demography ch3

DEMOGRAPHY III Statistics , AC 2014/15

Demography CH 3 A.R.Muralidharan, Asst. Prof. in statistics WU

DEMOGRAPHY

3. Mortality3.1.Concepts and data requirements of death statistics3.2. Percentage distribution of death3.3.Basic Mortality measures

3.3.1. Crude death rate3.3.2. Specific death rates3.3.3. Age specific death rates (ASDR)3.3.4. Graphical presentation of ASDR

3.4.Standardization methods3.5.Conventional infant mortality rates3.6.Maternal death rate3.7.Life tables

3.7.1. Types of life tables3.7.2. Life tables functions3.7.3. Construction of a simple life table3.7.4. Interpretation of a simple life table

3.0. Mortality

In demography, mortality is related to Death. It is a principal “Vital event” for which vital statisticsare collected and complied by the vital statistics registration system (VRS). The purposes of deathstatistics in demography are

1. Analysis of the present demographic status of the population as well as its potential growth2. Filling the administrative and research needs of public health agencies in connection with

the development, operation and evaluation of public health programs3. Determination of administrative policy and action in connection with the programs of

government agencies other than those concerned with public health4. Filling the need for information on population changes in relation to numerous professional

and commercial activities;

Death analysis are very much important in making analysis of past population changes which arerequired for making projections of population and other demographic characteristics

3.1.Concepts and data requirements of death statistics

Concepts:

It is necessary to gain knowledge about mortality. Mortality is one of the vital events.

The UN and WHO have proposed the following definition of “”Death”

“Death is the permanent disappearance of all evidence of life at any time after birth has takenplace”.



A death can occur only after a live birth has occurred. This definition of death can be easilyunderstandable. The definition of a “death” excludes deaths prior to birth that is so-called fetaldeath. A fetal death is formally defined as ”Death” prior to the complete expulsion or extractionfrom its mother of a product of conception irrespective of duration of pregnancy. The death isindicated by the fact that after such separation the fetus does not breathe or show any otherevidence of life such as beating of the heart, pulsation of the umbilical cord or definite movement ofvoluntary muscles. The term fetal dath is employed in present demographic practice to differencethe other deaths such as stillbirth, miscarriages, and abortions in popular, medical and legal usages.

The term stillbirth is defined as a death that occurs in the duration of 20 or 28 weeks of gestation ormore. This term is employed in the place of late fetal deaths.

The term Miscarriage is defined as spontaneous or accidental terminations of fetal life occurringearly in pregnancy.

The term abortion is popularly used to refer to induced early fetal deaths, including both thosewhich are legal or illegal. In medical usage, an abortion is the expulsion of the fetus prematurely,particularly at any time be for it is visible or capable of sustaining life. From a technical point of viewthe terms abortion and miscarriage can be hard to distinguish.

The recommendation of UN and WHO is to group all of these events : miscarriage and abortion aswell as still births under the heading of “Fetal Death” and to classify them as early, intermediate andlate according to the months of gestation.

Data requirements of death statistics

The basic data on deaths for mortality studies, for the statistically developed areas , come from vitalstatistics registration systems and less commonly, from national population register systems. Theanalysis of death statistics from the vital statistics registration depends on the availability ofappropriate population data from a census or survey or population estimates to be used as bases forcomputing rages of various kinds. This dependence on a second data collection is avoided where anadequate national population register system is in effect.

The VRS is likely to be inadequate in the underdeveloped countries: for these areas, other sources ofdata for measuring morality have to be considered. The principle alternative sources are

1. National census and2. National sample surveys.

Census data and sample surveys may provide

a. Data on age composition on recent mortality andb. Direct data on mortality



3.2.Percentage distribution of death

A distribution of deaths by age is percentage distribution of death. It has a pattern based on thedeath data. It is described as in x-axis with age and in y- axis percentage of deaths in the givenregion or area or country.

A combination of high rates and large proportion of children in the population as occurs in manyunder developed countries, results in a tremendous proportion of deaths among children under age5. On the other hand, in certain developed countries the proportion of deaths of young children isvery small.

