The Use of Information Theory for the Evaluation of Biomarkers of Aging and Physiological Age to Predict Aging-related Diseases and Frailty
Ilia Stambler and David Blokh
This article argues for the expanded application of information-theoretical measures, such as entropy and normalized mutual information, for research of biomarkers of aging and physiological age as an early predictive measure of age-related multimorbidity and frailty. The use of information theory enables unique methodological advantages for the study of aging processes, as it allows the researchers to evaluate non-linear relations between biological parameters, showing the precise quantitative strength of those relations, both for individual and multiple parameters, demonstrating cumulative or holistic (synergistic) effects. The diagnostic models can be built based on diagnostic parameters routinely available to physicians (frailty indexes, laboratory analysis, physical evaluations) as well as more advanced biomarkers (e.g. genetic and epigenetic analysis) – in relation with age and age-related diseases and frailty. The diagnostic systems that are built in this way can be open and can include any number of additional parameters correlated with age and age-related diseases.
The use of information-theoretical methods, utilizing normalized mutual information, can reveal the exact amount of information that various diagnostic parameters or their combinations contain about the persons’ physiological (or biological) age. Based on those exact diagnostic values for physiological age determination, it is possible to construct a diagnostic decision rule to evaluate a person’s physiological age, as compared to chronological age. The working hypothesis is that people characterized by higher physiological age will have increased risk of age-related frailty and diseases (e.g. heart disease, cancer, type 2 diabetes, neurodegenerative diseases, fractures, falls, mental and functional decline, etc.). Utilizing information-theoretical measures, with additional data, it may be possible to create comprehensive clinically applicable information-theory-based panels of markers and models for the evaluation of physiological age, its relation to age-related diseases and its potential modifications by therapeutic interventions, such as medications and behavioral interventions.1
Introduction: The increasing need for anti-aging intervention and longevity medicine
With the rapidly growing aging population, and the corresponding rise in the incidence of aging-related diseases (such as heart disease, cancer, type 2 diabetes, neurodegenerative disease, chronic obstructive pulmonary diseases, etc), there emerges a special need to estimate health conditions and effectiveness of treatments for a variety of aging-related diseases, based on the evaluation of the aging processes underlying those diseases. Such evaluation is also needed to assess the effectiveness of potential anti-aging interventions and interventions against aging-related diseases. Even more importantly, it is needed for an early preventive intervention in these diseases, based on the calculated physiological age. The importance of quantifying the effects of “normal” aging as compared to “abnormal,” “pathological,” “accelerated” or “premature” aging cannot be overestimated. It is critically important to be able to diagnose “early aging,” that is, to identify subjects in whom “biological” or “physiological age” markedly exceeds the “chronological age.” Thanks to such “early diagnosis” of aging, as a pre-clinical or concomitant condition for a variety of aging-related diseases, it may be possible to solve the problems of early diagnosis of those aging-derived diseases. In other words, it may be stated that pre-clinical diagnosis of aging-related diseases (such as Alzheimer’s disease, type 2 diabetes, cancer and heart disease) naturally belongs in the field of aging research, as aging can be seen as a pre-symptomatic, pre-clinical root determinant of a variety of aging-related diseases.2
Of special importance, early evaluation of physiological age may facilitate the early diagnosis of cancer with a prolonged preclinical period. This may considerably improve the efficacy of treatment for oncological diseases. There have been debates regarding the usefulness or lack thereof of mammography for subjects aged 40-49, that is regarding the possibility of preclinical diagnosis.3 It may be difficult to solve this problem in the framework of pure oncology, disregarding the factors of age or aging, but only in the framework of aging research, for which information-theoretical analysis can be meaningfully applied.
The same may be said for cardiovascular diseases, the main age-related cause of death in the world, including deaths due to ischemic heart disease and ischemic and hemorrhagic stroke.4 Yet, it is also known that cardiovascular diseases, and ischemic heart disease in particular, can be highly susceptible to therapeutic and lifestyle interventions, capable of dramatically extending the health and longevity of the subjects.5 Hence it is of primary importance to be able to early assess the entire array of risk factors, as well as the effects of therapeutic interventions on the risk factors, either individually or in combinations, including both biological and chronological age.6
Also for neurodegenerative diseases, such as Alzheimer’s disease, the vast plasticity of the brain of the aged and the feasibility of positive therapeutic interventions, or even cures, have been recognized. Yet, it has also been recognized that, in order to accomplish such interventions, the earliest possible detection and the consideration of polygenic etiologies will be necessary.7 Here too information-theoretical statistics, capable of utilizing time series methods for prediction from an earlier, preclinical age, and employing mutual information measures to establish non-linear diagnostic correlations of multiple disease determinants, including age, can be indispensable.
