Life expectancy improvement for multiple cure distributions

In many circumstances, the increase in life expectancy when certain causes of death are eliminated is sought. These calculations are typically based on the assumption that the causes in question are simply omitted, which is equivalent to the causes being taken out of consideration, from the outset, with certainty. In this paper, we propose models whereby probability distributions for the cures of specific causes of death over time can be incorporated so as to more accurately predict the increase in life expectancy that would ensue. The theoretical results are applied to a real data set involving Diabetes and HIV-related deaths from Denver, Colorado, United States of America, between the years 1990 and 2015 inclusive.