1. Columbia University - Research Seminars in Epidemiology Reliability-Theory Approach to Epidemiological Studies of Aging, Mortality and Longevity Dr. Leonid A. Gavrilov, Ph.D. Dr. Natalia S. Gavrilova, Ph.D. Center on Aging NORC and The University of Chicago Chicago, Illinois, USA

2. Columbia University - Research Seminars in Epidemiology What Is Reliability-Theory Approach? Reliability-theory approach is based on ideas, methods, and models of a general theory of systems failure known as reliability theory.

3. Columbia University - Research Seminars in Epidemiology Reliability theory was historically developed to describe failure and aging of complex electronic (military) equipment, but the theory itself is a very general theory based on probability theory and systems approach.

4. Columbia University - Research Seminars in Epidemiology Why Do We Need Reliability-Theory Approach? Because it provides a common scientific language (general paradigm) for scientists working in different areas of aging research, including epidemiological studies. Reliability theory helps to overcome disruptive specialization and it allows researchers to understand each other. Provides useful mathematical models allowing to explain and interpret the observed epidemiological data and findings.

5. Columbia University - Research Seminars in Epidemiology Some Representative Publications on Reliability-Theory Approach to Epidemiological Studies of Aging, Mortality and Longevity

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7. Gavrilov, L., Gavrilova, N. Reliability theory of aging and longevity. In: Handbook of the Biology of Aging. Academic Press, 6 th edition, 2006, pp.3-42.

8. Columbia University - Research Seminars in Epidemiology The Concept of System’s Failure In reliability theory failure is defined as the event when a required function is terminated.

9. Columbia University - Research Seminars in Epidemiology Failures are often classified into two groups: degradation failures, where the system or component no longer functions properly catastrophic or fatal failures - the end of system's or component's life

10. Columbia University - Research Seminars in Epidemiology Definition of aging and non-aging systems in reliability theory Aging: increasing risk of failure with the passage of time (age). No aging: 'old is as good as new' (risk of failure is not increasing with age) Increase in the calendar age of a system is irrelevant.

11. Columbia University - Research Seminars in Epidemiology Aging and non-aging systems Perfect clocks having an ideal marker of their increasing age (time readings) are not aging Progressively failing clocks are aging (although their 'biomarkers' of age at the clock face may stop at 'forever young' date)

12. Columbia University - Research Seminars in Epidemiology Mortality in Aging and Non-aging Systems non-aging system aging system Example: radioactive decay

13. Columbia University - Research Seminars in Epidemiology According to Reliability Theory: Aging is NOT just growing old Instead Aging is a degradation to failure: becoming sick, frail and dead 'Healthy aging' is an oxymoron like a healthy dying or a healthy disease More accurate terms instead of 'healthy aging' would be a delayed aging, postponed aging, slow aging, or negligible aging (senescence)

14. Columbia University - Research Seminars in Epidemiology Reliability-Theory Approach to Epidemiology of Aging (I) Focus on adverse health outcomes, “health failures” (disability, disease, death) rather than any age-related changes Focus on incidence of “health failures” rather than prevalence measures Focus on age-specific incidence rates rather than age-aggregated (age- adjusted) measures

15. Columbia University - Research Seminars in Epidemiology Reliability-Theory Approach to Epidemiology of Aging (II) Very inclusive system approach (not limited to humans). Extensive use of modeling: Mathematical models Animal models Failure models for manufactured items

16. Columbia University - Research Seminars in Epidemiology Aging is a Very General Phenomenon!

17. Columbia University - Research Seminars in Epidemiology Particular mechanisms of aging may be very different even across biological species (salmon vs humans) BUT General Principles of Systems Failure and Aging May Exist (as we will show in this presentation)

18. Columbia University - Research Seminars in Epidemiology Further plan of presentation Empirical laws of failure and aging in epidemiology Explanations by reliability theory Links between reliability theory and epidemiologic studies

19. Columbia University - Research Seminars in Epidemiology Empirical Laws of Systems Failure and Aging

20. Columbia University - Research Seminars in Epidemiology Stages of Life in Machines and Humans The so-called bathtub curve for technical systems Bathtub curve for human mortality as seen in the U.S. population in 1999 has the same shape as the curve for failure rates of many machines.