Diabetes – Metabolic syndrome
Also, for type 2 diabetes, “diagnosis of aging” can be very helpful for early diagnosis of diabetes, as the diagnostic parameters relevant to diabetes, as well as the underlying biological mechanisms have a great similarity with “normal” aging.8
Generally, the ability to reliably quantitatively diagnose “delayed aging” or “healthy aging” may pinpoint powerful factors facilitating healthy and productive longevity. Here “healthy aging” (or “healthy longevity”) may be understood as the absence of age-related frailty, as commonly defined in geriatric medicine, that is, an active and functional state of older adults characterized by a decreased risk for future poor clinical outcomes, diminished development of disability, dementia, falls, hospitalization, institutionalization or decreased mortality.9 The ability to provide early quantitative evaluation of frailty risks is also of great medical and economic significance.
Prospective economic benefits from the early detection of aging-related diseases thanks to improved diagnosis of aging itself
The humanitarian and economic importance of early detection of aging-related diseases is obvious. Early detection makes it possible to apply preventive medical interventions when the disease is in a more manageable and even curable state, ideally even before any clinical manifestations, thus significantly postponing the time it may take for the disease to progress to a severe, debilitating and more costly state. This postponement of morbidity is also the reason for the vast economic benefits of early detection, necessary for the early preventive intervention. As shown for the US, patients with chronic age-related diseases expend in their last year of life about one third of the total Medicare expenditures (~$15,000 per person).10 Any postponement of this high morbidity period thanks to early detection and preventive interventions can produce massive net health and economic benefits.
Some of the economic benefits of early detection derive from the improvement of individual health, averting direct medical costs and entitlement payments, reducing lost productivity, disability, and employee turnover.11 As of 2004, it was estimated that “75 percent of the $1.9 trillion spent on health care in the United States stem from preventable chronic health conditions … but only 1 percent is allocated to protecting health and preventing illness.”12
Specifically, regarding particular aging related diseases, such as Alzheimer’s disease and Cancer, the savings from early detection per patient are commonly estimated at several thousand dollars for the developed countries: $1,000-10,000+ for Alzheimer’s disease,13 $1,000-10,000+ for various forms of cancer.11 Comparable savings can be expected from the early detection of heart disease14 and diabetes.15
The numbers of patients suffering from these conditions globally are estimated at tens of millions, and are expected to strongly increase worldwide due to the rapid population aging.16 Thus, 36 million people worldwide are living with dementia, including ~10M in Europe and ~5M in the US, with their numbers expected to double every 20 years, reaching 66 million by 2030, and 115 million by 2050.13 Out of the total of 56 million deaths that occurred worldwide in 2012, about 38 million were due to non-communicable (NCD) aging-related diseases, in particular: cardiovascular diseases (17.5 million deaths, or 46.2% of NCD deaths), cancers (8.2 million, or 21.7% of NCD deaths), respiratory diseases, including asthma and chronic obstructive pulmonary disease (4.0 million, or 10.7% of NCD deaths) and diabetes (1.5 million, or 4% of NCD deaths).17
The costs of aging-related diseases worldwide are correspondingly vast, amounting to hundreds of billions and trillions of dollars: ~US$600 billion in 2010 only for dementia worldwide,13 approximately US$800 billion for heart disease; US$850 billion for type 2 diabetes; US$900 billion for cancer; US$300 billion for Chronic Obstructive Pulmonary Disease – COPD.18
Thus the healthcare benefits of even minor improvement in the ability of early diagnosis, necessary for early preventive treatments of aging-related diseases, could be immense. The economic benefits from the preventive approach, intervening in the aging processes underlying the non-communicable diseases before they take clinical forms, would be immense as well (hundreds of billions of dollars savings in health expenditures in the course of several decades just in the US, according to some models19). Yet, to accomplish this, improved diagnostic capabilities are needed for the aging process itself, capable to reliably estimate the person’s physiological and biological age and the effects of interventions on that age.
