Lesson 1: Introduction to Multiple-Decrement Life Tables

This lesson will introduce some basic concepts of multiple-decrement life tables. Specifically, the first section (1.1) presents the definition of a multiple-decrement life table, and the second section (1.2) explains the difference between an ordinary life table and a multiple-decrement life table.

1.1 Definitions

 Multiple-Decrement Life Table

A multiple-decrement life table summarizes the life experience of a cohort in which membership can be terminated by two or more attrition factors.

Note that the definition above includes several key terms:

Cohort
A cohort is a group of individuals to whom a certain event occurred at the same period of time.
Examples:
  • birth cohort is a group of people born at the same time (or in the same time interval).
  • marriage cohort is a group of people married at the same time (or in the same time interval).
  • cohort of contraceptive users is a group of individuals who began using contraceptives at the same time (or in the same time interval).
Attrition Factors
Attrition factors are events experienced by individuals of the cohort that make them no longer eligible to be members of the cohort.
Examples:
  • Members of a birth cohort lose their membership in a cohort by death due to different causes. In this case, the attrition factors are causes of death.
  • Members of a marriage cohort lose their membership in the cohort by marital disruption either by separation, divorce, or the death of spouse (widowhood). In this example, the attrition factors are the causes of marital disruption — namely, separation, divorce, and widowhood.
  • Members of a cohort of contraceptors lose their membership in the cohort by stopping use of the method due to various reasons, for example, accidental pregnancy, plan to conceive, or medical reasons. In this example, the attrition factors are the various reasons for terminating the use of the contraceptive.
Life Experience
In a multiple-decrement life table the life experience is measured by the time spent by an individual as a member of the cohort.
Examples:
  • If an individual leaves a birth cohort by death, the life experience of the individual is equal to the length of life.
  • If an individual leaves a marriage cohort by the termination of marriage, then the life experience is measured by the duration of marriage at the time of termination.
  • If an individual leaves a cohort of contraceptors by terminating the use of the contraceptive, the life experience is measured by the duration of use.

Exercise 1
If a cohort is defined as "professional soccer players," and the relevant life experience is defined as starting with the first game played as a professional and ending with the last game played as a professional, which of the following would not be a possible attrition factor?

  1. career-ending injury
  2. retirement
  3. death
  4. all of the above are possible attrition factors

1.2 Difference between an Ordinary Life Table and a Multiple-Decrement Life Table

In an ordinary life table, membership in a well-defined cohort can be terminated by a single attrition factor. In a multiple-decrement life table, there are multiple reasons for attrition.

Ordinary life tables can be used to answer questions about longevity. For example, the ordinary life table can be used to answer the question, "What is the probability that a newborn will survive to age 65?" or the complementary question, "What is the probability that a newborn will die before reaching age 65?"

multiple-decrement life table will be used to answer the question, "What is the probability that a newborn will die due to a specific cause before reaching age 65?"In an ordinary life table of mortality it is assumed that everyone eventually dies. The multiple-decrement life table will provide the probability that a person will eventually die due to a specific cause.

Exercise 2
Which of the following describes the main difference between an ordinary life table and a multiple-decrement life table?

  1. In a multiple-decrement life table, there are multiple attrition factors.
  2. In an ordinary life table, the cohort must be a birth cohort.
  3. In an ordinary life table, the measure of life experience is different from that of a multiple-decrement life table.
  4. In a multiple-decrement life table, the cohort must be a birth cohort.

Answers to Exercises

Exercise 1
If a cohort is defined as "professional soccer players," and the relevant life experience is defined as starting with the first game played as a professional and ending with the last game played as a professional, which of the following would not be a possible attrition factor?

4. All three (career-ending injury, retirement, death) are events that would cause a player to stop being a member of the cohort of professional soccer players.

Exercise 2
Which of the following describes the main difference between an ordinary life table and a multiple-decrement life table?

1. In a multiple-decrement life table, there are multiple attrition factors.

Related Terms
Because the multiple-decrement life table is traditionally used to study causes of death, the table is sometimes called a causes of death life table in studies of mortality.
The traditional statistical literature describes the attrition factors in multiple-decrement life tables as risk factors that are competing to occur in an individual. Such tables are called competing risk tables.

Lesson 2: Causes of Death

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