated libraries of pathways and processes, along with open-access ontologies, such as the GO and other [48]. We used several tools rather than just one since we wanted to feature pathways/processes that consistently show up among the top results of the enrichment analyses using the different tools.

We found that in most cases axonal guidance was among the top biological processes enriched for the 36 genes associated with the rate of increase in physiological dysregulation with age (DM-RS) (see examples in Supplementary Figure 5). These results were further supported by the information provided by NCBI Gene ( about biological effects of these 36 genes, and relevant research publications (e.g., [4951]).

Then we used the Pathway Map Creator tool, a part of the MetaCore platform [48], to create a custom map showing only products of those genes (of the 36) that participate in functionally related biological processes (Supplementary Figure 6). This figure, again, pointed to a common involvement of TRIO, PLXNA4 (Plexin A4) and CADM1 (TSLC1) in axon guidance and growth, and in cell-cell adhesion, which plays a role in both the axon guidance and cancer, and also featured the products of three more genes among those 36 (ALCAM (CD166), CNTN6 and RTN4 (Reticulon 4)) as involved in the axon guidance and nerve growth. We added these three genes to Table 8, to show their biological effects in the context of the top significant genes.

In summary, our analysis of the biological effects of the top 36 genes from GWAS of the DM-RS, based on (i) the up-to-date scientific literature and the NCBI Gene resource, (ii) commercial (MetaCore) and open online pathway/process enrichment tools, and (iii) a custom pathway map creator (a part of the MetaCore platform), pointed to a common biological process that shows up across all these analyses, namely axon guidance. Although axon growth is mainly observed during early development, the axon guidance genes can be functional in adults and impact the maintenance of neural circuits, synaptic function and plasticity, neuroinflammatory responses, and as result neurological disorders [44, 52, 53]. Also, a recent study of the changes in human proteome across the lifespan revealed that proteins corresponding to genes involved in axon guidance and synaptic function are significantly over-represented among the clusters of proteins whose plasma levels show the strongest correlation with increasing age [54], thus supporting the role of respective biological processes in human aging.

Our results thus indicate that the decline in axons ability to form and maintain complex neuroregulatory networks may potentially play an important role in the increase in physiological dysregulation during aging.

In our recent paper we showed that the level of physiological dysregulation (estimated through DM) can be a useful aggregate indicator of the whole-body resilience and robustness [23]. In this context, our current results of the functional analysis of genetic associations with DM may also indicate that the declining ability to form and maintain complex neuroregulatory networks could contribute to the decline in physical resilience with age, which is the key universal feature of aging [55]. This potential connection deserves further investigation.

One should note that our results do not imply that aging can be explained by a single biological process, such as the decline in axons ability to maintain complex networks that may lead to the increase in physiological dysregulation, in turn resulting in the decline in resilience and the increase in mortality risk with age. Aging is heterogeneous, and the increase in physiological dysregulation per se is one of potentially many processes contributing to its heterogeneity. Respectively, genes associated with the decline in physiological dysregulation are not the only genes involved in aging; however, they may significantly contribute to the genetic heterogeneity of aging.

Concluding remarks

The “geroscience” hypothesis posits that interventions aimed at slowing biological aging could prevent or delay many different diseases simultaneously thus prolonging healthy lifespan and total lifespan [56]. Recent projections showed that the economic value of delayed aging (with a moderate increase in life expectancy by about 2.2 years, most of which would be spent in good health) is estimated to be $7.1 trillion over fifty years and, “in contrast, addressing major diseases such as heart disease and cancer separately would yield diminishing improvements in health and longevity by 2060 –- mainly due to competing risks” [57] providing additional arguments on the importance of identifying systemic factors that can underlie increased vulnerability to multiple diseases (rather than a specific pathology) in aging organisms. One of the critical barriers in developing interventions to slow or delay aging is that aging in humans is a gradual and slow process spanning years and decades which is not feasible to investigate in the timeframe of clinical trials. Thus, developing “proxy” measures quantifying the process of biological aging and investigation of the effects of different genetic and non-genetic factors on such measures is of paramount importance for moving research on aging forward.