New methodologies are needed to provide early diagnosis of aging-related ill health
In view of the pressing global social need, new methodologies are required to enable early detection of aging-related ill health. We argue that information-theory-based approaches, utilizing such measures as entropy and mutual information, may provide powerful methodological tools for the solution of these problems. First of all, information theory may allow a more reliable estimation of biological and physiological correlates (biomarkers) of aging, due to its ability to estimate non-linear correlations between parameters, utilizing mutual information measures. The a priori reliance on linear statistical correlations when trying to determine such biomarkers has been failing to produce practically applicable results.20,21 Information-theoretical measures may provide new means to intensify and facilitate this search. Moreover, the preclinical diagnosis requires the simultaneous analysis of a large number of parameters of various kinds, including continuous parameters, with both Gaussian and non-Gaussian distribution, as well as discrete and ranked parameters. Presently, the only theoretically grounded method for the simultaneous analysis of multiple parameters of different kinds is information theory.22
Advantages of the information-theoretical methodology
Arguably, it is methodologically problematic to use the current approaches in biomarkers research and quantified health for practical assessments of physiological age and potential aging-ameliorating and healthspan-extending interventions. The methodological difficulties may derive from two major current shortcomings. Firstly, the current approaches, both in quantified health and biomarkers research, are mainly based on static or short term, average or median population values to define the norm. This makes personalization of clinical evaluations and treatments difficult. Secondly and crucially, the existing approaches commonly assume normal (Gaussian) distribution and linear relations of parameters. Hence, they mainly employ linear statistical measures of correlation, such as the correlation coefficient or linear regression. However, such measures do not correspond to physiological realities, where the relations between parameters are non-linear, including the non-linear alterations with age. Hence the currently used methods are ill suited to evaluate physiological age and aging-ameliorating and healthspan-extending interventions. The main advantage of the information-theoretical methodology is that it provides an integrated approach that can take into consideration the non-linear interrelation of a multitude of parameters – biomarkers and intervention factors, using information-theoretical measures, rather than linear statistical measures.1
Information theory can serve as a universal methodology to assess health and disease status, in relation to age, unifying a variety of model systems, focusing on age-related changes as the root cause of a variety of chronic age-related diseases and health impairments. Information theory may provide the following specific methodological capabilities, currently not available in any other system:
- The current health metrics mainly employ statistical measures. Yet, statistical measures are often inadequate, insofar as in biological systems, the relations between parameters are often non-linear. In contrast, information-theoretical methods allow for the estimation (measurement) of complex non-linear relations between parameters, hence they allow for the inclusion of a wider range of data for making health decisions.
- Currently, the results from different study models are described in incompatible terms, that do not permit an easy mutual inference. In contrast, the common terms and measures of information theory, such as entropy and mutual information, can serve as a universal language to describe, in a unified way, any number of diverse models and results.
- Currently, the degree of mutual applicability between animal model systems and humans, as well as between diverse human samples, is uncertain. In contrast, the evaluation of mutual information between different model systems, can be used as a standardized and convenient estimate of their mutual applicability.
- Currently, the effects of various treatments on human health are often examined in a disconnected manner, without knowing the precise interactions of various treatments. The information-theoretical measures of correlation (such as normalized mutual information) can be employed to test the effects of single or combinations of various treatment factors (such as drugs, genes and lifestyle factors) on the health span and the disease status. By the precise quantitative evaluation of the influence of such factors on the health span and disease status, both synergistic positive and antagonistic adverse effects of treatment interactions can be determined.
- The current systems lack the formal ability to select the most informative (and hence clinically useful) parameters. Using information-theoretical methods, the most informative single parameters or groups of parameters with the highest influence on the health span and disease status can be selected. The selection of the most informative parameters, such as those that contain information about other selected parameters, will allow for a more economic, convenient and efficient diagnostic system. This can save time and expenditures on unnecessary testing, by eliminating the less informative parameters from the outset.
- The current statistical systems are largely heuristic. In contrast, in the information-theoretical diagnostic systems, mutual information is able to provide the exact estimate of similarity between various model systems. Therefore it may be possible to predict the efficacy of a yet untested drug or treatment using the estimates of its similarity (mutual information) with other tested drugs and treatments along with the similarity of model systems to which they are applied. Such an approach may save on unnecessary animal and human testing and facilitate the development of new drugs and treatments.
- The current health assessment systems lack a unified standard or frame of reference. The information-theory-based combined metrics for measuring health status may be based on the convenient and standardized evaluation of system stability, using information-theoretical measures, such as entropy and mutual information. The current systems are mainly based on static, average or median population values. The proposed information-theoretical measures of system stability, assessing dynamic changes in a particular system, can be self-referential, and hence truly personalized.
