Abstract
Process point of view (POV) models of mortality, such as the Strehler–Mildvan and stochastic vitality models, represent death in terms of the loss of survival capacity through challenges and dissipation. Drawing on hallmarks of aging, we link these concepts to candidate biological mechanisms through a framework that defines death as challenges to vitality where distal factors defined the age-evolution of vitality and proximal factors define the probability distribution of challenges. To illustrate the process POV, we hypothesize that the immune system is a mortality nexus, characterized by two vitality streams: increasing vitality representing immune system development and immunosenescence representing vitality dissipation. Proximal challenges define three mortality partitions: juvenile and adult extrinsic mortalities and intrinsic adult mortality. Model parameters, generated from Swedish mortality data (1751–2010), exhibit biologically meaningful correspondences to economic, health and cause-of-death patterns. The model characterizes the twentieth century epidemiological transition mainly as a reduction in extrinsic mortality resulting from a shift from high magnitude disease challenges on individuals at all vitality levels to low magnitude stress challenges on low vitality individuals. Of secondary importance, intrinsic mortality was described by a gradual reduction in the rate of loss of vitality presumably resulting from reduction in the rate of immunosenescence. Extensions and limitations of a distal/proximal framework for characterizing more explicit causes of death, e.g. the young adult mortality hump or cancer in old age are discussed.
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Notes
The idea of partitioning mortality into intrinsic and extrinsic parts was originally proposed by Carnes and colleagues (Carnes and Olshansky 1997; Carnes et al. 1996). They defined extrinsic mortality as avoidable mortality and intrinsic mortality as unavoidable mortality. The partition was demonstrated using COD data to calculate extrinsic mortality and intrinsic mortality was calculated as the difference between extrinsic and all-cause mortality (Carnes et al. 2006). However, the partitions based on the two vitality processes (Li and Anderson 2013) and on COD yield different mortality patterns with age. For both partitions, extrinsic mortality dominates in younger ages but the intrinsic mortality patterns are significantly different in the two methods. In the COD method intrinsic mortality has a Gompertz-like age distribution while in the vitality method intrinsic mortality is negligible in young age, then rises rapidly and plateaus in old age (Weitz and Fraser 2001). Consequently, the two methods of partitioning mortality cannot be easily compared.
Other terms for vitality include viability (Weitz and Fraser 2001), vital capacity (Whitmore 1986) and whole organisms state variable (Stroustrup et al. 2016). Other frameworks have proposed similar ideas, e.g. frailty, a fixed quantity endowed at the beginning of life (Vaupel et al. 1979) and redundancy theory (Gavrilov and Gavrilova 2003), but these applications were based more in a mortality rate POV and are not explored here.
Example age distribution of the mortality from cardiovascular diseases for the female Swedish population 2000–2004 is available from the Institute for Health Metrics and Evaluation (IHME). Cause of Death (DOC) Visualization. Seattle, WA: IHME, University of Washington, 2016. Available from http://vizhub.health.ord/cod/. (Accessed 11/21/2016).
Example age distribution of incidence of colon and rectum cancer for male Swedish population 2000–2009 is available from the Institute for Health Metrics and Evaluation (IHME). Cause of Death (DOC) Visualization. Seattle, WA: IHME, University of Washington, 2016. Available from http://vizhub.health.ord/cod/. (Accessed 11/21/2016).
Human Mortality Database University of California, Berkeley (USAUN), and Max Planck Institute for Demographic Research (Germany). Data downloaded 01/11/2014 from www.mortality.org.