21. Columbia University - Research Seminars in Epidemiology Failure (Mortality) Laws 1. Gompertz-Makeham law of mortality 2. Compensation law of mortality 3. Late-life mortality deceleration

22. Columbia University - Research Seminars in Epidemiology The Gompertz-Makeham Law μ(x) = A + R e αx A – Makeham term or background mortality R e αx – age-dependent mortality; x - age Death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age. risk of death Non-aging component Aging component

23. Columbia University - Research Seminars in Epidemiology Gompertz Law of Mortality in Fruit Flies Based on the life table for 2400 females of Drosophila melanogaster published by Hall (1969). Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

24. Columbia University - Research Seminars in Epidemiology Gompertz-Makeham Law of Mortality in Flour Beetles Based on the life table for 400 female flour beetles (Tribolium confusum Duval). published by Pearl and Miner (1941). Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

25. Columbia University - Research Seminars in Epidemiology Gompertz-Makeham Law of Mortality in Italian Women Based on the official Italian period life table for 1964-1967. Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

26. Columbia University - Research Seminars in Epidemiology Compensation Law of Mortality (late-life mortality convergence) Relative differences in death rates are decreasing with age, because the lower initial death rates are compensated by higher slope of mortality growth with age (actuarial aging rate)

27. Columbia University - Research Seminars in Epidemiology Compensation Law of Mortality Convergence of Mortality Rates with Age 1 – India, 1941-1950, males 2 – Turkey, 1950-1951, males 3 – Kenya, 1969, males 4 - Northern Ireland, 1950- 1952, males 5 - England and Wales, 1930- 1932, females 6 - Austria, 1959-1961, females 7 - Norway, 1956-1960, females Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

28. Columbia University - Research Seminars in Epidemiology Compensation Law of Mortality (Parental Longevity Effects) Mortality Kinetics for Progeny Born to Long-Lived (80+) vs Short-Lived Parents SonsDaughters

29. Columbia University - Research Seminars in Epidemiology Compensation Law of Mortality in Laboratory Drosophila 1 – drosophila of the Old Falmouth, New Falmouth, Sepia and Eagle Point strains (1,000 virgin females) 2 – drosophila of the Canton-S strain (1,200 males) 3 – drosophila of the Canton-S strain (1,200 females) 4 - drosophila of the Canton-S strain (2,400 virgin females) Mortality force was calculated for 6-day age intervals. Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

30. Columbia University - Research Seminars in Epidemiology Epidemiological Implications  Be prepared to a paradox that higher actuarial aging rates may be associated with higher life expectancy in compared populations (e.g., males vs females)  Be prepared to violation of the proportionality assumption used in hazard models (Cox proportional hazard models)  Relative effects of risk factors are age- dependent and tend to decrease with age

31. Columbia University - Research Seminars in Epidemiology The Late-Life Mortality Deceleration (Mortality Leveling-off, Mortality Plateaus) The late-life mortality deceleration law states that death rates stop to increase exponentially at advanced ages and level-off to the late-life mortality plateau.

32. Columbia University - Research Seminars in Epidemiology Mortality deceleration at advanced ages. After age 95, the observed risk of death [red line] deviates from the value predicted by an early model, the Gompertz law [black line]. Mortality of Swedish women for the period of 1990-2000 from the Kannisto-Thatcher Database on Old Age Mortality Source: Gavrilov, Gavrilova, “Why we fall apart. Engineering’s reliability theory explains human aging”. IEEE Spectrum. 2004.

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34. M. Greenwood, J. O. Irwin. BIOSTATISTICS OF SENILITY

35. Columbia University - Research Seminars in Epidemiology Mortality Leveling-Off in House Fly Musca domestica Our analysis of the life table for 4,650 male house flies published by Rockstein & Lieberman, 1959. Source: Gavrilov & Gavrilova. Handbook of the Biology of Aging, Academic Press, 2006, pp.3-42.