Different measures to quantify biological aging (including DM) have been recently suggested in the literature and, as the recent comparative study of such measures reveals [58], they may not measure the same aspects of the aging process thus calling for further evaluation and refinement of such measures in additional studies. This, in particular, requires rich data containing relevant information on human aging and appropriate statistical methodology that would help utilize the full potential of such data. Our previous results [23] using Framingham Heart Study and Cardiovascular Health Study data suggested that multiple deviations of biomarkers from their baseline physiological states (reflected in higher physiological dysregulation levels summarized by DM) could be promising indicators of declining robustness and resilience during aging, and may precede clinical manifestation of not just one but many diseases (thus supporting a “geroscience” concept), even though deviations can be small and not clearly abnormal for individual biomarkers. The current paper is, to the best of our knowledge, the first study which revealed the significant genetic underpinnings of such composite measures of physiological dysregulation (DM) in the framework of the statistical approach relevant for joint analyses of longitudinal and time-to-event outcomes (joint models).

Results of GWAS of dynamic characteristics of DM constructed from the output of joint models yielded genes (Table 8) broadly involved in the axon guidance, synaptic function, neuroinflammatory responses, cognitive disorders and cancer, which points out to a potentially important role of the decline in neurons ability to maintain complex regulatory networks in the increase in physiological dysregulation and related mortality risk during aging.

These encouraging findings call for further exploration of the genetic mechanisms of the change in physiological dysregulation with age, and its role in the heterogeneity of human aging. They also call for future replication in independent large cohorts that collect repeated measurements of biomarkers similar to those used in the construction of composite measures of physiological dysregulation in the LLFS data.

Materials and Methods


The Long Life Family Study (LLFS) is a family-based, longitudinal study of healthy aging and longevity that enrolled more than 4,900 participants from 583 families selected for exceptional familial longevity [59]. Participants were recruited at three U.S. (Boston, New York, Pittsburgh) and one European (Denmark) field centers during 2006–2009 based on age, capacity to understand the study, and their Family Longevity Selection Score (FLoSS) [59]. This score was developed specifically to select the families for the LLFS and it takes into account both the exceptionality of family members’ survival and the presence of very old living family members. The FLoSS was later validated in an independent large-scale genealogically-based resource (the Utah Population Database [60]) as a selection criterion for family longevity studies [61]. Sibships were eligible for the LLFS if their FLoSS was greater than 7 (this threshold was chosen because it was determined that such families are rare but are still detectable with sufficient frequency [59]) and they had at least one living sibling and at least one offspring willing to be enrolled in the study. Written informed consent was obtained from all subjects following protocols approved by the respective field center’s Institutional Review Boards. In this paper, we performed secondary analyses of LLFS data collected at all field centers. The data used in this study were provided by the LLFS Data Management and Coordinating Center (Washington University, St. Louis). The LLFS data are also available in the database of Genotypes and Phenotypes (; Study Accession: phs000397.v1.p1).

Socio-demographic variables, data on past medical history and current medical conditions, medications use, physical and cognitive functioning, and blood samples were collected via in-person visits and phone questionnaires for all subjects at the time of enrollment, as described elsewhere [62]. Participants are followed-up annually to track their vital and health status. The analyses reported in this paper used the April, 20, 2018 release of LLFS data with the latest recorded date of death on January, 24, 2018. Ages at death for those participants who died within the follow-up period were computed from available dates of birth and death. Ages at censoring for those who did not die within the follow-up period were determined from dates of birth and last follow-up. The ages of the oldest participants were validated against external data [63]. Surviving participants underwent a second in-person evaluation in 2015–2018. Blood assays were centrally processed at a Laboratory Core (University of Minnesota) and protocols were standardized, monitored and coordinated through the LLFS Data Management and Coordinating Center. Genotyping was performed by the Center for Inherited Disease Research using Illumina Human Omni 2.5 v1 BeadChip array (see details on genotyping and quality control (QC) procedures in [64]).

We also reported disease-related characteristics of the analyzed sample that include the disease status at the baseline (prevalence) and new cases reported during the follow-up (incidence) for four major aging-related diseases available in the study: Alzheimer’s disease/dementia (AD), cancer, cardiovascular diseases (CVD), and diabetes. Information on diseases and health conditions was collected during the interviews either from the participants or proxies (if the participant was unable to respond). Using responses to questions about specific diseases (AD or dementia: Alzheimer’s Disease or Dementia; cancer: All cancer cites; CVD: Myocardial Infarction, Heart Attack, Coronary Angioplasty, Coronary Artery, Bypass Grafting, (Congestive) Heart Failure, Stroke, Cerebrovascular Accident, Transient Ischemic Attack, or Mini-Stroke; diabetes: Diabetes) from the baseline and the follow-up interviews, we computed the numbers of prevalent cases at the baseline and the numbers of new cases reported since the baseline.