References
Aalen OO, Gjessing HK (2001) Understanding the shape of the hazard rate: a process point of view. Stat Sci 16:1–22
Alai DH, Arnold S, Sherris M (2015) Modelling cause-of-death mortality and the impact of cause-elimination. Ann Actuar Sci 9:167–186. doi:10.1017/S174849951400027X
Anderson JJ (1992) A vitality-based stochastic model for organisms survival. In: DeAngelis DL, Gross LJ (eds) Individual-based models and approaches in ecology: populations, communities and ecosystems. Chapman & Hall, New York, pp 256–277
Anderson JJ (2000) A vitality-based model relating stressors and environmental properties to organism survival. Ecol Monogr 70:445–470. doi:10.1890/0012-9615(2000)070[0445:AVBMRS]2.0.CO;2
Anderson JJ, Gildea MC, Williams DW, Li T (2008) Linking growth, survival, and heterogeneity through vitality. Am Nat 171:E20–E43. doi:10.1086/524199
Arai Y et al (2015) Inflammation, but not telomere length, predicts successful ageing at extreme old age: a longitudinal study of semi-supercentenarians. EBioMedicine 2:1549–1558. doi:10.1016/j.ebiom.2015.07.029
Argiles JM, Busquets S, Stemmler B, Lopez-Soriano FJ (2014) Cancer cachexia: understanding the molecular basis. Nat Rev Cancer 14:754–762. doi:10.1038/nrc3829
Arking R (2006) Biology of aging: observations and principles. Oxford University Press, Oxford
Aubert G, Lansdorp PM (2008) Telomeres and aging. Physiol Rev 88:557–579
Aviv A, Kark JD, Susser E (2015) Telomeres, atherosclerosis, and human longevity: a causal hypothesis. Epidemiology 26:295–299. doi:10.1097/EDE.0000000000000280
Aw D, Silva AB, Palmer DB (2007) Immunosenescence: emerging challenges for an ageing population. Immunology 120:435–446. doi:10.1111/j.1365-2567.2007.02555.x
Beard RE (1971) Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes. Biol Asp Demogr 999:57–68
Beisel WR (1996) Nutrition and immune function: overview. J Nutr 126:2611S
Bengtsson T, Dribe M (2011) The late emergence of socioeconomic mortality differentials: a micro-level study of adult mortality in southern Sweden 1815–1968. Explor Econ Hist 48:389–400. doi:10.1016/j.eeh.2011.05.005
Birlie A, Tesfaw G, Dejene T, Woldemichael K (2015) Time to death and associated factors among tuberculosis patients in Dangila Woreda, Northwest Ethiopia. PLoS ONE 10:e0144244. doi:10.1371/journal.pone.0144244
Blackburn EH, Epel ES, Lin J (2015) Human telomere biology: a contributory and interactive factor in aging, disease risks, and protection. Science 350:1193–1198. doi:10.1126/science.aab3389
Bonafè M, Valensin S, Gianni W, Marigliano V, Franceschi C (2001) The unexpected contribution of immunosenescence to the leveling off of cancer incidence and mortality in the oldest old. Crit Rev Oncol/Hematol 39:227–233. doi:10.1016/S1040-8428(01)00168-8
Boonekamp JJ, Simons MJP, Hemerik L, Verhulst S (2013) Telomere length behaves as biomarker of somatic redundancy rather than biological age. Aging Cell 12:330–332. doi:10.1111/acel.12050
Booth LN, Brunet A (2016) The aging epigenome. Mol Cell 62:728–744. doi:10.1016/j.molcel.2016.05.013
Booth H, Tickle L (2008) Mortality modelling and forecasting: a review of methods. Ann Actuar Sci 3:3–43. doi:10.1017/S1748499500000440
Bots ML, Evans GW, Tegeler CH, Meijer R (2016) Carotid intima-media thickness measurements: relations with atherosclerosis, risk of cardiovascular disease and application in randomized controlled trials. Chin Med J 129:215–226. doi:10.4103/0366-6999.173500
