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The Long-Term Pattern of Adult Mortality and the Highest Attained Age Author(S): A The Long-Term Pattern of Adult Mortality and the Highest Attained Age Author(s): A. R. Thatcher Source: Journal of the Royal Statistical Society. Series A (Statistics in Society), Vol. 162, No. 1 (1999), pp. 5-43 Published by: Blackwell Publishing for the Royal Statistical Society Stable URL: http://www.jstor.org/stable/2680465 Accessed: 05/10/2010 21:57 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=black. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Royal Statistical Society and Blackwell Publishing are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. Series A (Statistics in Society). http://www.jstor.org J. R. Statist.Soc. A (1999) 162, Part 1,pp. 5-43 The long-termpattern of adult mortalityand the highest attained age A. R. Thatcher New Malden, UK [Read beforeThe Royal StatisticalSociety on Wednesday, June 17th, 1998, the President, Professor R. N. Curnow,in the Chair] Summary. Recerrtnew data on old age mortalitypoint to a particularmodel for the way in whichthe probabilityof dying increases withage. The model is foundto fitnot only modern data butalso some widelyspaced historicaldata forthe 19thand 17thcenturies, and even some estimatesfor the early mediaeval period.The resultsshow a patternwhich calls forexplanation. The model can also be used to predicta probabilitydistribution for the highest age which will be attained in given circumstances.The resultsare relevantto the currentdebate about whetherthere is a fixedupper limitto the lengthof human life. Keywords: Aging;Extreme values; Lifespan;Logistic model; Longevity;Mortality 1. Introduction 1. 1. Background At everyage, thereis a probabilityof dyingwithin 12 months.From soon after30 yearsof age thisprobability starts to rise by about 10% witheach successiveyear of age. In round numbers,the probability of dying(for modern males) increasesfrom 0.001 at age 30 to 0.1 at age 80 years.This inexorableincrease follows quite closelythe 'law of mortality'which was discoveredby Gompertz(1825). By 80 years the rate of increaseis noticeablyslower and thereis controversyabout what happens at higherages still.There are alternativemodels, whichwe shall discuss. In the 19thcentury, the probabilitiesof dyingat ages 30-80 yearswere much higherthan theyare today. However,until relatively recently it was widelybelieved that, although there had been spectacularimprovements at lowerages, therehad been littlechange in the prob- abilitiesof dyingabove 80 yearsof age. Many believedthat, somewhere above 100 yearsold, thereis a maximumlifespan which has remainedunchanged since ancient times. In a veryinfluential paper, Fries (1980) expressedhis beliefas a physicianthat thereis a naturallimit to thelength of human life, even in theabsence of disease,and thatthe maximum lifespandoes not change.However, the average length of lifehas risendramatically since the mid-19th century. This combinationof a risingaverage and a fixedupper limit means that the shape of thesurvival curve has becomemore rectangular. Fries thought that the expectation of life at birthcan be expectedto increaseto an 'ideal average life span' of about 85 years. Chronicillnesses can be postponedby changesin lifestyle. Adult vigourcan be extendedto higherages, but stillwithin the same maximumlifespan. As a result,morbidity will become compressedinto a period of senescencebefore the end of life.A researchstrategy on aging should be fundamentallyshifted, towards postponing chronic illness and maintainingvigour. Addressfor correspondence:A. R. Thatcher,129 ThetfordRoad, New Malden, Surrey,KT3 5DS, UK. ? 