Living to 100 monograph最新文献

Knowledge of future mortality levels and trends is important for actuarial practice but poses a challenge to actuaries and demographers. The Lee-Carter method, currently used for mortality forecasting, is based on the assumption that the historical evolution of mortality at all age groups is driven by one factor only. This approach cannot capture an additive manner of mortality decline observed before the 1960s. To overcome the limitation of the one-factor model of mortality and to determine the true number of factors underlying mortality changes over time, we suggest a new approach to mortality analysis and forecasting based on the method of latent variable analysis. The basic assumption of this approach is that most variation in mortality rates over time is a manifestation of a small number of latent variables, variation in which gives rise to the observed mortality patterns. To extract major components of mortality variation, we apply factor analysis to mortality changes in developed countries over the period of 1900-2014. Factor analysis of time series of age-specific death rates in 12 developed countries (data taken from the Human Mortality Database) identified two factors capable of explaining almost 94 to 99 percent of the variance in the temporal changes of adult death rates at ages 25 to 85 years. Analysis of these two factors reveals that the first factor is a "young-age" or background factor with high factor loadings at ages 30 to 45 years. The second factor can be called an "oldage" or senescent factor because of high factor loadings at ages 65 to 85 years. It was found that the senescent factor was relatively stable in the past but now is rapidly declining for both men and women. The decline of the senescent factor is faster for men, although in most countries, it started almost 30 years later. Factor analysis of time series of age-specific death rates conducted for the oldest-old ages (65 to 100 years) found two factors explaining variation of mortality at extremely old ages in the United States. The first factor is comparable to the senescent factor found for adult mortality. The second factor, however, is specific to extreme old ages (96 to 100 years) and shows peaks in 1960 and 2000. Although mortality below 90 to 95 years shows a steady decline with time driven by the senescent factor, mortality of centenarians does not decline and remains relatively stable. The approach suggested in this paper has several advantages. First, it is able to determine the total number of independent factors affecting mortality changes over time. Second, this approach allows researchers to determine the time interval in which underlying factors remain stable or undergo rapid changes. Most methods of mortality projections are not able to identify the best base period for mortality projections, attempting to use the longest-possible time period instead. We observe that the senescent factor of mortality continues to decline, and this decline does

The growing number of persons surviving to age 100 years and beyond raises questions about the shape of mortality trajectories at exceptionally high ages, and this problem may become significant for actuaries in the near future. However, such studies are scarce because of the difficulties in obtaining reliable age estimates at exceptionally high ages. The current view about mortality beyond age 110 years suggests that death rates do not grow with age and are virtually flat. The same assumption is made in the new actuarial VBT tables. In this paper, we test the hypothesis that the mortality of supercentenarians (persons living 110+ years) is constant and does not grow with age, and we analyze mortality trajectories at these exceptionally high ages. Death records of supercentenarians were taken from the International Database on Longevity (IDL). All ages of supercentenarians in the database were subjected to careful validation. We used IDL records for persons belonging to extinct birth cohorts (born before 1895) since the last deaths in IDL were observed in 2007. We also compared our results based on IDL data with a more contemporary database maintained by the Gerontology Research Group (GRG). First we attempted to replicate findings by Gampe (2010), who analyzed IDL data and came to the conclusion that "human mortality after age 110 is flat." We split IDL data into two groups: cohorts born before 1885 and cohorts born in 1885 and later. Hazard rate estimates were conducted using the standard procedure available in Stata software. We found that mortality in both groups grows with age, although in older cohorts, growth was slower compared with more recent cohorts and not statistically significant. Mortality analysis of more numerous 1884-1894 birth cohort with the Akaike goodness-of-fit criterion showed better fit for the Gompertz model than for the exponential model (flat mortality). Mortality analyses with GRG data produced similar results. The remaining life expectancy for the 1884-1894 birth cohort demonstrates rapid decline with age. This decline is similar to the computer-simulated trajectory expected for the Gompertz model, rather than the extremely slow decline in the case of the exponential model. These results demonstrate that hazard rates after age 110 years do not stay constant and suggest that mortality deceleration at older ages is not a universal phenomenon. These findings may represent a challenge to the existing theories of aging and longevity, which predict constant mortality in the late stages of life. One possibility for reconciliation of the observed phenomenon and the existing theoretical consideration is a possibility of mortality deceleration and mortality plateau at very high yet unobservable ages.

