gms | German Medical Science

Life expectancy or remaining lifetime is an essential concept in the analysis of mortality in epidemiology or demography. It comes with the advantage of being communicated on the absolute time scale, e.g. age scale. Common summary measures for the remaining lifetime, conditional upon having survived until a certain age, are mean and median residual lifetimes. However, the modal remaining lifetime, that is, the remaining time to the most probable time of death might also be a comprehensive and easy-to-communicate measure [1]. Indeed, the modal age at death has been termed “the most central and natural characteristic of human longevity” as early as 1878 [2].

We introduce the idea of modal residual lifetime and show a surprisingly general linearity property of it: For each and every possible age-at-death distribution with existed modal value, the modal residual lifetime decays linearly with slope -1 for every year survived. Admittedly this comes with the disadvantage that modal residual lifetime is only defined until the mode of the age-at-death distribution is reached.

We illustrate the modal residual lifetime with data from all statutory health-insured persons in Germany in that were aged 30 years or older and were diagnosed or free from type 2 diabetes in 2013. As we observed previously that, the involved age-at-death distributions follow nearly perfectly Gompertz distributions [3] we use the Gompertz distribution to compare the differences in modal age at death for persons without and with diabetes. The modal age at death for women without diabetes is 90.22 [90.11, 90.35] and with diabetes is 86.08 [85.94, 86.22]. Respectively for men without diabetes is 86.32 [86.25, 86.38] and with diabetes is 80.74 [80.64, 80.88].

The modal residual lifetime extends the familiar concept of the mean and median residual lifetime by another measure of central tendency for the distribution of residual lifetime. The modal value is not only easy to interpret, but it also provides important statistical advantages and could be more widely used in describing mortality in epidemiology or clinical research.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.