36. Columbia University - Research Seminars in Epidemiology Non-Aging Mortality Kinetics in Later Life If mortality is constant then log(survival) declines with age as a linear function Source: Economos, A. (1979). A non-Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. AGE, 2: 74-76.

37. Columbia University - Research Seminars in Epidemiology Non-Aging Failure Kinetics of Industrial Materials in ‘Later Life’ (steel, relays, heat insulators) Source: Economos, A. (1979). A non-Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. AGE, 2: 74-76.

38. Columbia University - Research Seminars in Epidemiology Testing the “Limit-to-Lifespan” Hypothesis Source: Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span

39. Columbia University - Research Seminars in Epidemiology Epidemiological Implications There is no fixed upper limit to human longevity - there is no special fixed number, which separates possible and impossible values of lifespan. This conclusion is important, because it challenges the common belief in existence of a fixed maximal human life span.

40. Columbia University - Research Seminars in Epidemiology Additional Empirical Observation: Many age changes can be explained by cumulative effects of cell loss over time Atherosclerotic inflammation - exhaustion of progenitor cells responsible for arterial repair (Goldschmidt-Clermont, 2003; Libby, 2003; Rauscher et al., 2003). Decline in cardiac function - failure of cardiac stem cells to replace dying myocytes (Capogrossi, 2004). Incontinence - loss of striated muscle cells in rhabdosphincter (Strasser et al., 2000).

41. Columbia University - Research Seminars in Epidemiology Like humans, nematode C. elegans experience muscle loss Body wall muscle sarcomeres Left - age 4 days. Right - age 18 days Herndon et al. 2002. Stochastic and genetic factors influence tissue- specific decline in ageing C. elegans. Nature 419, 808 - 814. “…many additional cell types (such as hypodermis and intestine) … exhibit age- related deterioration.”

42. Columbia University - Research Seminars in Epidemiology What Should the Aging Theory Explain Why do most biological species including humans deteriorate with age? The Gompertz law of mortality Mortality deceleration and leveling-off at advanced ages Compensation law of mortality

43. Columbia University - Research Seminars in Epidemiology The Concept of Reliability Structure The arrangement of components that are important for system reliability is called reliability structure and is graphically represented by a schema of logical connectivity

44. Columbia University - Research Seminars in Epidemiology Two major types of system’s logical connectivity Components connected in series Components connected in parallel Fails when the first component fails Fails when all components fail  Combination of two types – Series-parallel system P s = p 1 p 2 p 3 … p n = p n Q s = q 1 q 2 q 3 … q n = q n

45. Columbia University - Research Seminars in Epidemiology Series-parallel Structure of Human Body Vital organs are connected in series Cells in vital organs are connected in parallel

46. Columbia University - Research Seminars in Epidemiology Redundancy Creates Both Damage Tolerance and Damage Accumulation (Aging) System with redundancy accumulates damage (aging) System without redundancy dies after the first random damage (no aging)

47. Columbia University - Research Seminars in Epidemiology Reliability Model of a Simple Parallel System Failure rate of the system: Elements fail randomly and independently with a constant failure rate, k n – initial number of elements  nk n x n-1 early-life period approximation, when 1-e -kx  kx  k late-life period approximation, when 1-e -kx  1 Source: Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span

48. Columbia University - Research Seminars in Epidemiology Failure Rate as a Function of Age in Systems with Different Redundancy Levels Failure of elements is random Source: Gavrilov, Gavrilova, IEEE Spectrum. 2004.

49. Columbia University - Research Seminars in Epidemiology Standard Reliability Models Explain Mortality deceleration and leveling-off at advanced ages Compensation law of mortality

50. Columbia University - Research Seminars in Epidemiology Standard Reliability Models Do Not Explain The Gompertz law of mortality observed in biological systems Instead they produce Weibull (power) law of mortality growth with age: μ(x) = a x b

51. Columbia University - Research Seminars in Epidemiology An Insight Came To Us While Working With Dilapidated Mainframe Computer The complex unpredictable behavior of this computer could only be described by resorting to such 'human' concepts as character, personality, and change of mood.

