In this paper, we focus our analyses on —99 birth cohorts because we found that data quality for earlier cohorts is not particularly good. On the other hand, aggregation of deaths for several calendar periods creates a heterogeneous mixture of cases from different birth cohorts. 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 Statistical methods Study of data quality control at advanced ages suggests that age reporting among the oldest-old in the United States is good until age Gavrilov and Gavrilova 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. For the DMF dataset, we used a subsample of deaths for individuals who applied for Social Security numbers in the non-Southern states described above and born in —99 because data for these birth cohorts have reasonably good quality. This resource covered deaths starting in Faig and captured about 95 percent of deaths recorded by the National Death Index Sesso, Paffenbarger and Lee
This is the latest available complete version of DMF and the last deaths occurred in September In this paper, we focus our analyses on —99 birth cohorts because we found that data quality for earlier cohorts is not particularly good. Age-specific exposure values were used as weights Muller, Wang and Capra On the other hand, aggregation of deaths for several calendar periods creates a heterogeneous mixture of cases from different birth cohorts. Until recently, DMF was a publicly available data resource, which allowed a search for deceased individuals in the United States using various search criteria: In the first stage of our analyses, we calculated an individual life span in completed months. British actuary Robert Eric Beard introduced a model of population heterogeneity with gamma-distributed individual risk to explain mortality deceleration at older ages Beard 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. It means that comparing mortality models beyond this age is not feasible because of the poor quality of mortality data. Taking into account that the accuracy of age reporting is positively correlated with education, it is reasonable to expect improvement in age reporting over time and less expressed mortality underestimation at older ages. Finally, the problem of age misreporting by older people may still be a problem affecting estimates of mortality at advanced ages Coale and Kisker ; Elo et al. It is believed mortality at advanced ages has a tendency to deviate from the Gompertz law Gavrilov and Gavrilova so the logistic model is suggested for fitting human mortality after age 80 Horiuchi and Wilmoth ; Wilmoth et al. This is now considered to be the most common explanation of the mortality deceleration phenomenon Horiuchi and Wilmoth Mortality was fitted by the Gompertz and logistic Kannisto models using weighted nonlinear regression and Akaike information criterion as the goodness-of-fit measure. This problem is sometimes overlooked by researchers who believe that mortality estimates, which work well at young adult ages like one-year probability of death can work equally well at very old ages. 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 This approach was applied to DMF data in our earlier study and showed that data quality in DMF is acceptable up to the age Gavrilov and Gavrilova To minimize statistical noise in estimates of mortality at advanced ages, researches have to pool data for several calendar periods Depoid ; Thatcher Human Mortality Database HMD was created to provide detailed mortality and population data to researchers, students, journalists, policy analysts and others interested in the history of human longevity. Data for extremely long-lived individuals are scarce and subject to age exaggeration. They proposed a logistic formula for fitting mortality growth with age to account for mortality leveling off at advanced ages Perks ; Beard , 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 extreme ages, while the Sacher estimate turns out to be the most accurate estimate of hazard rate. The United States has the largest population size among the advanced economies. The remaining 7—9 percent of individuals with unknown sex had approximately the same mean life span as the remaining percent of individuals with identified sex pooled together checked with the t-test statistics , so the existence of possible sex nonidentification bias in mortality seems unlikely. In addition to the heterogeneity problem, there is the issue of using proper empirical estimates of hazard rate at extreme ages when mortality is high and grows with age very rapidly.
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