Multiple Decrement Life Tables

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Multiple Decrement Life Tables
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Multiple Decrement Life Tables

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

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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?

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Cohort MDLT

• Example in text, p.74

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Creating a period MDLT(See Box 4.1 on p. 77)

• Prepare a basic life table
• Take the nqx series from that table and apportion
  it to various causes of decrement
• 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.

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Notation
nqix (n nmix ) / 1 (n-nax)(nmix
nmx-i) nqix nqx (nmix / nmx )
nqx (nDix / nDx) ndix nqix lx lix S
ndia
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Dependence

• nqix (n nmix ) / 1 (n-nax)(nmix nmx-i)
• 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.

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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