- The current systems do not permit formal assessment of system stability due to treatments. In contrast, information theory may permit to estimate the effects of particular drugs and treatments, or their combinations, on the stability of a particular system for the short and/or long term, by calculating the system alterations at the input and output caused by the particular treatments. This may provide a common measure of health status and effects of interventions, for the short and long term.
These capabilities are based on the known abilities of information theory, such as 1) to estimate non-linear relations; 2) to describe diverse systems in common terms of entropy change; 3) to estimate the degree of similarity or difference between various systems; 4) to examine combined effects of different parameters on a parameter of choice; 5) to select the most informative parameters; 6) to predict outcomes, as was shown by the wide use of information theory in diagnosis, especially of age related diseases,1 including cancer;23 7) to estimate the general system stability;22 8) to estimate changes in system stability, heterogeneity, regulation and information loss in response to external stimuli.
A critical requirement for building an information-theoretical diagnostic model of physiological age and aging-related diseases is the availability of a large range of clinical and biological data on a large population sample. The data can be as diverse as possible, any data may be of interest. The more data are available and the more diverse they are, the more interesting correlations may be discovered and the better may be the diagnostic power. The data may include biomarkers of aging and the types of data that are commonly used in quantified health applications. For example, cellular, molecular and biochemical markers for biological age may include: age-related changes in telomere length (telomere measurement), advanced glycation endproducts (AGE), 8-hydroxyguanine in DNA and amino acids with oxidized side chains as biomarkers of oxidative stress, levels of proteins that are essential for critical functions, DNA repair capacity, decrease in one or more stem cell populations, T-lymphocyte subsets, gene expression micro-array analysis (e.g. for such genes as Sirtuins, Foxo, Clotho, etc.), epigenetic markers (e.g. methylation), measures of oxidative-reductive and acid-base balance, and more. Furthermore, functional markers for aging may include: muscle strength (manual muscle-testing; dynamometer: hand-grip strength), vascular rarefaction and dysfunction (capillaroscopy; forearm blood flow techniques), gait speed, step-to-step variability, balance, functional mobility (timed-up-and-go), endurance capacity (VO2 max), cardio-respiratory indicators (PaO2; PaO2/FiO2), EEG/ECG/EMG, nutritional state/intake, cognition (tests), psychological type profiling (tests), social participation, socio-economic status (income, employment).
Diverse therapeutic influences may be factored into the model in order to evaluate the efficacy of potential aging and lifespan improving interventions and their effects on the biological, physiological and functional age.24 Those interventions may include: pharmacological treatments (specific drugs, such as rapamycin, metformin, statins, aspirin, etc.), regenerative cell therapies, specific biomedical interventions (operations, physiotherapeutic techniques), reduction of risk factors (smoking, alcohol consumption), dietary factors (e.g. supplements, nutrients, functional foods), physical activity, exercise, rest and sleep, education.
Thus, thanks to the diversity of modeled parameters, various factors affecting aging – biological, environmental and social – can be inter-related and integrated. Of course, the costs of particular markers is an important consideration, hence it may become preferable, at least for practical applications, to use such parameters that would be routinely and inexpensively available to practicing physicians. Notably, however, the number of parameters and the amounts of data, collected, analyzed and made available to physicians and researchers, are constantly and rapidly increasing.
Another issue in selecting data to construct a diagnostic model for physiological age and aging-related ill health is the fact that there is currently no clear, formal and universally accepted clinical definition of aging that can serve as the basis for diagnosis and therapy, which can formally and reliably distinguish between “pathological/accelerated aging” as opposed to “healthy aging.” Not surprisingly, the World Health Organization’s “Global Strategy and Action Plan on Ageing and Health” (2015) includes “Strategic objective 5” – “Improving measurement, monitoring and research on Healthy Ageing” with such priority tasks as “Develop norms, metrics and new analytical approaches to describe and monitor Healthy Ageing” and “Develop resources, including standardized survey modules, data and biomarker collection instruments and analysis programs.”25 Such a formal understanding and measurement of healthy aging can be aided thanks to the use of standard information-theoretical measures.
An additional important issue for the diagnostic model construction may be the choice of subjects and samples. Arguably, it is preferable to rely on the long-term (longitudinal), rather than short-term (immediate benefit) analysis. Thus, for example, it may be desirable to consider a large number of medical histories of people who were, say, 65-70 a couple of decades back (say in 1990 for illustration) and who were at that time considered “clinically” healthy. From this set, we can form two subsets:
- The set of medical histories of people who died in 1990-1995, at the age of 65-75 years, from various aging-related diseases, such as type 2 diabetes, cancer, heart disease and Alzheimer’s disease.
