Transcript Multiple Decrement Life Tables Multiple Decrement Life Tables • More than one type of exit • Types of exit are mutually exclusive.

Multiple Decrement Life Tables
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 19th 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 nqx 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
i = (n × mi )
q
n x
n x
/ {1 + (n- a )( m
n x n
i
i = q × ( mi / m )
q
n x
n x
n x n x
= nqx × (nDix / nDx)
i = qi × l
d
n x
n x
x
li x = Σ nd i a
-i)}
+
m
x
n x
Dependence
i = (n × mi ) / {1 + (n- a )( mi + m -i)}
q
n x
n x
n x n x
n x
•Holding nmxi constant, the higher nmx-i is the lower nqxi
will be.
•When nmx-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