Markov models of aging: Theory and practice

Short-Term and Mid-Term Blood Pressure Variability and Long-Term Mortality

Until recently, there has been a focus on exploring the influence of average blood pressure (BP) on risk of mortality. We go beyond average BP to also investigate mortality risk with respect to variation in BP over 2 timescales-short-term variation among multiple measures at 1 visit, and medium-term variation among the measures at 2 visits several months apart. We present an application of Bayesian hierarchical modeling to the problem of estimating the effect of BP variability on all-cause and cardiovascular mortality. We use data from the Third National Health and Nutrition Examination Survey linked with up to 27 years of mortality follow-up. We find that medium-term systolic BP variability had a very significant predictive value for all-cause mortality in addition to mortality from cardiovascular disease, cerebrovascular disease and heart-attacks combined, approximately 1/3 as large as the well-established impact of mean systolic BP. Medium-term diastolic variability had an additional, although smaller, predictive effect. Short-term variability, in contrast, had little or no measurable predictive value. The medium-term variability effect persisted when controlling for Framingham Risk Score.

Predictors of transitions in frailty severity and mortality among people aging with HIV

BACKGROUND

People aging with HIV show variable health trajectories. Our objective was to identify longitudinal predictors of frailty severity and mortality among a group aging with HIV.

METHODS

Exploratory analyses employing a multistate transition model, with data from the prospective Modena HIV Metabolic Clinic Cohort Study, based in Northern Italy, begun in 2004. Participants were followed over four years from their first available visit. We included all 963 participants (mean age 46.8±7.1; 29% female; 89% undetectable HIV viral load; median current CD4 count 549, IQR 405-720; nadir CD4 count 180, 81-280) with four-year data. Frailty was quantified using a 31-item frailty index. Outcomes were frailty index score or mortality at four-year follow-up. Candidate predictor variables were baseline frailty index score, demographic (age, sex), HIV-disease related (undetectable HIV viral load, current CD4+ T-cell count, nadir CD4 count, duration of HIV infection, and duration of antiretroviral therapy [ARV] exposure), and behavioral factors (smoking, injection drug use (IDU), and hepatitis C virus co-infection).

RESULTS

Four-year mortality was 3.0% (n = 29). In multivariable analyses, independent predictors of frailty index at follow-up were baseline frailty index (RR 1.06, 95% CI 1.05-1.07), female sex (RR 0.93, 95% CI 0.87-0.98), nadir CD4 cell count (RR 0.96, 95% CI 0.93-0.99), duration of HIV infection (RR 1.06, 95% CI 1.01-1.12), duration of ARV exposure (RR 1.08, 95% CI 1.02-1.14), and smoking pack-years (1.03, 1.01-1.05). Independent predictors of mortality were baseline frailty index (OR 1.19, 1.02-1.38), current CD4 count (0.34, 0.20-0.60), and IDU (2.89, 1.30-6.42).

CONCLUSIONS

Demographic, HIV-disease related, and social and behavioral factors appear to confer risk for changes in frailty severity and mortality among people aging with HIV.

Aging, frailty and complex networks

When people age their mortality rate increases exponentially, following Gompertz's law. Even so, individuals do not die from old age. Instead, they accumulate age-related illnesses and conditions and so become increasingly vulnerable to death from various external and internal stressors. As a measure of such vulnerability, frailty can be quantified using the frailty index (FI). Larger values of the FI are strongly associated with mortality and other adverse health outcomes. This association, and the insensitivity of the FI to the particular health variables that are included in its construction, makes it a powerful, convenient, and increasingly popular integrative health measure. Still, little is known about why the FI works so well. Our group has recently developed a theoretical network model of health deficits to better understand how changes in health are captured by the FI. In our model, health-related variables are represented by the nodes of a complex network. The network has a scale-free shape or "topology": a few nodes have many connections with other nodes, whereas most nodes have few connections. These nodes can be in two states, either damaged or undamaged. Transitions between damaged and non-damaged states are governed by the stochastic environment of individual nodes. Changes in the degree of damage of connected nodes change the local environment and make further damage more likely. Our model shows how age-dependent acceleration of the FI and of mortality emerges, even without specifying an age-damage relationship or any other time-dependent parameter. We have also used our model to assess how informative individual deficits are with respect to mortality. We find that the information is larger for nodes that are well connected than for nodes that are not. The model supports the idea that aging occurs as an emergent phenomenon, and not as a result of age-specific programming. Instead, aging reflects how damage propagates through a complex network of interconnected elements.

Stochasticity, heterogeneity, and variance in longevity in human populations

Inter-individual variance in longevity (or any other demographic outcome) may arise from heterogeneity or from individual stochasticity. Heterogeneity refers to differences among individuals in the demographic rates experienced at a given age or stage. Stochasticity refers to variation due to the random outcome of demographic rates applied to individuals with the same properties. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity. We show how to use this approach to decompose the variance in longevity into contributions from stochasticity and heterogeneous frailty for male and female cohorts from Sweden (1751–1899), France (1816–1903), and Italy (1872–1899), and also for a selection of period data for the same countries.

