We are pleased to alert you about our new published peer-reviewed study
of old-age survival:
Mortality Trajectories at Extreme Old Ages:
A Comparative Study of Different Data Sources on U.S. Old-Age
Gavrilova N.S., Gavrilov L.A.
2014 Living to 100 Monograph
– August, 2014, http://livingto100.soa.org/
The Society of Actuaries, 2014, 23 pages
Full text is available at:
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 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
Comments and suggestions are most welcome!
, Ph.D., GSA Fellow
, Ph.D., GSA Fellow
Center on Aging, NORC at the University of Chicago