Construction of the measure of physiological dysregulation (DM)

The measure of physiological dysregulation (DM) is a recently developed approach for constructing a composite measure from multiple biomarkers [17, 18, 21]. It is a continuous measure which is essentially the statistical (Mahalanobis) distance [65] from “optimality” constructed for the joint distribution of multiple biomarkers and it uses the correlation structure of the biomarkers to measure how “aberrant each individual’s profile is with respect to the overall average (centroid) of the reference population” [19]. The “reference” centroid is assumed to represent the optimal physiological state. The “reference” population can be either a subsample of the same study population or it can come from some other study. For a set of biomarkers represented by a column vector x measured in an individual at age t, x(t), DM is defined as [17]:


where x¯ is a vector of means and S is the variance-covariance matrix for the respective biomarkers calculated from the “reference” population, and superscript T denotes transposition.

Information on biomarkers measured in the LLFS (number of measurements at each visit, correlations with age and pairwise correlations between biomarkers, p-values for testing the null hypothesis of a zero correlation, and number of observations used for computation of correlations) is given in Supplementary Table 3. For the purpose of this paper, we initially selected a set of biomarkers collected at both visits, for a total of 30 out of 47 biomarkers available in the study (see Supplementary Table 3). We then further reduced the list of biomarkers including only those moderately correlated with age (absolute value of the correlation ≥ 0.15; see description of sensitivity analyses for different correlation thresholds in Results) to consider for the computations of the statistical distance DM, following the ideas from previous work [17, 18]. Further, for the groups of related biomarkers (such as systolic/diastolic/pulse pressure; forced expiratory volume/forced vital capacity; red blood cell count/hematocrit/hemoglobin; total/low-density lipoprotein cholesterol; and white blood cell count/absolute neutrophil count), we randomly selected one biomarker for inclusion in DM. We constructed the DM variants from the resulting set of biomarkers, separating those negatively and positively correlated with age, i.e., declining versus increasing at old ages (~65+) in most people [66]. Resulting variants were denoted DM1 and DM1+, respectively. DM1 includes the following biomarkers: diastolic blood pressure, forced vital capacity, grip strength, hematocrit, and total cholesterol, and DM1+ includes: absolute monocyte count, creatinine, glycosylated hemoglobin, mean corpuscular volume, pulse pressure, red cell distribution width, and white blood cell count. DM1 is computed using the combined list of biomarkers from DM1 and DM1+.

We first constructed the DM variants (DM1, DM1+, DM1) using the conventional approach suggested in [17]. Specifically, the observed values of each biomarker were transformed using the Box-Cox transformation and standardized so that the transformed biomarkers were all on the same scale (with a zero mean and a unit variance). These standardized and transformed values were used in calculations of DM as in Eq. 1. We used individuals aged <60 years at the LLFS visit 1 as a “reference population.” This cutoff gave a reasonable number of participants in the reference population: 1,407 (834 females, 573 males), 1,437 (847, 590), 1,389 (821, 568), for DM1, DM1+, DM1, respectively. Computations of the means and variance-covariance matrix in the “reference” population were performed separately for females and males using the observed values of the biomarkers included in the definition of the respective DM. Note that in the LLFS there are at most two observations of biomarkers per individual. Therefore, we did not impute missing values of biomarkers as we did in our previous studies [22, 23] in applications to other datasets with longer series of measurements. Rather, the appropriate approach to handle missing not at random (MNAR) data is used here to jointly model the dynamics of DM and the risk of death (see section Specification of joint models). For DM1, we computed 6,244 values (4,056 at Visit 1, 2,188 at Visit 2) in 4,365 individuals. For DM1+, we calculated 6,557 (4,344, 2,213) values in 4,598 participants, and for DM1, the observations of 5,921 (4,010, 1,911) values in 4,290 persons were available. The resulting DM variables were also transformed using the Box-Cox transformation. We performed sensitivity analyses (for the joint models analyses and genetic associations, see below) using the DM in the original and the transformed scales which showed similar results so that only those for the Box-Cox transformed values are reported in the paper.