Byrnes JP, Miller DC, Schafer WD (1999) Gender differences in risk taking: a meta-analysis. Psychol Bull 125:367–383. doi:10.1037/0033-2909.125.3.367
Campisi J (2013) Aging, cellular senescence, and cancer. Ann Rev Physiol 75:685–705. doi:10.1146/annurev-physiol-030212-183653
Carnes BA, Olshansky SJ (1997) A biologically motivated partitioning of mortality. Exp Gerontol 32:615–631
Carnes BA, Olshansky SJ, Grahn D (1996) Continuing the search for a law of mortality. Popul Dev Rev 22:231–264
Carnes B, Holden L, Olshansky S, Witten M, Siegel J (2006) Mortality partitions and their relevance to research on senescence. Biogerontology 7:183–198. doi:10.1007/s10522-006-9020-3
Carnes BA, Staats DO, Sonntag WE (2008) Does senescence give rise to disease? Mech Ageing Dev 129:693–699. doi:10.1016/j.mad.2008.09.016
Chandra RK (1997) Nutrition and the immune system: an introduction. Am J Clin Nutr 66:460S–463S
Chhikara RS, Folks L (1989) The inverse Gaussian distribution: theory, methodology, and applications. Statistics, textbooks and monographs v. 95. M. Dekker, New York
Chung HY et al (2009) Molecular inflammation: underpinnings of aging and age-related diseases. Ageing Res Rev 8:18–30. doi:10.1016/j.arr.2008.07.002
Cohen ML (2000) Changing patterns of infectious disease. Nature 406:762–767
Cohen AA (2016) Complex systems dynamics in aging: new evidence, continuing questions. Biogerontology 17:205–220. doi:10.1007/s10522-015-9584-x
Collado M, Blasco MA, Serrano M (2007) Cellular senescence in cancer and aging. Cell 130:223–233. doi:10.1016/j.cell.2007.07.003
Control CfD, Prevention (2016) CDC Health Information for International Travel 2014: The Yellow Book. Oxford University Press, Oxford
Cornman JC, Glei DA, Goldman N, Weinstein M (2016) Physiological dysregulation, frailty, and risk of mortality among older adults. Res Aging. doi:10.1177/0164027516630794
Cuervo AM, Bergamini E, Brunk UT, Dröge W, Ffrench M, Terman A (2005) Autophagy and aging: the importance of maintaining “clean” cells. Autophagy 1:131–140. doi:10.4161/auto.1.3.2017
Čulić V, Eterović D, Mirić D (2005) Meta-analysis of possible external triggers of acute myocardial infarction. Int J Cardiol 99:1–8. doi:10.1016/j.ijcard.2004.01.008
Daniel TM (2006) The history of tuberculosis. Respir Med 100:1862–1870. doi:10.1016/j.rmed.2006.08.006
Denton D, Xu T, Kumar S (2015) Autophagy as a pro-death pathway. Immunol Cell Biol 93:35–42. doi:10.1038/icb.2014.85
Diderichsen F, Hallqvist J (1997) Trends in occupational mortality among middle-aged men in Sweden 1961–1990. Int J Epidemiol 26:782–787
Dobson AP, Carper ER (1996) Infectious diseases and human population history throughout history the establishment of disease has been a side effect of the growth of civilization. Bioscience 46:115–126
Dong X, Milholland B, Vijg J (2016) Evidence for a limit to human lifespan. Nature. doi:10.1038/nature19793
Dribe M, Olsson M, Svensson P (2012) Was the manorial system an efficient insurance institution? Economic stress and demographic response in Sweden, 1749–1859. Eur Rev Econ Hist 16:292–310. doi:10.1093/ereh/her008
Edvinsson S, Lindkvist M (2011) Wealth and health in 19th Century Sweden. A study of social differences in adult mortality in the Sundsvall region. Explor Econ Hist 48:376–388. doi:10.1016/j.eeh.2011.05.007
Epstein FH, Ross R (1999) Atherosclerosis—an inflammatory disease. N Engl J Med 340:115–126
Field N, Lim MS, Murray J, Dowdeswell RJ, Glynn JR, Sonnenberg P (2014) Timing, rates, and causes of death in a large South African tuberculosis programme. BMC Infect Dis 14:1–12. doi:10.1186/s12879-014-0679-9
