We are pleased to alert you that our new peer-reviewed study on Mortality Trajectories at Extreme Old Ages
is now publicly available at PubMed
Central® (PMC) - a free full-text archive of biomedical and life
sciences journal literature at the U.S. National Institutes of
Health's National Library of Medicine (NIH/NLM):
Comments and suggestions are most welcome!
-- Leonid and Natalia
-- Leonid Gavrilov
, Ph.D., GSA Fellow
-- Natalia Gavrilova
, Ph.D., GSA Fellow
Center on Aging, NORC at the University of Chicago
Mortality Trajectories at Extreme Old Ages:
A Comparative Study of Different Data Sources on U.S. Old-Age Mortality
Gavrilova N.S., Gavrilov L.A.
In: 2014 Living to 100 Monograph
[available in PMC 2015 Feb 5 ].
The Society of Actuaries, 2014, 23 pages, PMID: 25664347
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
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 extreme ages, while the Sacher
estimate turns out to be the most accurate estimate of hazard rate.
Possible reasons for finding apparent mortality deceleration in earlier
studies are also discussed.
This study was supported in part by National Institutes of Health grant R01 AG028620