1999 Royal StatisticalSociety 0964-1998/99/162005 6 A. R. Thatcher These viewswere controversial from the beginning and therehas been a livelydebate which is stillin progress.We have space to mentiononly a fewreferences, to give the flavour. Mantonet al. (1991) said that,although traditionalists might not expectthe average length of lifeto riseabove 85 years,there were nevertheless reasons for thinking that, with healthier lifestyles and continuingmedical progress and intervention,it mightbe possibleto raise the expectationof lifein the USA to 95 or even 100 years. Olshanskyet al. (1990, 1991) weremore sceptical, arguing that it would requirevery large fallsin death-ratesat highages to have muchfurther effect on theexpectation of lifeat birth. Longer lifemight often be attainableonly at the cost of a prolongedperiod of frailtyand dependence.More researchwas needed to improvethe quality of life of the elderlyby amelioratingnon-fatal diseases. Vaupel, quoted in Baringa (1991), challengedFries. Swedishdata showed that mortality ratesat ages 85 yearsand over had been fallingfor 50 years.Data on the lengthof lifeof a millionfruit-flies showed that their probability of dyingstarts by increasingwith age but then levelsoff. There was no evidenceof a biologicallimit to life.Gavrilov and Gavrilova (1991) reachedthe same conclusionindependently. 1.2. The maximumlength of life If thereis a virtuallyfixed upper limit to thelength of humanlife, then further falls in death- rates will make the survivalcurve even more rectangularand deaths will eventuallybe compressedinto a narrowerband of ages. In contrast,if thereis no fixedupper limit, or if a fixedlimit exists but is far higherthan the ages whichhave so farbeen attained,then there will be less rectangularizationand less compressionof theages at death,but people may live even longer. These differentpossible outcomeswill be reflectedin differentpatterns for the probabili- tiesof dyingabove age 80 years.In principlethere are threemain possibilities. The firstis that the probabilityof dyingwithin 12 monthsmay reach 1 at a finiteage. There will thenbe a definite,fixed upper limit to the lengthof human life.Many people believethere to be such a fixed,definite limit. The French demographerVincent (1951) thoughtthat therewere enormousodds againstanyone exceeding the age of 110 years.Fries (1980) and thebiologist Hayflick(1994) placed the upper limitat about 115 years,and indeed Hayflickused this supposed limit as a reason for rejectingvarious medical theories. Most recentlythe mathematicalstatisticians Aarsen and de Haan (1994) have inferred(though fromvery limiteddata) thatthere is an upperlimit to lifewhich lies, with 95% confidence,between 113 and 124 years. The secondpossibility is thatthe probability of dyingwithin 12 monthsdoes not reach 1 at a finiteage, but neverthelesstends asymptotically to 1. In thiscase thereis no definite,fixed upperlimit, but as age increasesthe probability of furthersurvival eventually becomes so tiny that for practicalpurposes it can be ignored.This is the scenariowhich is impliedby the originallaw of Gompertz(1825) and also by the more recentmodels of Weibull (1951) and Heligmanand Pollard (1980). The thirdpossibility is that the probabilityof dyingwithin 12 monthsmay continueto increasemonotonically as age increasesbut may tendto a limitwhich is less than 1. This is what is impliedby the 'logisticmodel', whichwas firstapplied to mortalityby Perks (1932) and later,under different names and notations,by severalothers. In thismodel thereis no definite,fixed upper limit to lifeand thereis not even an age whenthe probabilityof further survivalis negligible.However high the age, therewill always be a substantialprobability of Mortalityand HighestAttained Age 7 survivingfor at least 1 more year. This model tends towards a Poisson process, so the survivorswill graduallyapproach (but not quite reach) a statelike thatof radioactiveatoms awaitingdecay, with a half-life.Nevertheless, all the survivorswill die in the end and there willbe a probabilitydistribution for the highest age whichwill be attainedin a givengroup of survivors.This will depend on the absolute size of the group. Each of these theorieshas its supportersamong biologists,so there is at presentno consensusin thatquarter. These variousmodels, if considered solely from a theoreticalpoint of view withoutany referenceto actual data, providealmost unlimitedscope forargument about whetherthere is an upper limitto life. 1.3. New data Previousstudies of theforce of mortalityat highages have been based on data forindividual countries.More detailedanalyses can be made when thereare largernumbers, obtained by pooling the data for similarcountries. In 1990 Peter Laslett set up the CambridgeGroup project on the maximal lengthof life,and its members(Kannisto, Thatcherand Vaupel) assembledand computerizeda new database. This is part of theArchive on PopulationData on Aging,funded
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