Threshold ages for the relation between lifetime entropy and mortality risk (Q2021328)

This work is related to the study, which examines the effect of averting deaths on life disparity measured by life expectancy lost due to death. In this study showed that there exist, under general conditions on Keyfitz's entropy of the life table, a unique threshold age below which averting deaths reduces life disparity, and above which averting deaths increases life disparity. The existence and characterization of that unique threshold age is also studied recently but the author's our approach differs on three main grounds. First, it's focused on the effect of a change in mortality on risk about the duration of life not measured by means of lifetime disparity as measured by life expectancy lost due to death, but by means of Shannon's lifetime entropy index defined to the base 2. Second, at the technical level, the framework is in discrete time rather than in continuous time, which makes the identification of threshold ages more difficult to prove analytically. Third, at the level of results, authors identify, on the contrary, not one, but two threshold ages, by making assumptions on the pattern of age specific mortality. In addition, they show that there exists also another, lower threshold age, below which a rise in mortality reduces lifetime entropy. The authors show that this low threshold age, which was equal to 6 years in the early 19th century, has turned out to vanish to age 0 in the second half of the 20th century, leaving us with a unique threshold age, below which a rise in mortality raises lifetime entropy, and above which a rise in mortality reduces lifetime entropy.