Notation & key assumptions

The development of cause-deleted life tables requires the strong assumption that causes of death act independently. More specifically, this means that removing a cause of death leaves the hazards from all other causes unchanged. While it is clear that this assumption may be untenable in some circumstances (think, for example, of the interactions between diabetes and cardiovascular disease or TB and HIV), it is reasonably accurate for many other conditions.

Note that this assumption about the independence of cause-specific mortality hazards bears no relation to the competing risks property that we discussed earlier, i.e., the fact that the probability or risk of dying from a particular cause are dependent on the mortality hazards from all other causes.

Cause-deleted or associated single decrement life table functions are usually denoted with a '*'.

interaction Can you match each of the following quantities to their definitions by clicking on the table cells?

  *nmx-i *nqxi *5p30-i *5L75i *e0-i *e20-i – e20
The probability of surviving the age interval 30-35 after deletion of cause i
 
 
 
 
 
 
The anticipated gains in life expectancy at age 20 resulting from the deletion of cause i
 
 
 
 
 
 
The person-years lived between ages 75-80 if i were the only decrement operating in the population
 
 
 
 
 
 
Age-specific death rate in the absence of cause i
 
 
 
 
 
 
The life expectancy at birth after deletion of cause i
 
 
 
 
 
 
The associated single decrement age-specific probability of dying, or, the probability of dying from cause i in the age interval x, x+n if i were the only decrement operating in the population