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Separating the Signal From the Noise: Evidence for Deceleration in Old-Age Death Rates

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Demography

Abstract

Widespread population aging has made it critical to understand death rates at old ages. However, studying mortality at old ages is challenging because the data are sparse: numbers of survivors and deaths get smaller and smaller with age. I show how to address this challenge by using principled model selection techniques to empirically evaluate theoretical mortality models. I test nine models of old-age death rates by fitting them to 360 high-quality data sets on cohort mortality after age 80. Models that allow for the possibility of decelerating death rates tend to fit better than models that assume exponentially increasing death rates. No single model is capable of universally explaining observed old-age mortality patterns, but the log-quadratic model most consistently predicts well. Patterns of model fit differ by country and sex. I discuss possible mechanisms, including sample size, period effects, and regional or cultural factors that may be important keys to understanding patterns of old-age mortality. I introduce mortfit, a freely available R package that enables researchers to extend the analysis to other models, age ranges, and data sources.

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Notes

  1. In this article, I use the terms “advanced ages” and “oldest ages” to refer to ages over 80.

  2. Although my focus is on old-age mortality, these models can also be applied to other age ranges.

  3. Jdanov et al. (2008) developed methods to quantify several different ways that age patterns of deaths and population counts can be irregular. The researchers then systematically applied their methods to each cohort in the K-T database, producing comparable indicators for data quality across cohorts. Finally, they summarized their results using hierarchical clustering, producing four tiers of data quality: best, acceptable, conditionally acceptable, and weak.

  4. I also use several R packages, including Daróczi and Tsegelskyi (2015), R Core Team (2014), Wickham (2009), Slowikowski and Irisson (2016), Schloerke et al. (2014), and Wickham et al. (2016).

  5. The distance metric used in Fig. A5 in the online appendix is group average difference in ΔAIC values. Hastie et al. (2009) has more details on hierarchical clustering.

  6. The figure omits the Weibull model, which consistently fit poorly across all countries (Fig. 4).

  7. Section C in the online appendix shows that this conclusion is robust to the choice of AIC, BIC, or cross-validation as the principled model fit technique.

  8. This finding that France and Italy do not fit Gompertzian old-age mortality patterns is confirmed even when other methods of assessing model fit, based on different statistical theories, are considered (online appendix, section C).

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Acknowledgments

The author thanks Vladimir Canudas-Romo, Scott Lynch, Matthew J. Salganik, and three anonymous reviews for helpful comments on early drafts of the manuscript.

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  1. Department of Demography, University of California, Berkeley, 2232 Piedmont Avenue, MC #2120, Berkeley, CA, 94720-2120, USA

    Dennis M. Feehan

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Feehan, D.M. Separating the Signal From the Noise: Evidence for Deceleration in Old-Age Death Rates. Demography 55, 2025–2044 (2018). https://doi.org/10.1007/s13524-018-0728-x

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