Life Expectancy Improvement with a Cure Distribution for a Cause of Death

In many circumstances, the increase in life expectancy when a certain cause of death is eliminated is sought. Traditionally, these calculations have been based on the assumption that the cause in question is simply omitted, which is equivalent to the cause being taken out of consideration, from the outset, with certainty. In this paper, we propose continuous and discrete models whereby a probability distribution for the cure of a specific cause of death over time can be incorporated so as to more accurately predict the increase in life expectancy. The theoretical results are applied to a real data set involving HIV-related deaths from the State of Colorado, United States of America, between the years 2000 and 2012