52. Columbia University - Research Seminars in Epidemiology Reliability structure of (a) technical devices and (b) biological systems Low redundancy Low damage load Fault avoidance High redundancy High damage load Fault tolerance X - defect

53. Columbia University - Research Seminars in Epidemiology Models of systems with distributed redundancy Organism can be presented as a system constructed of m series-connected blocks with binomially distributed elements within block (Gavrilov, Gavrilova, 1991, 2001)

54. Columbia University - Research Seminars in Epidemiology Model of organism with initial damage load Failure rate of a system with binomially distributed redundancy (approximation for initial period of life): x 0 = 0 - ideal system, Weibull law of mortality x 0 >> 0 - highly damaged system, Gompertz law of mortality Source: Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span where - the initial virtual age of the system The initial virtual age of a system defines the law of system’s mortality: Binomial law of mortality

55. Columbia University - Research Seminars in Epidemiology People age more like machines built with lots of faulty parts than like ones built with pristine parts. As the number of bad components, the initial damage load, increases [bottom to top], machine failure rates begin to mimic human death rates. Source: Gavrilov, Gavrilova, IEEE Spectrum. 2004

56. Columbia University - Research Seminars in Epidemiology Statement of the HIDL hypothesis: (Idea of High Initial Damage Load ) "Adult organisms already have an exceptionally high load of initial damage, which is comparable with the amount of subsequent aging-related deterioration, accumulated during the rest of the entire adult life." Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

57. Columbia University - Research Seminars in Epidemiology Why should we expect high initial damage load in biological systems? General argument: -- biological systems are formed by self-assembly without helpful external quality control. Specific arguments: 1.Most cell divisions responsible for DNA copy-errors occur in early development leading to clonal expansion of mutations 2.Loss of telomeres is also particularly high in early-life 3.Cell cycle checkpoints are disabled in early development

58. Columbia University - Research Seminars in Epidemiology Birth Process is a Potential Source of High Initial Damage Severe hypoxia and asphyxia just before the birth. oxidative stress just after the birth because of acute reoxygenation while starting to breathe. The same mechanisms that produce ischemia-reperfusion injury and the related phenomenon, asphyxia- reventilation injury known in cardiology.

59. Columbia University - Research Seminars in Epidemiology Mutation Frequencies are Already High Early in Life Spontaneous mutant frequencies with age in heart and small intestine of mouse Source: Presentation by Jan Vijg at the IABG Congress, Cambridge, 2003

60. Columbia University - Research Seminars in Epidemiology Practical implications from the HIDL hypothesis: "Even a small progress in optimizing the early-developmental processes can potentially result in a remarkable prevention of many diseases in later life, postponement of aging-related morbidity and mortality, and significant extension of healthy lifespan." Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

61. Columbia University - Research Seminars in Epidemiology Implications for Epidemiological Studies If the initial damage load is really important, then we may expect significant effects of early-life conditions (like season-of-birth, birth order, or paternal age at conception) on late-life morbidity and mortality

62. Columbia University - Research Seminars in Epidemiology Life Expectancy and Month of Birth Data source: Social Security Death Master File Published in: Gavrilova, N.S., Gavrilov, L.A. Search for Predictors of Exceptional Human Longevity. In: “Living to 100 and Beyond” Monograph. The Society of Actuaries, Schaumburg, Illinois, USA, 2005, pp. 1-49.

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64. Birth Order and Chances to Become a Centenarian Cases - centenarians born in the United States between 1890 and 1899 Controls – their siblings born in the same time window Model: Log(longevity odds ratio)= ax + bx 2 + cz + d where x – birth order; z – family size; a, b, c, d – parameters of polynomial regression model

65. Columbia University - Research Seminars in Epidemiology Birth Order and Survival to 100 Source: Gavrilova, N.S., Gavrilov, L.A. Search for Predictors of Exceptional Human Longevity. In: “Living to 100 and Beyond” Monograph. The Society of Actuaries, Schaumburg, Illinois, USA, 2005, pp. 1-49.