Flynn JL, Chan J (2001) Tuberculosis: latency and reactivation. Infect Immun 69:4195–4201. doi:10.1128/iai.69.7.4195-4201.2001
Foreman KJ, Lozano R, Lopez AD, Murray CJL (2012) Modeling causes of death: an integrated approach using CODEm. Popul Health Metr. doi:10.1186/1478-7954-10-1
Franceschi C et al (2007) Inflammaging and anti-inflammaging: a systemic perspective on aging and longevity emerged from studies in humans. Mech Ageing Dev 128:92–105. doi:10.1016/j.mad.2006.11.016
Frasca D, Blomberg BB (2015) Inflammaging decreases adaptive and innate immune responses in mice and humans. Biogerontology 17:7–19. doi:10.1007/s10522-015-9578-8
Gavrilov LA, Gavrilova NS (2003) The quest for a general theory of aging and longevity. Sci Aging Knowl Environ 2003:re5. doi:10.1126/sageke.2003.28.re5
Gems D, Partridge L (2013) Genetics of longevity in model organisms: debates and paradigm shifts. Annu Rev Physiol 75:621–644. doi:10.1146/annurev-physiol-030212-183712
Gladyshev VN (2016) Aging: progressive decline in fitness due to the rising deleteriome adjusted by genetic, environmental, and stochastic processes. Aging Cell 15:594–602. doi:10.1111/acel.12480
Glei DA, Goldman N, Risques RA, Rehkopf DH, Dow WH, Rosero-Bixby L, Weinstein M (2016) Predicting survival from telomere length versus conventional predictors: a multinational population-based cohort study. PLoS ONE 11:e0152486. doi:10.1371/journal.pone.0152486
Gompertz B (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans R Soc Lond 115:513–583. doi:10.1098/rstl.1825.0026
Gosselin JL, Anderson JJ (2013) Resource competition induces heterogeneity and can increase cohort survivorship: selection-event duration matters. Oecologia 173:1321–1331. doi:10.1007/s00442-013-2736-2
Gruver AL, Hudson LL, Sempowski GD (2007) Immunosenescence of ageing. J Pathol 211:144–156. doi:10.1002/path.2104
Hamilton WD (1966) The moulding of senescence by natural selection. J Theor Biol 12:12–45. doi:10.1016/0022-5193(66)90184-6
Han K, Kim J, Choi M (2015) Autophagy mediates phase transitions from cell death to life. Heliyon. doi:10.1016/j.heliyon.2015.e00027
Hanahan D, Weinberg RA (2011) Hallmarks of cancer: the next generation. Cell 144:646–674. doi:10.1016/j.cell.2011.02.013
Haycock PC, Heydon EE, Kaptoge S, Butterworth AS, Thompson A, Willeit P (2014) Leucocyte telomere length and risk of cardiovascular disease: systematic review and meta-analysis. BMJ. doi:10.1136/bmj.g4227
Heron M (2015) Deaths: leading causes for 2012. Natl Vital Stat Rep 64:1–94
Holt PG, Jones CA (2000) The development of the immune system during pregnancy and early life. Allergy 55:688–697. doi:10.1034/j.1398-9995.2000.00118.x
Janeway CA, Travers P, Walport M, Capra JD (2005) Immunobiology: the immune system in health and disease. Curr Biol 1:11
Kenyon CJ (2010) The genetics of ageing. Nature 464:504–512
Klasen S (1998) Marriage, bargaining, and intrahousehold resource allocation: excess female mortality among adults during early German development, 1740–1860. J Econ Hist 58:432–467
Kline KA, Bowdish DME (2016) Infection in an aging population. Curr Opin Microbiol 29:63–67. doi:10.1016/j.mib.2015.11.003
Köhler L (1991) Infant mortality: the Swedish experience. Annu Rev Publ Health 12:177–193. doi:10.1146/annurev.pu.12.050191.001141
Kuballa P, Nolte WM, Castoreno AB, Xavier RJ (2012) Autophagy and the immune system. Annu Rev Immunol 30:611–646. doi:10.1146/annurev-immunol-020711-074948