Heterogeneity in mortality is described by the gamma-Gompertz–Makeham model, in which a gamma distributed “frailty” modifies a baseline Gompertz–Makeham mortality schedule. Model parameters were estimated by maximum likelihood for a range of starting ages. The estimates were used to construct an age×frailty-classified matrix model, from which we compute the variance of longevity and its components due to heterogeneous frailty and to individual stochasticity. The estimated fraction of the variance in longevity due to heterogeneous frailty (averaged over time) is less than 10% for all countries and for both sexes. These results suggest that most of the variance in human longevity arises from stochasticity, rather than from heterogeneous frailty.

Declining performance of master athletes: silhouettes of the trajectory of healthy human ageing?

Analysis of world record performances by master athletes suggests an essentially linear decline with age until around the eighth decade after which performance decline accelerates. Because these records are obtained from highly trained individuals they can be viewed as being reflective of the diminution of integrative physiological prowess that occurs solely as a result of ageing, unaffected by the confounding effects of inactivity. It can also be argued that these performance profiles mirror and provide an insight into the trajectory of the physiology of the human ageing process. Here we propose a set point theory that hypothesises that a given threshold of physical activity is needed to age optimally and to maximise the 'healthspan'. Exercising at levels below the set point will result in ageing being contaminated by the unpredictable and pathological effects of inactivity. Exercise above this threshold stimulates adaptations towards maximising athletic performance, but is unlikely to have further beneficial effects on health. Thus the decades-long, controlled diminution in athletic performance, should not be seen as a disease process. The ageing process is separate from, and independent of, exercise-mediated processes that maintain or adapt physiological function. Whether an understanding of these mechanisms will also help uncover mechanisms underpinning the ageing process itself is open to question. However, any model which does not take into account the effects of activity will not adequately describe the inherent ageing process.

Network model of human aging: Frailty limits and information measures

Aging is associated with the accumulation of damage throughout a persons life. Individual health can be assessed by the Frailty Index (FI). The FI is calculated simply as the proportion f of accumulated age-related deficits relative to the total, leading to a theoretical maximum of f≤1. Observational studies have generally reported a much more stringent bound, with f≤f_{max}<1. The value of f_{max} in observational studies appears to be nonuniversal, but f_{max}≈0.7 is often reported. A previously developed network model of individual aging was unable to recover f_{max}<1 while retaining the other observed phenomenology of increasing f and mortality rates with age. We have developed a computationally accelerated network model that also allows us to tune the scale-free network exponent α. The network exponent α significantly affects the growth of mortality rates with age. However, we are only able to recover f_{max} by also introducing a deficit sensitivity parameter 1-q, which is equivalent to a false-negative rate q. Our value of q=0.3 is comparable to finite sensitivities of age-related deficits with respect to mortality that are often reported in the literature. In light of nonzero q, we use mutual information I to provide a nonparametric measure of the predictive value of the FI with respect to individual mortality. We find that I is only modestly degraded by q<1, and this degradation is mitigated when increasing number of deficits are included in the FI. We also find that the information spectrum, i.e., the mutual information of individual deficits versus connectivity, has an approximately power-law dependence that depends on the network exponent α. Mutual information I is therefore a useful tool for characterizing the network topology of aging populations.

Biologic aging, frailty, and age-related disease in chronic HIV infection

PURPOSE OF REVIEW

Effective therapies have transformed HIV infection into a chronic disease, and new problems are arising related to aging. This article reviews the aging process, age-related deficit accumulation and frailty, and how these might be affected by chronic HIV infection.

RECENT FINDINGS

Aging is characterized by acceleration in the rate of unrepaired physiologic damage an organism accumulates. HIV infection is associated with many factors that might affect the aging process, including extrinsic behavioral risk factors and co-infections, and multiple intrinsic factors, including intercellular communication, inflammation, and coagulation pathways. Whether each factor affects the aging process, they likely result in an increase in the risk of adverse health outcomes, and so give rise to frailty, likely with several clinical manifestations.

SUMMARY

Age-related deficit accumulation is influenced by both the background or environmental rate of insults an organism sustains and the efficacy of intrinsic damage control and repair mechanisms. Both processes are likely affected in people living with HIV infection.

Robustness and aging--a systems-level perspective

The theory of robustness describes a system level property of evolutionary systems, which predicts tradeoffs of great interest for the systems biology of aging, such as accumulation of non-heritable damage, occurrence of fragilities and limitations in performance, optimized allocation of restricted resources and confined redundancies. According to the robustness paradigm cells and organisms evolved into a state of highly optimized tolerance (HOT), which provides robustness to common perturbations, but causes tradeoffs generally characterized as "robust yet fragile". This raises the question whether the ultimate cause of aging is more than a lack of adaptation, but an inherent fragility of complex evolutionary systems. Since robustness connects to evolutionary designs, consideration of this theory provides a deeper connection between evolutionary aspects of aging, mathematical models and experimental data. In this review several mechanisms influential for aging are re-evaluated in support of robustness tradeoffs. This includes asymmetric cell division improving performance and specialization with limited capacities to prevent and repair age-related damage, as well as feedback control mechanisms optimized to respond to acute stressors, but unable to halt nor revert aging. Improvement in robustness by increasing efficiencies through cellular redundancies in larger organisms alleviates some of the damaging effects of cellular specialization, which can be expressed in allometric relationships. The introduction of the robustness paradigm offers unique insights for aging research and provides novel opportunities for systems biology endeavors.