Longevity à la mode

Abstract

BACKGROUND The modal age at death (mode) is an important indicator of longevity, that is associated with different mortality regularities. Accurate estimates of the mode are essential, but existing methods are not always able to provide them. OBJECTIVE Our objective is to develop a method to estimate the modal age at death, using its mathematical properties, in an assumptions-free setting. METHODSThe mode maximizes the density of the age-at-death distribution. In addition, at the mode, the rate of aging equals the force of mortality. Using these properties, we developed a discrete procedure to estimate the mode. We compare our estimates with those of other models.RESULTS Both the modal age at death and the rate of aging have been increasing since 1960 in low-mortality countries. The method we suggest produces close estimates to the ones generated by the P-splines smoothing. CONCLUSIONSThe modal age at death plays a central role in estimating progress in longevity, quantifying mortality postponement, and estimating the rate of aging. The novel method proposed here allows for a simple and assumptions-free estimation of the modal age at death, which fulfills its mathematical properties and is not computationally demanding.CONTRIBUTION Our research was motivated by James W. Vaupel, who wanted to find a way to estimate the mode based on its mathematical properties as a part of one of his latest research grants. This article also expands on some of his last research papers that link the modal age at death for populations to the one for individuals.