Legein B, Temmerman L, Biessen EAL, Lutgens E (2013) Inflammation and immune system interactions in atherosclerosis. Cell Mol Life Sci 70:3847–3869. doi:10.1007/s00018-013-1289-1
Levine B, Deretic V (2007) Unveiling the roles of autophagy in innate and adaptive immunity. Nat Rev Immunol 7:767–777
Levitis DA (2011) Before senescence: the evolutionary demography of ontogenesis. Proc R Soc B 278:801–809. doi:10.1098/rspb.2010.2190
Levy O (2007) Innate immunity of the newborn: basic mechanisms and clinical correlates. Nat Rev Immunol 7:379–390
Li T, Anderson JJ (2009) The vitality model: a way to understand population survival and demographic heterogeneity. Theor Popul Biol 76:118–131
Li T, Anderson JJ (2013) Shaping human mortality patterns through intrinsic and extrinsic vitality processes. Demogr Res 28:341–372
Li T, Anderson JJ (2015) The Strehler–Mildvan correlation from the perspective of a two-process vitality model. Popul Stud 69:91–104. doi:10.1080/00324728.2014.992358
Li T, Yang Y, Anderson J (2013) Mortality increase in late-middle and early-old age: heterogeneity in death processes as a new explanation. Demography 50:1563–1591. doi:10.1007/s13524-013-0222-4
Li Q, Wang S, Milot E, Bergeron P, Ferrucci L, Fried LP, Cohen AA (2015) Homeostatic dysregulation proceeds in parallel in multiple physiological systems. Aging Cell 14:1103–1112. doi:10.1111/acel.12402
López-Otín C, Blasco MA, Partridge L, Serrano M, Kroemer G (2013) The hallmarks of aging. Cell 153:1194–1217. doi:10.1016/j.cell.2013.05.039
Makeham WM (1867) On the law of mortality. J Inst Actuar (1866-1867) 13:325–358
McCabe C, Kirchner C, Zhang H, Daley J, Fisman DN (2009) Guideline-concordant therapy and reduced mortality and length of stay in adults with community-acquired pneumonia: playing by the rules. Arch Intern Med 169:1525–1531. doi:10.1001/archinternmed.2009.259
Medvedev ZA (1990) An attempt at a rational classification of theories of ageing. Biol Rev 65:375–398. doi:10.1111/j.1469-185X.1990.tb01428.x
Mielke JH, Pitkänen KJ (1989) War demography: the impact of the 1808–09 war on the civilian population of Åland. Finl Eur J Popul 5:373–398
Möller J (1990) Towards agrarian capitalism: the case of southern Sweden during the 19th century. Geogr Ann Ser B 72:59–72. doi:10.2307/490551
Mouton CP, Bazaldua OV, Pierce B, Espino DV (2001) Common infections in older adults. Am Fam Phys 63:257–268
Oeppen J, Vaupel JW (2002) Broken limits to life expectancy. Science 296:1029–1031. doi:10.1126/science.1069675
Olshansky SJ, Carnes BA, Désesquelles A (2001) Prospects for human longevity. Science 291:1491–1492
Olsson M, Svensson P (2010) Agricultural growth and institutions: Sweden, 1700–1860. Eur Rev Econ Hist 14:275–304
Ongrádi J, Kövesdi V (2010) Factors that may impact on immunosenescence: an appraisal. Immun Ageing. doi:10.1186/1742-4933-7-7
Palmer DB (2013) The effect of age on thymic function. Front Immunol 4:316. doi:10.3389/fimmu.2013.00316
Palucka AK, Coussens LM (2016) The basis of oncoimmunology. Cell 164:1233–1247. doi:10.1016/j.cell.2016.01.049
Patton GC et al (2009) Global patterns of mortality in young people: a systematic analysis of population health data. Lancet 374:881–892. doi:10.1016/S0140-6736(09)60741-8
Pawelec G, Derhovanessian E, Larbi A, Strindhall J, Wikby A (2009) Cytomegalovirus and human immunosenescence. Rev Med Virol. doi:10.1002/rmv.598
Pawelec G, McElhaney JE, Aiello AE, Derhovanessian E (2012) The impact of CMV infection on survival in older humans. Curr Opin Immunol 24:507–511. doi:10.1016/j.coi.2012.04.002