3.3.Basic Mortality measures3.3.1. Crude death rate (C.D.R)

It is the simplest of all the indices of mortality. It is defined as “the number of deaths per K personsin the population of any given region or community during a given period”. Thus in particular theannual Crude death rate denoted by m for any given region or community is given by= where k = 1000 usually

The CRD for any period gives the rate at which the population is depleted through deaths over thecourse of the period.

The midyear population is employed as an approximation to the average population “exposed torisk” of death during the year. The midyear population may approximated by combining data onbirths, deaths and immigration for the period between the census date and the estimated date withthe count from the last census, as an arithmetic or geometric mean of the population estimateddirectly on the basis of these components for two successive dates usually it will be January 1 and inother ways.

Crude death rates may be computed for any period, but typically they are computed for the calendaryear or the “Fiscal year”. That is the 12 month period from July1 to June 30.

In the latter case, the population figure should relate to January 1 of the fiscal year. Crude deathrates are calculated for 12 month periods such as calendar years or fiscal years so as to eliminate theeffect of seasonal or monthly variations on the comparability of the rates.

Merits and demerits

Merits

1. It is simple and easy to calculate2. CRD is perhaps the most widely used of any vital statistics rates3. By CDR is a probability that a person belonging to the given population will die in the given

period



Demerits

1. It ignores the age and sex distribution of the population2. CDR is not suitable for comparing the mortality in two places.

Remark

We can compute the CDR for males and females separately.

For male the formula: 1000 where mD is number of male deaths and mP is male population in

the given region during the given period. Similarly for female the formula is 1000CDR usually lies between 8 and 30 per thousand and female CDR is generally less than male CDR.

3.3.2. Specific death rates

The CDR gives only a very general indication of the level of mortality and its changes In other wordswhile computing CDR, there was a drawback that it ignores the age and sex of the population. Thereis also need for measures that describe the specific components of the overall number of deaths andthe crude rate. Various types of specific death rates are interest in the analysis. To overcome thisdrawback we must need a more useful figure than CDR, we must take into the fact that the mortalitypattern is different in different segments of the population. Various segments may be age, sex,occupation, etc.,

Death rate computed for a particular specified section of the population is termed as specific deathrate (SDR). SDR for given geographical region during a given period is

SDR =

Usually SDR is computed specific to age and sex.

3.3.3. Age specific death rates (ASDR)

As we know age is the most important variable in the analysis of mortality. Most tabulation ofdeaths requires cross- classification with age if they are to be useful. The tabulations of deaths byage are subject to a number of deficiencies. The principal ones are substantial and variable under-registration of deaths by age, extensive misreporting of the age of the decedent, and an excessiveproportion of “age not stated”. Reporting of age decedents among the extreme aged is believed tobe quite inaccurate.

The principle way of measuring the variation in mortality by age is in terms of age-specific deathrates.

An ASDR is defined conventionally as the number of deaths of persons of a given age during a yearper1000 of the midyear population at the age.

ASDR = 1000



To formulate the ideas mathematically,

Let = Number of deaths in the age group (x, x+n)=total opulation of the age group (x, x+n)

The age-specific death rate for the age group(x,x+n) denoted by

Then = 1000Merits and Demerits

Merits

1. SDR provide more appropriate measures of the relative mortality situation in the regions2. It is the one of the most important and widely applicable types of death rates3. It useful in construction of life table4. It supplies one of the essential component required for the computation of Net

reproduction rate

Demerits

1. It is not much useful for overall comparison of mortality conditions2. SDR completely ignore differential mortality3.3.4. Graphical presentation of ASDR(Refer percentage distribution)3.4.Standardization methods

The procedure to adjustment of crude rates to eliminate from them the effect of differences inpopulation composition with respect to age and other variables is sometimes referred as“Standardization”.

Death rates are adjusted or standardized for both age and sex, even for variables for which deathrates may be adjusted or standardized are racial composition nativity composition, urban-ruralcomposition etc. it is important to recognize that age-adjusted or age-standardized rate have nodirect meaning in them. They are meaningful only in comparison with other similarly computedrates.

A number of methods have been developed for adjusting death rates for age composition or forderiving indexes of age adjusted rates

1. Age-adjusted death rate by direct method2. Age-adjusted death rate by indirect method.3. Comparative mortality index and4. Life table death rate.