- The set of medical histories of people, with a comparable birth time, who are alive presently (in 2017). These persons are at the time approximately 90-100 years old. We assume that the second subset is characterized by greater resilience or delayed aging as compared to the first set. Despite the potential issues with incomplete data and changing measurement techniques, the use of such a sample selection may allow the investigators to solve the following problems:
- To quantitatively determine the risk factors, related to the emergence and course (severity) of the aging-related diseases: diabetes, cancer, heart disease and Alzheimer’s disease.
- To quantitatively determine the influence of those factors on the emergence and course of the diseases.
- To quantitatively estimate the combined influence of groups of factors on the diseases and reveal the factors producing cumulative effects.
- To construct algorithms of pre-clinical diagnosis of the aging-related diseases, such as diabetes, cancer, heart disease and Alzheimer’s disease.
For the solution of each of these problems, out of the two subsets, it may be possible to select further subdivisions corresponding to the particular diagnostic tasks at hand. Such a two-fold sample set may also allow the researchers to quantitatively and formally investigate the process of aging, as an underlying and common factor of these diseases, by utilizing a multi-factorial model which corresponds to the understanding of aging as a complex process depending on multiple factors of different etiology. In other words, rather than attempting to infer from the poorly defined concept of biological aging toward its derivative conditions (diseases), it may be possible to formally define pathological or early aging from these diagnosable conditions, seeking common age-related denominators between them.
It should be noted that information-theoretical models of physiological age and aging-related ill health do not need to restrict themselves from the outset to any particular kinds of parameter data or hypothesis. The information-theoretical approach may allow the researchers to utilize any kind of data, at any level, into a single diagnostic model. Thus it can, for example, combine diverse biochemical, molecular-biological, cellular, tissue, physiological, functional and other parameters related to aging. Thus the more parameters of different kinds the researchers may be able to obtain, and the larger the investigated sample they will be able to obtain – the stronger and more informative the model will be. Yet, for practical concerns, and at the initial stages, it may be preferable to strive to first utilize the parameters commonly used in the clinic, such as blood work (biochemistry and cytology). It should also be noted that the choice of the 2 subsets, as indicated above, is not restrictive either. The two subsets allow the convenient primary distinction between subjects presumably characterized by different levels of resilience in aging. Yet, with the addition of more age cohorts, including the young (e.g. across several decades of life) – the diagnostic capabilities may be improved, depending on the availability of data.
Even though the information-theoretical approach can incorporate any number of subjects into the model, improving its diagnostic capabilities, at the initial stage it may be desirable to analyze data from at least 2000 subjects, say 1000 from each subset, as this number of subjects is a putative desirable requirement to establish combined diagnostic indicators from 3 or 4 different parameters. The following rule of thumb can be applied for the selection of the sample size: In the analysis of tables of conjunction, we assume that for almost all the cells, the expected number of elements should be no less than 5 in each cell.26 We consider discrete parameters that can assume 3 values (i.e. below, equal or above some normative of delimiting value). The rule of thumb, to fulfill the sufficiency criteria for the estimation of the sample size, is: the number of cells in the conjunction matrix (say 9 for 2 parameters – 3×3) x 5 (5 elements in each cell) x 5 (to increase the probability that there will be 5 elements in each cell, though this latter number can be more). Thus for a correlation between 2 single parameters, it is 9x5x5=225 (~200-250), for a correlation of 2 parameters with a third one: 27x5x5=675 (~500-700), for a correlation of 3 combined parameters with a fourth one: 81x5x5=2025 (~2000), etc. 2000 subjects is also the typical number involved in FDA phase 3 clinical trials.27 However, with further increasing the sample size, the diagnostic value will be further increased. The sample sizes will also depend on the nature of the relations examined. For example, when the parameters are strongly mechanistically related, the sample size could be less. And once again, costs of analysis need to be considered, obviously increasing with a greater sample size.
Evaluation of age-related multimorbidity
Using information-theoretical methodology, it may be possible to establish diagnostic decision rules not just for individual diseases,22 or for physiological age,28 but also for combined age-related diseases (age-related multimorbidity). Out of several individual disease variables, a single “multimorbidity” variable can be established composed of several diseases (e.g. diabetes and heart disease and dementia, etc.). And this new composite variable can be correlated to individual or combined risk factors by normalized mutual information. Based on the values of normalized mutual information (strength of correlations), the decision rule could be constructed for the entire multimorbidity variable, or for different types of multimorbidities.
