EVALUATION OF DEMOGRAPHIC DATA

Presented By

Andrew Banda

DEM 3210: LEXIS DIAGRAM

DEPARTMENT OF POPULATION STUDIES

UNZA

The two types of Death rate

–Period (Central) Rates: Rates based on a specific calendar time period

–Cohort Rates: Rates based on an experience of people born in a specific calendar period)

Principle of Correspondence

• When we attempt to calculate or estimate rates, it is important to ensure that the events in the numerator correspond with the exposed – to – risk in the denominator.

Principle of Correspondence

• By ‘correspondence’ we mean that, if a person is included in the exposed – to –risk in the denominator and s/he experiences the event during the relevant time period, then the particular event which involves him or her must be included numerator.

Principle of Correspondence

• Conversely, if a person experiences the event during the relevant time period, and the particular event which involves him or her is recorded in the numerator, then s/he must be included in the exposed – to – risk in the denominator.

Principle of correspondence

• Example 1: Someone who dies in the year of interest, but before 30 June, will not be included in the mid-year population calculated, yet that person’s death will be included in the numerator.

Principle of correspondenceExample 2

–Consider someone whose birthday is on 7 September, and who dies on 9 October. Suppose this person is aged x years last birthday on 30 June. Then when he dies he will be aged x + 1 years last birthday.

–He will be included in the denominator of the age-specific rate at age x last birthday, but his death will be included in the numerator of the age-specific rate at age x + 1 years last birthday.

m-type and q-type rates

• m-type rates (Central rates): the exposed-to-risk is an estimate of the number of persons aged x last birthday at the time the event took place.

• The average age of these persons is x + ½ years

• Since they are based on specific calendar time period, hence termed period approach of measuring mortality.

m-type and q-type rates

• q-type rates (initial rates): the exposed-to-risk is defined at the start, or initiation, of the year of age under investigation (that is, when the members of the exposed-to-risk celebrate their xth birthday)

• it follows that they must all have been born during a period of the same length x years earlier.

• Such a group of people is known as a birth cohort, and this approach is called the cohort approach.

Understanding Demographic Events

• Demographic events are determined by;

– Period under which an event occurs

– Age (how long someone lived/something has been there)

– Cohort (which generational group an event or person belong to)

Observing Demographic Events

What is a Lexis Chart?

• A Lexis chart/diagram is an illustrative presentation to clarify relations between exposure segments for cohorts and exposure segments for periods.

What is a Lexis Chart?

• It’s a 2 dimension figure in which AGE and CALENDAR TIME are the main segment types, age is on the vertical axis and time (calendar years) is on the horizontal axis. The units for age and time are usually the same (years)

What is a Lexis Chart?

• Every demographic event is characterized by two numbers: the TIME (e.g., year) at which

it occurs and the AGE (or other duration measure) of the person to whom it occurs

Lexis Chart

Life Lines

• Since people get older as time goes on, the life of any person can be represented on a Lexis chart by a diagonal line running from the horizontal axis until a point which corresponds to the person’s age at death measured on the vertical axis and this is called a “life line”

• The line begins on the time axis at the time of the person’s birth

1995 1996 1997 1998 1999 20000

1

2

3

4

5

A B

Person A: Born on 1/1/1995 to age 3 on 1998 Person B:Born on 1/1/1996 to age 3 year and 6 months on 1/7/1999

Life lines, Example (1)

Life Lines

Life lines, example (2)

Life Lines..

• The sum of all the life line lengths in a particular portion of the diagram represents person-years lived or exposure in that area

• Life lines and events can be considered from a cohort or period perspective

Life Lines

Exposure types

• Cohort Exposure

• Period Exposure

Period and Cohort Observation

Cohort Exposure

• COHORT—A group of persons who experience an event in the same time period, e.g., birth, marriage

• The Lexis diagram can show the experience of a cohort in a particular age interval (A)

• It can also show the experience of a cohort as they move through life (B)

Cohort Exposure

Period Exposure

• Most demographic data are period data

• Square (C) = person-time of exposure at a particular age and period

• A square includes the life lines from experiences of two different cohorts

• Column (D) = experience of all age groups of interest during a specific time period

Period Exposure

Summary Exposure Types

1995 1996 1997 1998 1999 20000

1

2

3

4

5

A-C

C-P

A-P

A-C: Cohort-Age Observation (2 diagonal Parallel lines)A-P: Period-Age Observation (Rectangle)C-P: Period-Cohort Observation (Vertical lines)

Summary of Exposure Types

Calculating Rates from a Lexis Chart

Rates from a Lexis Chart

• B0 (95) - number of Births in 1995

• B1 (95) - Number of first birthdays in 1995

• B1 (96) - Number of first birthdays in 1996

• sD0 (95) - number of deaths at age 0 in 1995 to people who reached age 0 in the same year

• pD0 (95) - number of deaths at age 0 in 1995 to people who reached age 0 in the previous year

• pD0 (96) - number of deaths at age 0 in 1996 to people who reached age 0 in the previous year

Example

• Lets do it together (questions handout)

Solutions …

Calculation of Basic Rates

a. Calculate the Crude Death Rate in 1996

b. Calculate the Crude death rate for the population in 2000 for people below the age of 3 years?

The relationship between the two types of mortality rate

Cont’

• We assume that:

– Mortality only varies with age, and not with calendar time;

– Deaths are evenly distributed across each single year of age.

• on the Lexis chart, within any horizontal band representing the ages between x and x + 1, deaths are evenly distributed.

• This means that the number of deaths is proportional to the area of any portion of the chart.

• Two sections of the chart which both lie within the horizontal band representing ages between x and x + 1 exactly and which have the same area will represent the same number of deaths.

• Since the area of the parallelogram TMWN in Figure 1.6 is equal to the area of the square PQRS, then number of deaths represented by the parallelogram TMWN will also be x.

• The m-type mortality rate, mx, is then given by

• (1.1)

A Final Note….

“I never guess. It is a capital mistake to theorize before one has data.

Insensibly one begins to twist facts and theories, instead of theories to suit facts.”

--Sir Arthur Conan Doyle

Thank you!