Daunted by the prospect of estimating old-age mortality with too little data? Joseph Lu and Steve Bale provide a potential lifeline
The increasing number of people living to very old ages has attracted much public attention lately. This highlights the need for accurate estimates of mortality rates. Obtaining sufficiently credible datasets for analysing mortality experience at these ages can be challenging though. For example, most Continuous Mortality Investigation (CMI) life tables are often based on low data volumes above age 90 and rely upon extrapolation of younger age mortality. This introduces uncertainty in the derived mortality rates at higher ages.
The general population
Industry and general population life tables usually have different mortality rates. We believe that this is largely attributable to differences in socio-economic distribution between their respective populations. Interestingly, though, differences in mortality rates for different socio-economic groups have been observed to narrow at older ages (Hoffmann, 2005; CMI working paper 66). If this is the case, then we might be able to use the population data to determine the mortality rates at these higher ages. This overcomes the problem of insufficient data for the ages in most datasets used by the insurance or pension industry.
A key problem with UK demographic data is that the number of people alive each year is estimated from the most recent census, and is therefore subject to reporting or calculation bias. We discuss a method that estimates mortality rates at higher ages using death data of cohorts born many years ago, that can be expected to no longer have any surviving members, for example those born in 1890. This is known as the 'extinct generation' method. It has the advantage of using the more reliable death data alone to construct mortality rates, without relying on census data so avoids the problems related to census estimates.
So does mortality between socio-economic groups converge at very old ages? We have analysed CMI Self-Administered Pension Scheme (SAPS) mortality data from 2005 to 2009. This is split by pension band, which we have assumed to be a good proxy for socio-economic circumstances of the SAPS population. The results are summarised
in Figure 1.
The chart shows that as age increases, the difference in mortality between the pension bands does in fact narrow. The differences between pension bands are less pronounced for females and the convergence is less distinct, as described in CMI working paper 66. We have also observed this socio-economic convergence in larger datasets, including the General Practice Research Database (GPRD) and Office for National Statistics total English population (Lu et al, 2013).
More research is required to confirm the trajectories, but
? Differences in mortality rates between people in different socioeconomic groups might converge as assumed in CMI SAPS draft S2 life tables for pensioners in different pension amount categories.
? Differences in mortality rates between people in different socio-economic groups might converge and cross over as observed between ill and normal health retirement populations in CMI working paper 35.
? Differences in mortality rates between people in different socio-economic groups might remain if a more sophisticated way of differentiating the population - including factors such as lifelong total wealth and education level - were used.
We have assumed henceforth that socio-economic convergence to general population mortality at higher ages does indeed occur.
Extinct generation method
The extinct generation method can be used to estimate population mortality rates at higher ages for cohorts that have no surviving members. The population estimate for a cohort at age x is the sum of all future deaths for the cohort. For example, the population size of the cohort at age 100 is the number of deaths among cohort members, from the year that the cohort turned 100 until the year that the last member of the cohort died.
We looked at the population of lives born between 1875 and 1900 inclusive, so those lives reaching age 100 between 1975 and 2000. For lives born after 1900, their registered death information will not be complete for ages less than 109 years. Working backwards from the oldest life, populations, and so mortality at previous points in time, can be constructed.
This approach arguably provides a better estimate of population than census-based projections, and at least maintains consistency between death and exposure data.
We have used the extinct generation approach to determine and compare mortality for different countries. The derived mortality rates are summarised in Figure 2.
Different countries will be exposed to different healthcare, lifestyle and socio-economic risk drivers, which will influence their mortality in different ways. However, we can see that for most countries analysed, older age mortality rates are clustered fairly closely. The two outliers appear to be Japan and the US. In Japan, under-reporting of deaths at very old ages has been discovered in a number of cases. Further investigation is needed into the US data.
Key data issues of the extinct generation approach when used for other countries include territorial changes over time, significant war mortality and estimation of military population, and changes in recording and validating deaths over time.
Other countries' data are subject to differing recording and quality checks and may have different approaches to inclusion/exclusion of mortality related to non-residents. The approach also assumes that there is negligible migration for very old ages.
Information from extra data
The above results could be used to inform the derivation of life tables at higher ages. For example, the initial mortality rates (Qx) above age 100 of the recent CMI SAPS draft S2PMA are higher than those of most countries examined here.
The Qx between age 95 and 105 calculated using the extinct generation method for England and Wales are on average about
4% lower than those implied by the CMI SAPS draft S2PMA and
about 8% lower than the S1PMA mortality rate tables.
On the other hand, the same rates from our calculation are about 6% higher than that of CMI PNMA00 life table. These are not direct comparisons, in that the rates shown above have not been adjusted to allow for any changes in mortality rates over time. The extinct generation method's mortality rates would have to be adjusted with changes in mortality improvement, potentially giving lower mortality rates and increasing the differences from the SAPS table.
Pension schemes' liabilities calculated using the SAPS tables would increase if mortality rates above age 95 were to be replaced with those estimated from the extinct generation method. This method could potentially help inform the derivation of higher-age mortality, especially for the purpose of sense-checking.
Our initial research does show that differences in mortality rates eventually converges at higher ages, but we appreciate that more detailed research to refine this assumption is needed.
The extinct generation method may be advantageous as is does not rely on census estimates, but further analysis of how mortality rates have changed in the past at higher ages is required. With questions remaining on how best to estimate higher-age mortality, we hope to encourage further research into mortality rates and longevity drivers at these older ages.
Joseph Lu and Steve Bale would like to thank Andrea Peterson for her contribution and Wun Wong for the provision of GPRD data