The added value and even necessity of estimating physiological age and age-related multimorbidity, in addition to diagnosing individual diseases, is due to the following reasons:
- Knowing chronological and physiological age is necessary for diagnosis. It is necessary to accomplish early diagnosis also for individual diseases. The degenerative aging process is the main contributor to age-related diseases. Hence, not being able to evaluate it, discards one of the main, most informative diagnostic parameters. Moreover, the corresponding inability to intervene into degenerative aging, discards one of the most promising therapeutic targets.
- There is a need for an integrative, time-related approach. Evaluation of only single diagnostic parameters and risk factors, or only single diseases, without their connection to each other and to the patients’ age, without considering their dynamic changes in time, their long-term and synergistic effects, can produce misleading results in diagnosis, and ineffective and even unsafe therapy. The various diagnostic parameters, including age and period, should be evaluated together and intervened together.
- Evidence-based criteria for physiological age and multimorbidity are needed to develop new therapies and interventions. Furthermore, establishing quantitative and holistic criteria for healthy aging/longevity can help validate the new treatments. The currently existing therapies and interventions are not always effective. There is a critical need to advance novel biomedical research of aging and aging-related diseases, to develop and test new treatments, to improve the healthspan of the elderly. The development of diagnostic criteria for healthy longevity (healthspan), like physiological age or multimorbidity, can help gauge the effects of new treatments and interventions.
It is hoped that information-theoretical methodology will contribute to the advancement of these tasks.
References and notes
- David Blokh, Ilia Stambler, “Estimation of heterogeneity in diagnostic parameters of age-related diseases,” Aging and Disease, 5, 218-225, 2014, http://www.aginganddisease.org/EN/10.14336/AD.2014.0500218; David Blokh, Ilia Stambler, “Information theoretical analysis of aging as a risk factor for heart disease,” Aging and Disease, 6, 196-207, 2015, http://www.aginganddisease.org/EN/10.14336/AD.2014.0623;
David Blokh, Ilia Stambler, “Applying information theory analysis for the solution of biomedical data processing problems,” American Journal of Bioinformatics, 3(1), 17-29, 2015, http://thescipub.com/abstract/10.3844/ajbsp.2014.17.29;
David Blokh, Ilia Stambler, “The application of information theory for the research of aging and aging-related diseases,” Progress in Neurobiology, 157, 158-173, 2017, doi: http://dx.doi.org/10.1016/j.pneurobio.2016.03.005;
David Blokh, Ilia Stambler, “The use of information theory for the evaluation of biomarkers of aging and physiological age,” Mechanisms of Ageing and Development, 163, 23-29, 2017, doi: http://dx.doi.org/10.1016/j.mad.2017.01.003;
David Blokh, Ilia Stambler, “Quantified Longevity Guide (QLG),” Comorbidity Detection Technologies, 2017,
- Michael J. Rae, Robert N. Butler, Judith Campisi, Aubrey DNJ de Grey, Caleb E. Finch, Michael Gough, George M. Martin, Jan Vijg, Kevin M. Perrott, Barbara J. Logan, “The demographic and biomedical case for late-life interventions in aging,” Science Translational Medicine, 2, 40cm21, 2010, http://stm.sciencemag.org/content/2/40/40cm21.full;
Luigi Fontana, Brian K. Kennedy, Valter D. Longo, Douglas Seals, Simon Melov, “Medical research: treat ageing,” Nature, 511(7510), 405-407, 2014, http://www.nature.com/news/medical-research-treat-ageing-1.15585;
Kunlin Jin, James W. Simpkins, Xunming Ji, Miriam Leis, Ilia Stambler, “The critical need to promote research of aging and aging-related diseases to improve health and longevity of the elderly population,” Aging and Disease, 6, 1-5, 2015, http://www.aginganddisease.org/EN/10.14336/AD.2014.1210;
Ilia Stambler, “Recognizing degenerative aging as a treatable medical condition: methodology and policy,” Aging and Disease, 8(5), 583-589, 2017, http://www.aginganddisease.org/EN/10.14336/AD.2017.0130;
Ilia Stambler, “Human life extension: opportunities, challenges, and implications for public health policy,” in Alexander Vaiserman (Ed.), Anti-aging Drugs: From Basic Research to Clinical Practice, Royal Society of Chemistry, London, 2017, pp. 535-564, http://pubs.rsc.org/en/content/ebook/978-1-78262-435-6#!divbookcontent.