Next, we constructed the “age-dependent” DM variants (denoted, accordingly, DMa1, DMa1+, DMa1) using a conceptually different approach in constructing the measure of physiological dysregulation. In the original specification [17], it was assumed that there is a fixed “normal” physiological state represented by the reference population (typically, a relatively younger sample) so that the DM measures deviations from that state at respective ages. Here, in the definition of the “age-dependent” DM we considered deviations of the biomarker values from those typical of age peers rather than those of younger individuals. That is, the means and variance-covariance matrix in Eq. 1 were defined in the respective age groups. Ideally, such values should be calculated for each age, however, due to small sizes of one-year age groups in our data, we computed these quantities for five-year age groups <50, 50-54, …, 90-94, 95+. For example, for a female aged 83 years at visit 1, the means and variance-covariance matrix were calculated based on a sample of females aged 80-84 years at visit 1 from which the DM value at visit 1 was computed using the observations of biomarkers at visit 1 according to Eq. 1. Altogether, we computed 6,244 values (4,056 at Visit 1, 2,188 at Visit 2) for 4,365 individuals for DMa1, 6,557 (4,344, 2,213) values for 4,598 participants for DMa1+, and 5,921 (4,010, 1,911) values for 4,290 persons for DMa1.

Specification of joint models

We used joint models [15, 16] as a tool to jointly estimate the longitudinal (DM) and time-to-event (mortality) outcomes (see Introduction). The R-package JM [67] version 1.4-8 was used to estimate the parameters of joint models. We applied the standard version of joint models as described below using the notations from [67]. The survival part of joint models quantifies the association between the longitudinal outcome and the risk of an event:


where hi(t|) is the hazard rate (mortality rate in our applications) for i-th individual at time point t, Mi(t)={mi(u),0u<t} denotes the history of the “true” (i.e., unobserved) longitudinal outcome (mi(), see below) up to t, h0()is the baseline hazard, wi is a vector of baseline covariates, γ is a corresponding vector of regression coefficients, and α is the parameter quantifying the effect of the longitudinal outcome on the risk of an event (this is usually the main parameter of interest in applications of joint models). A linear mixed effects model describes the dynamics of the longitudinal outcome (DM in our case):


where yi(t) is the observed longitudinal process (with available observations yij={yi(tij),j=1ni} for i-th individual), β is a vector of fixed effects parameters, bi is a vector of random (normally distributed) effects, xi(t) and zi(t) are corresponding design vectors for fixed and random effects, and εi(t) denotes a normally distributed error term (assumed to be independent of bi) with zero mean and variance σ2. The quantity mi(t)=xiT(t)β+ziT(t)bi (that is, the observed value minus the error term) represents the “true” value of the longitudinal outcome which is included in the formula for the hazard rate (Eq. 2). This distinguishes joint models from the Cox model with time-dependent covariates which includes the observed values of the longitudinal process in the hazard rate. Ignoring measurement errors (or natural biological variation) in such variables in the latter model can result in underestimation of the strength of association between the hazard and the underlying longitudinal process [9, 10] which can be correctly inferred from joint models in such cases.

In our applications, the longitudinal trajectories of DM (the longitudinal sub-model in joint models) were specified as a linear mixed effects model with linear (random intercept and random slope) random effects and time since visit 1 as a time variable (as implemented in the R-package JM). The list of covariates in the fixed effects part included: sex (1 – male, 0 – female), age at visit 1, country (1 – Denmark, 0 – USA), education (1 – below high school, 0 – otherwise), smoking (smoked >100 cigarettes in lifetime: yes [1]/no [0]), medication use (anti-diabetic, lipid-lowering, anti-hypertensive) (1 – used, 0 – did not use), and fasting (1 – ≥8 hours, 0 – otherwise). The groups of medications indicated above were constructed by the LLFS investigators in a separate study from original medications records using the corresponding Anatomical Therapeutic Chemical Classification System codes. We note that this list of medications does not include all possible groups of medications that might be relevant for this analysis (e.g., osteoporosis related medications). The time-to-event outcome (the survival sub-model in joint models) was modeled as the standard relative risk form [68] with the “true” or unobserved value of DM (i.e., the estimate from the longitudinal sub-model [15]) included in the hazard (the “value” parameterization in the R-package JM, as in Eq. 2) along with the baseline covariates (the same list as above except medication use and fasting which are time-dependent covariates). The baseline hazard was represented as a piecewise constant function and the pseudo-adaptive Gauss-Hermite quadrature rule [69] was chosen to approximate the required integrals in the estimation algorithm (the "piecewise-PH-aGH" method in the R-package JM). We kept the default values for the number of internal knots (6 knots) in the baseline hazard and for the number of Gauss-Hermite quadrature points (3 points) used to approximate the integrals over the random effects. In some cases, the estimation algorithm in the R-package JM did not converge for the default values. In such situations, we varied the numbers (10 knots and/or 6 points) to achieve convergence. Sensitivity analyses confirmed that, in the cases of convergence, using models with different values for knots and points had little effect on the estimates of the parameter of interest (association parameter for DM in the survival sub-model). See also sensitivity analyses with other specifications of JM described in Results.