66. Columbia University - Research Seminars in Epidemiology Genetic Justification for Paternal Age Effects Advanced paternal age at child conception is the main source of new mutations in human populations. James F. Crow, geneticist PNAS USA, 1997, 94(16): 8380-6 Professor Crow (University of Wisconsin-Madison) is recognized as a leader and statesman of science. He is a member of the National Academy of Sciences, the National Academy of Medicine, The American Philosophical Society, the American Academy of Arts and Sciences, the World Academy of Art and Science.

67. Columbia University - Research Seminars in Epidemiology Paternal Age and Risk of Schizophrenia Estimated cumulative incidence and percentage of offspring estimated to have an onset of schizophrenia by age 34 years, for categories of paternal age. The numbers above the bars show the proportion of offspring who were estimated to have an onset of schizophrenia by 34 years of age. Source: Malaspina et al., Arch Gen Psychiatry.2001.

68. Columbia University - Research Seminars in Epidemiology Daughters' Lifespan (30+) as a Function of Paternal Age at Daughter's Birth 6,032 daughters from European aristocratic families born in 1800-1880  Life expectancy of adult women (30+) as a function of father's age when these women were born (expressed as a difference from the reference level for those born to fathers of 40-44 years).  The data are point estimates (with standard errors) of the differential intercept coefficients adjusted for other explanatory variables using multiple regression with nominal variables.  Daughters of parents who survived to 50 years.

69. Columbia University - Research Seminars in Epidemiology Contour plot for daughters’ lifespan (deviation from cohort mean) as a function of paternal lifespan (X axis) and paternal age at daughters’ birth (Y axis) 7984 cases 1800-1880 birth cohorts European aristocratic families Distance weighted least squares smooth

70. Columbia University - Research Seminars in Epidemiology Daughters’ Lifespan as a Function of Paternal Age at Daughters’ Birth Data are adjusted for other predictor variables Daughters of shorter-lived fathers (<80), 6727 cases Daughters of longer-lived fathers (80+), 1349 cases

71. Columbia University - Research Seminars in Epidemiology Preliminary Conclusion Being conceived to old father is a risk factor, but it is moderated by paternal longevity It is OK to be conceived to old father if he lives more than 80 years Epidemiological implications: Paternal lifespan should be taken into account in the studies of paternal-age effects

72. Columbia University - Research Seminars in Epidemiology Conclusions (I) Redundancy is a key notion for understanding aging and the systemic nature of aging in particular. Systems, which are redundant in numbers of irreplaceable elements, do deteriorate (i.e., age) over time, even if they are built of non-aging elements. An apparent aging rate or expression of aging (measured as age differences in failure rates, including death rates) is higher for systems with higher redundancy levels.

73. Columbia University - Research Seminars in Epidemiology Conclusions (II) Redundancy exhaustion over the life course explains the observed ‘compensation law of mortality’ (mortality convergence at later life) as well as the observed late-life mortality deceleration, leveling-off, and mortality plateaus. Living organisms seem to be formed with a high load of initial damage, and therefore their lifespans and aging patterns may be sensitive to early-life conditions that determine this initial damage load during early development. The idea of early-life programming of aging and longevity may have important practical implications for developing early-life interventions promoting health and longevity.