- Bonnie N. Joe, “Risk-based screening misses breast cancers in women in their forties,” Radiological Society of North America, 2014, http://www.rsna.org/;
Hakan Jonsson, Lars-Gunnar Larsson, Per Lenner, “Detection of breast cancer with mammography in the first screening round in relation to expected incidence in different age groups,” Acta Oncologica, 42, 22-29, 2003.
- Rafael Lozano, et al. (189 authors), “Global and regional mortality from 235 causes of death for 20 age groups in 1990 and 2010: a systematic analysis for the Global Burden of Disease Study 2010,” Lancet, 380, 2095-2128, 2012.
- JudithMeadows, Jacqueline Suk Danik, Michelle A. Albert, “Primary prevention of ischemic heart disease,” in Elliott M. Antman (Ed.), Cardiovascular Therapeutics: A Companion to Braunwald’s Heart Disease, Third edition, Saunders Elsevier, Philadelphia PA,2007, pp. 178-220.
- David Blokh, Ilia Stambler, “Information theoretical analysis of aging as a risk factor for heart disease,” Aging and Disease, 6, 196-207, 2015, http://www.aginganddisease.org/EN/10.14336/AD.2014.0623.
- Zaven S. Khachaturian, “Perspectives on Alzheimer’s disease: past, present and future,” Advances in Biological Psychiatry, 28, 179-188, 2012.
- David Blokh, Ilia Stambler, “Estimation of heterogeneity in diagnostic parameters of age-related diseases,” Aging and Disease, 5, 218-225, 2014, http://www.aginganddisease.org/EN/10.14336/AD.2014.0500218; Diane Chau, Steven V. Edelman, “Clinical management of diabetes in the elderly,” Clinical Diabetes, 19, 172-175, 2001.
- Linda P. Fried, Jeremy Walston, “Frailty and failure to thrive,” in William R. Hazzard, John P. Blass, Walter H. Ettinger, Jeffrey B. Halter, Joseph G. Ouslander (Eds.), Principles of Geriatric Medicine and Gerontology, 4th Ed., McGraw Hill, New York, 1999, pp. 1387-1402.
- Amber E. Barnato, Mark B. Mcclellan, Christopher R. Kagay, Alan M. Garber, “Trends in inpatient treatment intensity among medicare beneficiaries at the end of life,” Health Services Research, 39(2), 363-376, 2004.
- C-Change: Collaborating to Conquer Cancer, Making the Business Case: How Engaging Employees in Preventive Care Can Reduce Healthcare Costs, 2008, http://c-changetogether.org/Websites/cchange/images/Risk_Reduction/C-Change_Business_Case_White_Paper_(1).pdf.
- National Committee for Quality Assurance, Executive Summary. The State of Health Care Quality 2004, National Committee for Quality, Washington DC, 2005, quoted in C-Change: Collaborating to Conquer Cancer, Making the Business Case: How Engaging Employees in Preventive Care Can Reduce Healthcare Costs, 2008, http://c-changetogether.org/Websites/cchange/images/Risk_Reduction/C-Change_Business_Case_White_Paper_(1).pdf.
- Alzheimer’s Disease International, World Alzheimer Report 2011. The benefits of early diagnosis and intervention, Martin Prince, Renata Bryce, Cleusa Ferri (Eds.), Institute of Psychiatry, King’s College, London, 2011, https://www.alz.co.uk/research/world-report-2011.
- National Association of Chronic Disease Directors, “Why we need public health to improve healthcare,” 2015, http://www.chronicdisease.org/?page=WhyWeNeedPH2impHC.
- WHO Media Center, “Diabetes: the cost of diabetes,” Fact sheet N°236, 2015, http://www.who.int/mediacentre/factsheets/fs236/en/.
- Stephen S. Lim, et al., “A comparative risk assessment of burden of disease and injury attributable to 67 risk factors and risk factor clusters in 21 regions, 1990–2010: a systematic analysis for the Global Burden of Disease Study 2010,” Lancet, 380, 2224-2260, 2012;
Rafael Lozano, et al., “Global and regional mortality from 235 causes of death for 20 age groups in 1990 and 2010: a systematic analysis for the Global Burden of Disease Study 2010,” Lancet, 380, 2095-2128, 2012.
- World Health Organization, Global Status Report on Noncommunicable diseases 2014, http://www.who.int/nmh/publications/ncd-status-report-2014/en/.