Direct standardization

This method is simplest and most straight forward measure. For most comparisons, this is the mostpreferred procedure and serves to provide the best basis for determining the relative differencebetween mortality in two areas or at two dates.

In this method, a standard population is selected and employed in deriving all the age-adjusted ratesin a set to be compared. The formula for this measure is= ∑ 1000

Where = = − ℎ ℎ ;= ℎ ℎ ∑ = ℎEach age specific rate is multiplied by the proportion of standard population in each age group. Theage-specific death rate for the standard population is the same as its own crude death rate, since theage-specific death rates for the standard population would be weighted by its own population. Therelative mortality of the given area is derived by dividing the age-standardized rate for the area bythe crude death rate of the standard population.

The steps in calculating the age-adjusted death rate by the direct method is

1. Record the population in each age group for the standard population.2. Record the age-specific death rate for the area to find3. Compute the cumulative product of the population of standard population and death rate

for the area to find4. Divide the result of cumulative product of the population of standard population and death

rate for the area to find by the total population of standard population.

There are a number of possible choices with respect to the selection of the standard to be used incomputing the age-adjusted death rate by the direct method. The standard selected may be the agedistribution of one of the areas or dates being compared, or the sum or average of the agedistributions for the areas or dates being compared or an “External” real or theoretical distribution

Standardization

Direct


Demography CH 3 A.R.Muralidharan, Asst. Prof. in statistics WU Page 6










Standardization

Indirect


Demography CH 3 A.R.Muralidharan, Asst. Prof. in statistics WU Page 6












of some sort. Different result for the relative differences between adjusted rates will be obtaineddepending on the age distribution selected as a standard. In fact, the choice of standard may evenaffect the direction of the difference between the rates for the populations being compared. Hence,it is desirable to select the standard population carefully. The general rules to select as a standard anage distribution that is similar to the age distributions of the various populations under study. If themortality of two populations is being compared, this may be achieved by using a standard un-weighted average of the two distributions.

The need for age-adjustment is particularly great in connection with cause-specific death rates.Certain causes of death are concentrated in one or another part of the age distribution. Hence thelevel of the observed death rate from these causes is particularly affected by the age distribution ofthe population.

Indirect standardization

Since calculation of the age-adjusted death rate by the direct method requires age-specific deathrates or death by age for the area under study. These may not be available even though a count orestimate of the total number of deaths and an estimate of the crude death rate are at hand. In thiscase, if counts or estimated of the age distribution of the population are also available, it is possibleto adjust the death rate by an indirect method. The formula for indirect standardization is

= ∑Where , for the standard populationℎ ℎ ; ℎ ℎℎ ℎThis formula calls for adjusting the CDR of the standard population by a factor representing the ratioof the recorded number of deaths to the number expected on the basis of the age-specific deathsrates for the standard population.

The steps in calculating the age specific death rate by indirect standardization method is

1. Set down the age-specific death rates for standard population2. Set down the population by age for the given area3. Compute the cumulative product of death rates in step1 and step 2. This number of death

expected on the basis of the age specific death rates in standard population4. Divide the result in step 3 into the total number of deaths registered in given area5. Multiply the result in step 4 by CDR of standard population to derive the adjusted death

rate.



3.5.Conventional infant mortality rates

Analysis of infant mortality has commonly been carried out in terms of the “Infant mortality rate”rather than the infant death rate, in order to approximate the probability of death among infants ina given year. The accuracy of the approximation varies from one situation to another but depends ingeneral on the annual fluctuations in the number of births. This is termed to be “Conventional InfantMortality Rates” (CIMR).

The term CIMR is defined as “ the number of infant deaths per year per 1000 live birth during theyear.

CIMR = 1000 −deaths of infants during a year and B-live birth during the same year.

The CIMR gives a sufficiently close approximation to the chance of dying between birth andattainment of the first birthday for the year to which the basic data on deaths relate. It has beenwidely used as an indicator of the health conditions of a community and hence of its level of livingalthough it may not be particularly appropriate for this purpose in “developed” areas.

3.6.Maternal death rate

In Ethiopia Maternal mortality rate: 350 deaths/100,000 live births (2010)

The definition of maternal death is:

"The death of a woman while pregnant or within 42 days of termination of pregnancy,irrespective of the duration and the site of the pregnancy, from any cause related to oraggravated by the pregnancy or its management, but not from accidental or incidentalcauses."

