Why do lifespan variability trends for the young and old diverge? A perturbation analysis

Abstract

BACKGROUNDVariation in lifespan has followed strikingly different trends for the young and old: while total lifespan variability has decreased as life expectancy at birth has risen, the variability conditional on survival to older ages has increased. These diverging trends reflect changes in the underlying demographic parameters determining age-specific mortality.OBJECTIVEWe ask why the variation in the ages at death after survival to adult ages has followed a different trend than the variation at younger ages, and aim to explain the divergence in terms of the age pattern of historical mortality changes.METHODSUsing simulations, we show that the empirical trends in lifespan variation are well characterized using the Siler model, which describes the mortality trajectory using functions representing early-life, later-life, and background mortality. We then obtain maximum likelihood estimates of the Siler parameters for Swedish females from 1900 to 2010. We express mortality in terms of a Markov chain model, and apply matrix calculus to compute the sensitivity of age-specific variance trends to the changes in Siler model parameters.RESULTSOur analysis quantifies the influence of changing demographic parameters on lifespan variability at all ages, highlighting the influence of declining childhood mortality on the reduction of lifespan variability, and the influence of subsequent improvements in adult survival on the rising variability of lifespans at older ages.CONCLUSIONSThese findings provide insight into the dynamic relationship between the age pattern of survival improvements and time trends in lifespan variability.

Decomposing changes in life expectancy: Compression versus shifting mortality

“…In general, increasing β t will lead to a smaller variability of the age at death, while increasing M t would have the opposite effect. These results are consistent with the results of Engelman, Caswell, and Agree (2014). Using a Siler model, the authors show that a decrease in the timing parameter for senescent mortality (α 2 ) will increase the variability (Engelman, Caswell, and Agree 2014).…”

“…These results are consistent with the results of Engelman, Caswell, and Agree (2014). Using a Siler model, the authors show that a decrease in the timing parameter for senescent mortality (α 2 ) will increase the variability (Engelman, Caswell, and Agree 2014). However, Table 6 and Figure 6 show that this variability expansion resulting from a shift in M t will generally be too small to drive substantial changes in lifespan disparities.…”

“…Vaupel, Zhang, and van Raalte (2011) report relatively stable variability patterns for survivors beyond age 50 in the last 100 years. Engelman, Caswell, and Agree (2014) and Engelman, Canudas-Romo, and Agree (2010), however, provide evidence for a modest expansion of lifespan variability for survivors at older ages, resulting from mortality improvement at these same ages.…”

“…Canudas-Romo (2010) analytically demonstrated that, in a mortality declining scenario, as the one experienced in developed countries, the mode will be maintained when reduction of mortality occurs at younger ages than the modal age at death. Using a Siler model, Engelman, Caswell, and Agree (2014) showed that improvement in childhood components of mortality (α t and b t ) and in background mortality parameter (c t ) influenced lifespan variability reduction. The first four terms of the above equation would then have an impact on variability reduction.…”

Taylor's power law in human mortality

“…Among these indices are, for instance, simple measures such as the variance, the standard deviation or the interquartile range, but also more complex measures such as e † (Vaupel and Canudas Romo 2003). Engelman, Caswell, and Agree (2014) point out that the variation of longevity declined in highly developed countries, but they also show that the variability regarding the progress of relatively high survival improvements in older ages persists in those countries.…”