Polak JF, Backlund J-YC, Cleary PA, Harrington AP, O’Leary DH, Lachin JM, Nathan DM (2011) Progression of carotid artery intima-media thickness during 12 years in the diabetes control and complications trial/epidemiology of diabetes interventions and complications (DCCT/EDIC) study. Diabetes 60:607–613
Puleston DJ, Simon AK (2014) Autophagy in the immune system. Immunology 141:1–8. doi:10.1111/imm.12165
Reichert T, Chowell G, McCullers JA (2012) The age distribution of mortality due to influenza: pandemic and peri-pandemic. BMC Med 10:1–15. doi:10.1186/1741-7015-10-162
Riera CE, Merkwirth C, Filho CDDM, Dillin A (2016) Signaling networks determining life span. Annu Rev Biochem. doi:10.1146/annurev-biochem-060815-014451
Ritz BW, Gardner EM (2006) Malnutrition and energy restriction differentially affect viral immunity. J Nutr 136:1141–1144
Rudan I, Boschi-Pinto C, Biloglav Z, Mulholland K, Campbell H (2008) Epidemiology and etiology of childhood pneumonia. Bull World Health Organ 86:408–416B
Salinger DH, Anderson JJ, Hamel OS (2003) A parameter estimation routine for the vitality-based survival model. Ecol Model 166:287–294. doi:10.1016/s0304-3800(03)00162-5
Sansoni P et al (2014) New advances in CMV and immunosenescence. Exp Gerontol 55:54–62. doi:10.1016/j.exger.2014.03.020
Santo AH, Pinheiro CE, Jordani MS (1998) Multiple-causes-of-death related to tuberculosis in the State of Sao Paulo, Brazil. Rev Saude Publ 37:714–721
Savva GM et al (2013) Cytomegalovirus infection is associated with increased mortality in the older population. Aging Cell 12:381–387. doi:10.1111/acel.12059
Schaible UE, Kaufmann SHE (2007) Malnutrition and infection: complex mechanisms and global impacts. PLoS Med 4:e115. doi:10.1371/journal.pmed.0040115
Schumann B, Edvinsson S, Evengård B, Rocklöv J (2013) The influence of seasonal climate variability on mortality in pre-industrial Sweden. Glob Health Action 2013:6. doi:10.3402/gha.v6i0.20153
Sharrow DJ, Anderson JJ (2016a) Quantifying intrinsic and extrinsic contributions to life span during the epidemiological transition: application of a two-process vitality model to the human mortality database. Demography. doi:10.1007/s13524-016-0524-4
Sharrow DJ, Anderson JJ (2016b) A twin protection effect? Explaining twin survival advantages with a two-process mortality model. PLoS ONE 11:e0154774. doi:10.1371/journal.pone.0154774
Shulman EP, Smith AR, Silva K, Icenogle G, Duell N, Chein J, Steinberg L (2016) The dual systems model: review, reappraisal, and reaffirmation. Dev Cogn Neurosci 17:103–117. doi:10.1016/j.dcn.2015.12.010
Simon AK, Hollander GA, McMichael A (2015) Evolution of the immune system in humans from infancy to old age. Proc R Soc Lond B. doi:10.1098/rspb.2014.3085
Steinsaltz D, Evans SN (2004) Markov mortality models: implications of quasistationarity and varying initial distributions. Theor Popul Biol 65:319–337. doi:10.1016/j.tpb.2003.10.007S00
Strehler BL (1959) Origin and comparison of the effects of time and high-energy radiations on living systems. Q Rev Biol 34:117–142
Strehler BL, Mildvan AS (1960) General theory of mortality and aging. Science 132:14–21
Stroustrup N et al (2016) The temporal scaling of Caenorhabditis elegans ageing. Nature 530:103–107. doi:10.1038/nature16550
Sundin J, Willner S (2007) Social change and health in Sweden: 250 years of politics and practice
Tomasetti C, Vogelstein B (2015) Variation in cancer risk among tissues can be explained by the number of stem cell divisions. Science 347:78–81. doi:10.1126/science.1260825