Genome-wide association study (GWAS) of DM-related traits

We performed GWAS of two DM-related traits constructed using the output of the joint models estimation procedure for the respective DM variants specified above: random intercept (DM-RI) and random slope (DM-RS). These characteristics were computed for each study participant and define how the baseline value of DM (DM-RI) and the age dynamics of DM (DM-RS) in the particular individual differed from the average values in the study sample (adjusted for the respective covariates, as estimated by the fixed effects part of the longitudinal sub-model in joint models).

The QC procedure was performed according to the protocol described in [70] before running the association analyses. The original data contained 4,693 genotyped individuals (2,581 females, 2,112 males) and 2,225,478 SNPs. The sample QC check removed individuals with call rate below 95% and/or heterozygosity rate beyond ± 3 standard deviations (SD) from the mean as well as individuals of divergent ancestry (those for whom the first two principal components (PC) scores were beyond 8 SD from the respective mean scores for the HapMap Phase III European reference populations). The SNP’s QC check removed duplicated SNPs, variants with missing allele code information, indels, SNPs with call rate below 95%, minor allele frequency (MAF) below 1%, and those with a significant deviation from Hardy-Weinberg equilibrium (HWE) with p-value < 10-5. The resulting sample after QC contained 4,608 individuals of European ancestry (2,536 females, 2,072 males) and 1,464,300 autosomal SNPs which passed the QC procedure.

The R-package GENESIS (Bioconductor) [71] was used for the association testing and for computation of PCs using the PC-AiR method [72] to take into account the relatedness among individuals in the LLFS sample. The KING-robust kinship coefficient estimator [73] was used as the measure of ancestry divergence to identify a mutually unrelated and ancestry representative subset of individuals, as implemented in the PC-AiR algorithm. The mixed model was used for genetic association testing which included 20 PC-AiR PCs as fixed effects covariates to adjust for population stratification in the baseline scenario and a genetic relationship matrix (GRM) to account for genetic similarity among sample individuals. The kinship coefficient estimates from PC-Relate [74] (implemented in GENESIS) were used to construct the GRM. Genomic control (GC) [75, 76] was also applied as an additional tool to control for population stratification. In all analyses the GC lambdas were close to 1 indicating that the PCs were sufficient for this purpose.

We also performed sensitivity analyses to test the sensitivity of our results to various aspects of the analytic procedures. This included running GWAS for DM variants computed from biomarkers selected using different thresholds for correlation with age, GWAS for separate biomarkers constituting the specific DM variant, and analyses with different number of PCs, as described in Results.


AD: Alzheimer’s disease/dementia; CI: confidence interval; CVD: cardiovascular diseases; DM: the statistical (Mahalanobis) distance measure; FLoSS: Family Longevity Selection Score; GC: genomic control; GRM: genetic relationship matrix; GWAS: genome-wide association study; HR: hazard ratio; HWE: Hardy-Weinberg equilibrium; JM: joint model; LD: linkage disequilibrium; LLFS: Long Life Family Study; MAF: minor allele frequency; MNAR: missing not at random; PC: principal component; QC: quality control; RI: random intercept; RS: random slope; SD: standard deviation; SNP: single nucleotide polymorphism; SPM: stochastic process model.

Author Contributions

K.G.A.: conceived and designed the study, contributed to statistical analyses, and wrote the manuscript; O.B.: prepared data, performed statistical analyses, and contributed to writing Methods section; S.V.U.: performed functional annotation and interpretation of results of genetic analyses, and wrote the manuscript; D.W., H.D.: contributed to data preparation and statistical analyses; A.M.K., E.S., K.C., J.H.L., B.T., J.M.Z., A.I.Y.: contributed to writing the manuscript.

Conflicts of Interest

Authors declare no conflicts of interest.


Research reported in this publication was supported by the National Institute on Aging of the National Institutes of Health (NIA/NIH) under Award Numbers U01 AG023712 and U19AG063893. The work of K.G.A., O.B., S.V.U., D.W., H.D., A.M.K., E.S., and A.I.Y. was also partly supported by the NIA/NIH grant P01AG043352. The work of K.G.A., O.B., S.V.U., D.W., H.D., and A.I.Y. was also partly supported by the NIA/NIH grant R01AG062623. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.


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