Modeling Mortality at Older Ages - Benefits and Challenges
When one looks at a curve of the mortality rates by age in developed countries, we notice a very regular pattern. Especially the middle-age groups - age 30 to 70+, for example - seem to have close to an exponential curve in mortality rates. This observation, originally identified by Gompertz almost 200 years ago, led to the concept that there is an underlying regularity, explained by laws we only need to discover.
Although this concept is still as striking today as it was when it was first made, a more detailed view of the data suggests some issues. Refinements were developed to better understand the accidental component of mortality. This led in turn to an ever-expanding set of analytical techniques to answer the burning question, Where will mortality rates be?
Models to Forecast Mortality Rate
Beyond the more simplistic models of projecting life expectancy by expert opinion and backfilling the mortality producing this expectancy, there are a number of other models created for forecasting mortality rates. For example, the seminal work of Lee and Carter in 1997 inspired a series of refinements or new models meant to address some of the implicit shortcomings of their method.1 The SOA’s Living to 100 Symposium is a good resource for exploring a number of these models. The literature review on them, published and updated after each symposium, is a good source of guidance for the pros and cons of the selected models.2
Extrapolative models, like the Lee-Carter model, attempt to fit the parameters of the model to existing data and use those fitted values to predict future values. One of the drawbacks of the Lee-Carter model is its sensitivity to outliers in the data. Some variations were developed with the specific aim to improve the performance of the Lee-Carter model or explore alternative parametrization. One of the major drawbacks of all those models is that none of them has the ability to perform well on all the mortality curves of developed countries.
Cohort Effects on Mortality
For instance, observation of UK data suggests a strong cohort effect on mortality. If a cohort is a group of people born around the same time, we can assume they were subject to similar conditions growing up. The cohort’s effect on mortality could be due to behavior; for example, during World War II Danish women represented a group whose smoking prevalence was much higher than in other generations, and this behavior had a strong effect on their life expectancy.3 A strong cohort effect can also be due to deprivation experienced by all people born in a certain period in a country; for example, the Dutch Hunger Winter cohort of children in Holland during World War II who experienced nutritional deprivations at a crucial time in their development.4 The impact of the cohort effect on mortality in the UK has led researchers to adopt models factoring cohort components.
The general use of a cohort component when analyzing mortality rates has been more controversial in the U.S. Nonetheless, the SOA has sponsored some research using the Age-Period-Cohort (APC) decomposition modeling. Results have encountered mixed success, especially in the interpretability of the components and the variation in impact on different age groupings (younger vs. older).5 More research is underway.
As we refine our models, are we just over-fitting the data or are we getting to some underlying reality? I find that models that project population mortality as a whole, even if sometimes practical, are intellectually hard to accept. Mortality is the result of a variety of components, causes and drivers that have their own temporal trends. Should we not explore those trends individually as well as combine them to get a better result? Attractive though this may be, there are several challenges to these methods concerning mortality. The fact that mortality for each cause is not fully independent - e.g., to be counted as having Alzheimer’s, you first must have survived cancer - makes the formulation quite challenging. This is also explored in the literature from the Living to 100 Symposia. Beyond the complexity, it is a challenge to access valid data with causes of death that have enough historical consistency and granularity.
Despite the complexities, models allow us to mitigate the curse of the traditional experience study: The more granularity, the less credibility in each cell.6 Imposing a model, and therefore a structure, on the data allows us to benefit from what we do know about mortality; for example, we know the relationship between male and female mortality, or between smoker and nonsmoker. To oversimplify, if I have credible mortality at ages 55 and 57, the fact that I may not have the desired credibility at age 56 may not be much of an issue. This revolution in our methodology is currently being explored in a variety of formats by research under the auspices of the SOA.
Stay tuned and feel free to reach out to me for a bit more information on that upcoming research.
- Lee-Carter model, https://en.wikipedia.org/wiki/Lee–Carter_model.
- SOA Living to 100 Symposia Monographs: https://livingto100.soa.org/monographs.aspx
Living to 100 Insights on the Challenges and Opportunities of Longevity Literature review 2002-2014: https://www.soa.org/globalassets/assets/Files/Research/Projects/research-2016-living-100-insights.pdf
Living to 100 Insights on the Challenges and Opportunities of Longevity Literature review 2002-2017: https://www.soa.org/globalassets/assets/files/resources/research-report/2019/living-100-insights-challenges.pdf
- R Lindahl-Jacobsen, et al., Rise, stagnation, and rise of Danish women’s life expectancy. PNAS April 12, 2016 113 (15) 4015-4020. https://www.pnas.org/content/113/15/4015.
- P Ekamper, et al., Independent and additive association of prenatal famine exposure and intermediary life conditions with adult mortality between age 18–63 years. Social Science & Medicine Volume 119, October 2014, Pages 232-239. https://www.sciencedirect.com/science/article/abs/pii/S0277953613005753?via%3Dihub.
- The StMoMo R-language package developed by Andres Villegas, a regular presenter at Living to 100 symposia, greatly simplifies the practical applications of a number of models. https://cran.r-project.org/web/packages/StMoMo/index.html.