Multiple Decrement Life Tables

More than one type of exit Types of exit are mutually exclusive and exhaustive “Competing risks”

Problems that MDLTs can address: What is the probability that a 20 yr old will eventually die of heart disease? How many years does cancer subtract from our life expectancy? What would have been the effect of eliminating smallpox in 19 th century UK?

Cohort MDLT Example in text, p.74

Creating a period MDLT (See Box 4.1 on p. 77) 1.Prepare a basic life table 2.Take the n q x series from that table and apportion it to various causes of decrement 3.Compute the number of decrements from cause i in each interval 4.Compute the number of persons aged x* who will eventually leave the table from cause i.

Notation n q i x = (n × n m i x ) / {1 + (n- n a x )( n m i x + n m x -i )} n q i x = n q x × ( n m i x / n m x ) = n q x × ( n D i x / n D x) n d i x = n q i x × l x l i x = Σ n d i a

Dependence n q i x = (n × n m i x ) / {1 + (n- n a x )( n m i x + n m x -i )} Holding n m x i constant, the higher n m x -i is the lower n q x i will be. When n m x -i is higher, more of the potential victims of i will be carried off by other causes in the interval.

What if? Associated single decrement life tables –Cause-deleted life tables –Section 4.4 provides detailed description of pros and cons of various approaches BOX 4.2, p. 85