# International Futures Help System

## Mortality probabilities

IFs allows the user to compute the probability that a person of a given age (e.g. 15) will live to reach another age (e.g. 60)–to compute it look for under the Display Type Options on the specialized display for a J-curve (there are probabilities and rates for children and adults). In this example, the probability of a 15-year old dying before she reaches 60 equals 1 minus the cumulative probability of surviving (lx) to 59 given that she has survived to 15:

P(15-59) = 1 – lx(59) / lx(15)

In order to compute lx at age j we need to consider the cumulative effect of the previous age category and the probability of death in the current age category (nqx). Lx(0) is assumed to be 1, given that we are only considering deaths for people that are born alive:

lx(j) = lx(j-1) * (1 - nqx)

The probability of death at the current category is computed based on the mortality of the age category nMx, the number of years in the given category N (5 for most of the IFs age categories), and the average years lived within the same category nax, which in most cases is 2.5, but can be lower for shorter age categories:

nqx = (N * nMx) / (1 + ((N - nax) * nMx))

This adjustment is necessary because nMx is the mortality rate of the 5 year period (which is not the same for each of the 1 year periods within it). The mortality rate nMx already considers that some people die in the middle of the period, which we don’t need for the probability nqx, which is why in general probabilities are lower than mortality rates and more pertinent for older ages where people tend to die earlier in the age category.

Although the infant age category covers a shorter age range, the rate correction is in some ways a bigger issue because infants tend to die within the first days of life. The basic framework for understanding nax in this category is thus that the higher the mortality, the higher the average years lived nax. In a highly developed country such as Sweden, nearly all infant mortality takes place in the neonatal period (so nax is almost = 0). Alternately, in a country such as the Congo, infant mortality takes place throughout the year (though it is still concentrated in the neonatal period) and nax rises fairly consistently with nMx. This has been implemented in the following way:

Average years lived by those who die (per Keyfitz) for Infants

If nMx >= 0.107 Then

nax = 0.34

Else

nax = 0.049 + 2.742 * nMx

When estimating nax for children aged between 1 and 4, the logic becomes that child deaths between age 1 and 5 are a prolonged extension of infant mortality. Estimations have thus shown that nax is more directly tied to infant mortality than it is to nMx for its own age category. In other words, countries with very high infant mortality also experience elevated child mortality, mostly concentrated in the 1 - 2 age range. Thus as infant mortality rises so does child mortality, pulling nax away from 2:

Average years lived by those who die (per Keyfitz) for children 1 to 4

If infMort >= 0.107 Then

nax = 1.356

Else

nax = 1.587 - 2.167 * infMort