Tuljapurkar S (1998) Forecasting mortality change. N Am Actuar J 2:127–134. doi:10.1080/10920277.1998.10595758
Turner JE (2016) Is immunosenescence influenced by our lifetime “dose” of exercise? Biogerontology 17:581–602. doi:10.1007/s10522-016-9642-z
Ukraintseva S, Yashin A (2003) Individual aging and cancer risk: how are they related? Demogr Res 9:163–196
Vangen-Lønne AM, Wilsgaard T, Johnsen SH, Carlsson M, Mathiesen EB (2015) Time trends in incidence and case fatality of ischemic stroke: the Tromsø study 1977–2010. Stroke 46:1173–1179. doi:10.1161/strokeaha.114.008387
Vasto S, Carruba G, Lio D, Colonna-Romano G, Di Bona D, Candore G, Caruso C (2009) Inflammation, ageing and cancer. Mech Ageing Dev 130:40–45. doi:10.1016/j.mad.2008.06.003
Vaupel JW, Yashin AI (1986) Cancer rates over age, time and place: insights from stochastic models of heterogeneous populations. International Institute for Applied Systems Analysis, Laxenburg
Vaupel JW, Manton KG, Stallard E (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16(3):439–454
Wachter KW, Evans SN, Steinsaltz D (2013) The age-specific force of natural selection and biodemographic walls of death. Proc Natl Acad Sci 110:10141–10146. doi:10.1073/pnas.1306656110
Wachter KW, Steinsaltz D, Evans SN (2014) Evolutionary shaping of demographic schedules. Proc Natl Acad Sci 111:10846–10853. doi:10.1073/pnas.1400841111
Weiskopf D, Weinberger B, Grubeck-Loebenstein B (2009) The aging of the immune system. Transpl Int 22:1041–1050. doi:10.1111/j.1432-2277.2009.00927.x
Weitz JS, Fraser HB (2001) Explaining mortality rate plateaus. Proc Natl Acad Sci USA 98:15383–15386. doi:10.1073/pnas.261228098
Wensink MJ, Caswell H, Baudisch A (2016) The rarity of survival to old age does not drive the evolution of senescence. Evol Biol. doi:10.1007/s11692-016-9385-4
Whitmore GA (1986) First-passage-time models for duration data: regression structures and competing risks. J R Stat Soc Ser D 35:207–219. doi:10.2307/2987525
World Health Organization (2010) World health statistics 2010
Wu S, Powers S, Zhu W, Hannun YA (2016) Substantial contribution of extrinsic risk factors to cancer development. Nature 529:43–47. doi:10.1038/nature16166
Yashin AI, Iachine IA, Begun AS (2000) Mortality modeling: a review. Math Popul Stud 8:305
Yashin AI, Arbeev KG, Akushevich I, Kulminski A, Ukraintseva SV, Stallard E, Land KC (2012) The quadratic hazard model for analyzing longitudinal data on aging, health, and the life span. Phys Life Rev 9:177–188. doi:10.1016/j.plrev.2012.05.002
Yashin AI et al (2016) How the effects of aging and stresses of life are integrated in mortality rates: insights for genetic studies of human health and longevity. Biogerontology 17:89–107. doi:10.1007/s10522-015-9594-8
Ygberg S, Nilsson A (2012) The developing immune system—from foetus to toddler. Acta Paediatr 101:120–127. doi:10.1111/j.1651-2227.2011.02494.x
Yin D, Chen K (2005) The essential mechanisms of aging: irreparable damage accumulation of biochemical side-reactions. Exp Gerontol 40:455–465
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This research was supported by National Institute of Health Grant R21AG046760.
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Anderson, J.J., Li, T. & Sharrow, D.J. Insights into mortality patterns and causes of death through a process point of view model. Biogerontology 18, 149–170 (2017). https://doi.org/10.1007/s10522-016-9669-1
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DOI: https://doi.org/10.1007/s10522-016-9669-1