Christina Bohk-Ewald

Probabilistic mortality forecasting with varying age-specific survival improvements

Many mortality forecasting approaches extrapolate past trends. Their predictions of the future development can be quite precise as long as turning points and/or age-shifts of mortality decline are not present. To account even for such mortality dynamics, we propose a model that combines recently developed ideas in a single framework. It (1) uses rates of mortality improvement to model the aging of mortality decline, and it (2) optionally combines the mortality trends of multiple countries to catch anticipated turning points. We use simulation-based Bayesian inference to estimate and run this model that also provides prediction intervals to quantify forecast uncertainty. Validating mortality forecasts for British and Danish women from 1991 to 2011 suggest that our model can forecast regular and irregular mortality developments and that it can perform at least as well as other widely accepted approaches like, for instance, the Lee-Carter model or the UN Bayesian approach. Moreover, prospective mortality forecasts from 2012 to 2050 suggest gradual increases for British and Danish life expectancy at birth.

Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts

Evaluating the predictive ability of mortality forecasts is important yet difficult. Death rates and mean lifespan are basic life table functions typically used to analyze to what extent the forecasts deviate from their realized values. Although these parameters are useful for specifying precisely how mortality has been forecasted, they cannot be used to assess whether the underlying mortality developments are plausible. We therefore propose that in addition to looking at average lifespan, we should examine whether the forecasted variability of the age at death is a plausible continuation of past trends. The validation of mortality forecasts for Italy, Japan, and Denmark demonstrates that their predictive performance can be evaluated more comprehensively by analyzing both the average lifespan and lifespan disparity—that is, by jointly analyzing the mean and the dispersion of mortality. Approaches that account for dynamic age shifts in survival improvements appear to perform better than others that enforce relatively invariant patterns. However, because forecasting approaches are designed to capture trends in average mortality, we argue that studying lifespan disparity may also help to improve the methodology and thus the predictive ability of mortality forecasts.

Surface Plots for Cancer Survival

While previous chapters focused only on the event of death, this chapter investigates the dynamics over age and time for the duration between being diagnosed with a specific cancer and death. We use five year survival as our indicator of survival in general, disease-specific survival and relative survival for selected cancer sites such as breast cancer, colorectal cancer, lung cancer or pancreatic cancer. The major impact of the stage of the tumor at the time of diagnosis for survival is illustrated using stage 1 and stage 4 of colorectal cancer as an example.

Surface Plots of Rates of Mortality Improvement for Selected Causes of Death in the United States

This chapter shows that ROMI plots, as presented in the previous chapter, can not only be employed for mortality from all-causes but also for cause-specific mortality. They allow us to demonstrate that the slow increase in life expectancy among women in the United States during the 1980s and 1990s can not be attributed to heart diseases or stroke. Instead, mortality from respiratory diseases and from lung cancer, the latter featuring a pronounced cohort effect, suppressed faster gains in life expectancy.

Data and Software

This chapter describes the major data sets used in this monograph: The Human Mortality Database, data from the National Center for Health Statistics of the United States for the analysis of causes of death, and the individual-level, longitudinal data of the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute of the United States. The latter is used to illustrate the dynamics of cancer survival.

Surface Plots of Smoothed Mortality Data

The surface maps of the previous chapter showed that random fluctuations can be quite large. The present chapter on smoothing mortality data explains how we smoothed the observed mortality with P-splines. We illustrate our smoothing results with the same set of countries as in the previous chapter for unsmoothed data.

The Lexis Diagram

The second chapter specifies how a Lexis diagram is constructed and shows that cohorts are depicted on the 45∘ line. It briefly discusses the so-called identification problem of standard methods of age-, period-, and cohort analysis and explains how those effects look like in the Lexis diagram. The chapter concludes with a brief history of the depiction of population dynamics in three dimensions.

Surface Plots of Observed Death Rates

The chapter on observed death rates illustrates why demographic rates need to be adjusted by the number of person years lived and shows surface maps of such “raw” death rates for a few selected national populations. One can easily see that random fluctuations can turn out be problematic for smaller populations as they may lead to misinterpretations.

Surface Plots of Rates of Mortality Improvement

Surface maps of unsmoothed and smoothed mortality data have been used widely before. In this chapter, we present surface plots of rates of mortality improvement (“ROMI”), which are the derivative of age-specific mortality with respect to time. They have been introduced rather recently. By showing a large set of surface maps for countries from the Human Mortality Database, we argue that those ROMI plots are better able to detect period and cohort effects than standard mortality surface maps.

Surface Plots of Age-Specific Contributions to the Increase in Life Expectancy

Rates of mortality improvement, as presented in the previous two chapters, are an excellent tool to illustrate mortality dynamics. They can not be directly translated to contributions to changes in life expectancy. Using Arriaga’s decomposition approach, we plot maps for selected countries from the Human Mortality Database, showing which ages contributed most to the respective change in life expectanc over time.