74. Columbia University - Research Seminars in Epidemiology Acknowledgments This study was made possible thanks to: generous support from the National Institute on Aging, and stimulating working environment at the Center on Aging, NORC/University of Chicago

75. Columbia University - Research Seminars in Epidemiology For More Information and Updates Please Visit Our Scientific and Educational Website on Human Longevity: http://longevity-science.org

76. Columbia University - Research Seminars in Epidemiology Possible Change of Paradigm in Epidemiology Mortality of Swedish females Before the 1960sAfter the 1960s

77. Columbia University - Research Seminars in Epidemiology Mortality Before the 1960s Can be Modeled Using the Gompertz-Makeham law By studying the historical dynamics of the mortality components in this law: μ(x) = A + R e αx Makeham componentGompertz component

78. Columbia University - Research Seminars in Epidemiology Historical Stability of the Gompertz Mortality Component Before the 1980s Historical Changes in Mortality for 40-year-old Swedish Males 1. Total mortality, μ 40 2. Background mortality (A) 3. Age-dependent mortality (Re α40 ) Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

79. Columbia University - Research Seminars in Epidemiology Predicting Mortality Crossover Historical Changes in Mortality for 40-year-old Women in Norway and Denmark 1. Norway, total mortality 2. Denmark, total mortality 3. Norway, age- dependent mortality 4. Denmark, age- dependent mortality Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

80. Columbia University - Research Seminars in Epidemiology Predicting Mortality Divergence Historical Changes in Mortality for 40-year-old Italian Women and Men 1. Women, total mortality 2. Men, total mortality 3. Women, age- dependent mortality 4. Men, age-dependent mortality Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

81. Columbia University - Research Seminars in Epidemiology Hypothesis of Death Quota for Total Mortality The Idea of Non-Specific Vulnerability Intermediate State Normal state of organism State of nonspecific vulnerability Death Extreme situations producing background mortality Various diseases and “causes” of death Aging (limiting stage)

82. Columbia University - Research Seminars in Epidemiology Mortality Decline After the 1960s May Be a Result of Improvement in Early-Life Conditions Birth cohorts of Swedish women (Source of data: HMD )

83. Columbia University - Research Seminars in Epidemiology Extension of the Gompertz-Makeham Model Through the Factor Analysis of Mortality Trends Mortality force (age, time) = = a 0 (age) + a 1 (age) x F 1 (time) + a 2 (age) x F 2 (time) Where: a i (age) – a set of numbers; each number is fixed for specific age group F j (time) – “factors,” a set of standardized numbers; each number is fixed for specific moment of time (mean = 0; st. dev. = 1)

84. Columbia University - Research Seminars in Epidemiology Factor Analysis of Mortality Trends Swedish Females “Factor analysis of the time series of mortality confirms the preferential reduction in the mortality of old-aged and senile people [in recent years]…” Gavrilov, Gavrilova, The Biology of Life Span, 1991. Data source for the current slide: Human Mortality Database

85. Columbia University - Research Seminars in Epidemiology Testing hypothesis of statistical independence between causes of death Based on 179 values of male mortality at age 55-64 from 26 countries (WHO) Cause of death VIIIth revision of ICD Correlation coefficient with total mortality Coefficient of mortality amplification (2)/(1) Expected value * (1) Observed value (2) Ischaemic heart disease (A83) +0.770+0.6060.79 Cerebrovascular disease +0.246+0.3451.40 Lung cancer (A51) +0.215+0.6012.80 Cirrhosis of liver (A102) +0.139+0.0270.19 Bronchitis, emphysema, asthma (A93) +0.121+0.6034.98 Stomach cancer (A47) +0.114+0.1481.30 Diseases of arteries, arterioles and capillaries (A86) +0.036+0.68018.89 * Expected value = std(cause of death)/std(all causes) Preston, Nelson, 1974

86. Columbia University - Research Seminars in Epidemiology A Broader View on the Historical Changes in Mortality Swedish Females Data source: Human Mortality Database

87. Columbia University - Research Seminars in Epidemiology Preliminary Conclusions There was some evidence for ‘ biological’ mortality limits in the past, but these ‘limits’ proved to be responsive to the recent technological and medical progress. Thus, there is no convincing evidence for absolute ‘biological’ mortality limits now. Analogy for illustration and clarification: There was a limit to the speed of airplane flight in the past (‘sound’ barrier), but it was overcome by further technological progress. Similar observations seems to be applicable to current human mortality decline.