- David E. Bloom, et al., The Global Economic Burden of Non-Communicable Diseases: A report by the World Economic Forum and the Harvard School of Public Health, World Economic Forum, Geneva, 2011, http://www3.weforum.org/docs/WEF_Harvard_HE_GlobalEconomicBurdenNonCommunicableDiseases_2011.pdf.
- Dana P. Goldman, David M. Cutler, John W. Rowe, Pierre-Carl Michaud, Jeffrey Sullivan, Jay S. Olshansky, Desi Peneva, “Substantial health and economic returns from delayed aging may warrant a new focus for medical research,” Health Affairs, 32(10), 1698-1705, 2013, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3938188/;
Dana P. Goldman, “The economic promise of delayed aging,” in Stuart Jay Olshansky, George M. Martin, James L. Kirkland (Eds.), Aging: The Longevity Dividend, Cold Spring Harbor Laboratory Press, 2016.
- Robert N. Butler, Richard Sprott, Huber Warner, Jeffrey Bland, Richie Feuers, Michael Forster, Howard Fillit, S. Mitchell Harman, Michael Hewitt, Mark Hyman, Kathleen Johnson, Evan Kligman, Gerald McClearn, James Nelson, Arlan Richardson, William Sonntag, Richard Weindruch, Norman Wolf, “Biomarkers of aging: from primitive organisms to humans,” Journal of Gerontology. A. Biological Sciences Medical Sciences, 59, B560-567, 2004.
- Arthur K. Balin (Ed.), Practical Handbook of Human Biologic Age Determination, CRC Press, Boca Raton FL, 1994.
- David Blokh, Ilia Stambler, “The application of information theory for the research of aging and aging-related diseases,” Progress in Neurobiology, 157, 158-173, 2017, doi: http://dx.doi.org/10.1016/j.pneurobio.2016.03.005; http://www.sciencedirect.com/science/article/pii/S0301008215300599.
- David Blokh, Elena Afrimzon, Ilia Stambler, Eden Korech, Yana Shafran, Naomi Zurgil, Mordechai Deutsch, “Breast cancer detection by Michaelis-Menten constants via linear programming,” Computer Methods and Programs in Biomedicine, 85, 210-213, 2006;
David Blokh, Ilia Stambler, Elena Afrimzon, Yana Shafran, Eden Korech, Judith Sandbank, Ruben Orda, Naomi Zurgil, Mordechai Deutsch, “The information-theory analysis of Michaelis–Menten constants for detection of breast cancer,” Cancer Detection and Prevention, 31, 489-498, 2007;
David Blokh, Naomi Zurgil, Ilia Stambler, Elena Afrimzon, Yana Shafran, Eden Korech, Judith Sandbank, Mordechai Deutsch, “An information-theoretical model for breast cancer detection,” Methods of Information in Medicine, 47, 322-327, 2008;
David Blokh, Ilia Stambler, Elena Afrimzon, Max Platkov, Yana Shafran, Eden Korech, Judith Sandbank, Naomi Zurgil, Mordechai Deutsch, “Comparative analysis of cell parameter groups for breast cancer detection,” Computer Methods and Programs in Biomedicine, 94, 239-249, 2009.
David Blokh, “Information-theory analysis of cell characteristics in breast cancer patients,” International Journal on Bioinformatics & Biosciences (IJBB), 3(1), 2013.
- Imre Zs.-Nagy, Denham Harman, Kenichi Kitani (Eds.), Pharmacology of Aging Processes: Methods of Assessment and Potential Interventions, Annals of the New York Academy of Sciences, Volume 717, 1994;
Alexander Vaiserman (Ed.), Anti-aging Drugs: From Basic Research to Clinical Practice, Royal Society of Chemistry, London, 2017.
- World Health Organization, Global Strategy and Action Plan on Ageing and Health, World Health Organization, Geneva, November 2015, http://who.int/ageing/global-strategy/en/.
- Solomon Kullback, Information Theory and Statistics, John Wiley & Sons, New York, 1958;
John H. Pollard, A Handbook of Numerical and Statistical Techniques. With Examples Mainly From The Life Sciences, Cambridge University Press, Cambridge, 1977.
- US Food and Drug Administration, “The Drug Development Process. Step 3: Clinical Research,” accessed June 2017, http://www.fda.gov/ForPatients/Approvals/Drugs/ucm405622.htm.
- David Blokh, Ilia Stambler, “The use of information theory for the evaluation of biomarkers of aging and physiological age,” Mechanisms of Ageing and Development, 163, 23-29, 2017, doi: http://dx.doi.org/10.1016/j.mad.2017.01.003.