The growing number of individuals living beyond age 80 underscores the need for accurate measurement of mortality at advanced ages. Our earlier published study challenged the common view that the exponential growth of mortality with age (Gompertz law) is followed by a period of deceleration, with slower rates of mortality increase (Gavrilov and Gavrilova 2011). This refutation of mortality deceleration was made using records from the U.S. Social Security Administration's Death Master File (DMF). Taking into account the significance of this finding for actuarial theory and practice, we tested these earlier observations using additional independent datasets and alternative statistical approaches. In particular, the following data sources for U.S. mortality at advanced ages were analyzed: (1) data from the Human Mortality Database (HMD) on age-specific death rates for 1890-99 U.S. birth cohorts, (2) recent extinct birth cohorts of U.S. men and women based on DMF data, and (3) mortality data for railroad retirees. In the case of HMD data, the analyses were conducted for 1890-99 birth cohorts in the age range 80-106. Mortality was fitted by the Gompertz and logistic (Kannisto) models using weighted nonlinear regression and Akaike information criterion as the goodness-of-fit measure. All analyses were conducted separately for men and women. It was found that for all studied HMD birth cohorts, the Gompertz model demonstrated better fit of mortality data than the Kannisto model in the studied age interval. Similar results were obtained for U.S. men and women born in 1890-99 and railroad retirees born in 1895-99 using the full DMF file (obtained from the National Technical Information Service, or NTIS). It was also found that mortality estimates obtained from the DMF records are close to estimates obtained using the HMD cohort data. An alternative approach for studying mortality patterns at advanced ages is based on calculating the age-specific rate of mortality change (life table aging rate, or LAR) after age 80. This approach was applied to age-specific death rates for Canada, France, Sweden and the United States available in HMD. It was found that for all 24 studied single-year birth cohorts, LAR does not change significantly with age in the age interval 80-100, suggesting no mortality deceleration in this interval. Simulation study of LAR demonstrated that the apparent decline of LAR after age 80 found in earlier studies may be related to biased estimates of mortality rates measured in a wide five-year age interval. Taking into account that there exists several empirical estimates of hazard rate (Nelson-Aalen, actuarial and Sacher), a simulation study was conducted to find out which one is the most accurate and unbiased estimate of hazard rate at advanced ages. Computer simulations demonstrated that some estimates of mortality (Nelson-Aalen and actuarial) as well as kernel smoothing of hazard rates may produce spurious mortality deceleration at

Knowledge of strong predictors of mortality and longevity is very important for actuarial science and practice. Earlier studies found that parental characteristics as well as early-life conditions and midlife environment play a significant role in survival to advanced ages. However, little is known about the simultaneous effects of these three factors on longevity. This ongoing study attempts to fill this gap by comparing centenarians born in the United States in 1890-91 with peers born in the same years who died at age 65. The records for centenarians and controls were taken from computerized family histories, which were then linked to 1900 and 1930 U.S. censuses. As a result of this linkage procedure, 765 records of confirmed centenarians and 783 records of controls were obtained. Analysis with multivariate logistic regression found that parental longevity and some midlife characteristics proved to be significant predictors of longevity while the role of childhood conditions was less important. More centenarians were born in the second half of the year compared to controls, suggesting early origins of longevity. We found the existence of both general and gender-specific predictors of human longevity. General predictors common for men and women are paternal and maternal longevity. Gender-specific predictors of male longevity are the farmer occupation at age 40, Northeastern region of birth in the United States and birth in the second half of year. A gender-specific predictor of female longevity is surprisingly the availability of radio in the household according to the 1930 U.S. census. Given the importance of familial longevity as an independent predictor of survival to advanced ages, we conducted a comparative study of biological and nonbiological relatives of centenarians using a larger sample of 1,945 validated U.S. centenarians born in 1880-95. We found that male gender of centenarian has significant positive effect on survival of adult male relatives (brothers and fathers) but not female blood relatives. Life span of centenarian siblings-in-law is lower compared to life span of centenarian siblings and does not depend on centenarian gender. Wives of male centenarians (who share lifestyle and living conditions) have a significantly better survival compared to wives of centenarians' brothers. This finding demonstrates an important role of shared familial environment and lifestyle in human longevity. The results of this study suggest that familial background, early-life conditions and midlife characteristics play an important role in longevity.