In other words Definition of the maternal mortality rate (MMR) is the annual number offemale deaths per 100,000 live births from any cause related to or aggravated bypregnancy or its management (excluding accidental or incidental causes). The MMRincludes deaths during pregnancy, childbirth, or within 42 days of termination ofpregnancy, irrespective of the duration and site of the pregnancy, for a specified year.

The four measures of maternal death are the maternal mortality ratio (MMR), maternalmortality rate, lifetime risk of maternal death and proportion of maternal deaths amongdeaths of women of reproductive years (PM).

Maternal mortality ratio (MMR): the ratio of the number of maternal deaths during a giventime period per 100,000 live births during the same time-period.[1] The MMR is used as ameasure of the quality of a health care system.

Maternal mortality rate (MMRate): the number of maternal deaths in a population dividedby the number of women of reproductive age, usually expressed per 1,000 women.

Lifetime risk of maternal death: refers to the probability that a 15-year-old female will dieeventually from a maternal cause if she experiences throughout her lifetime the risks ofmaternal death and the overall levels of fertility and mortality that are observed for a



given population. The adult lifetime risk of maternal mortality can be derived using eitherthe maternal mortality ratio (MMR), or the maternal mortality rate (MMRate).

Proportion of maternal deaths among deaths of women of reproductive age (PM): thenumber of maternal deaths in a given time period divided by the total deaths amongwomen aged 15–49 years.

Approaches to measuring maternal mortality includes civil registration system, householdsurveys, census, reproductive age mortality studies (RAMOS) and verbal autopsies.

At a country level, India (19% or 56,000) and Nigeria (14% or 40,000) accounted forroughly one third of the maternal deaths in 2010.Democratic Republic of theCongo, Pakistan, Sudan, Indonesia, Ethiopia, United Republic ofTanzania, Bangladesh and Afghanistan comprised between 3 to 5 percent of maternaldeaths each. These ten countries combined accounted for 60% of all the maternaldeaths in 2010 according to the United Nations Population Fund report. Countries withthe lowest maternal deaths were Estonia, Greeceand Singapore.

According to the 2010 United Nations Population Fund report, developing nationsaccount for ninety-nine percent of maternal deaths with majority of those deathsoccurring in Sub-Saharan Africa and Southern Asia. Globally, high and middle incomecountries experience lower maternal deaths than low income countries

3.7.Life tables

In demography, a life table (also called a mortality table or actuarial table) is a table whichshows, for each age, what the probability is that a person of that age will die before his orher next birthday ("probability of death"). From this starting point, a number of inferences canbe derived.

the probability of surviving any particular year of age

remaining life expectancy for people at different ages

There are two types of life tables:

Period or static life tables show the current probability of death (for people of differentages, in the current year)

Cohort life tables show the probability of death of people from a given cohort (especiallybirth year) over the course of their lifetime.

Static life tables sample individuals assuming a stationary population with overlappinggenerations. "Static Life tables" and "cohort life tables" will be identical if population is inequilibrium and environment does not change. "Life table" primarily refers to period lifetables, as cohort life tables can only be constructed using data up to the current point, anddistant projections for future mortality.

Life tables can be constructed using projections of future mortality rates, but more often theyare a snapshot of age-specific mortality rates in the recent past, and do not necessarilypurport to be projections. For these reasons, the older ages represented in a life table may



have a greater chance of not being representative of what lives at these ages mayexperience in future, as it is predicated on current advances in medicine, public health, andsafety standards that did not exist in the early years of this cohort.

Life tables are usually constructed separately for men and for women because of theirsubstantially different mortality rates. Other characteristics can also be used to distinguishdifferent risks, such as smoking status, occupation, and socioeconomic class.

Life tables can be extended to include other information in addition to mortality, for instancehealth information to calculate health expectancy. Health expectancies such asdisability-adjusted life year and Healthy Life Years are the remaining number of years a person canexpect to live in a specific health state, such as free of disability. Two types of life tables areused to divide the life expectancy into life spent in various states:

Multi-state life tables (also known as increment-decrements life tables) are based ontransition rates in and out of the different states and to death

Prevalence-based life tables (also known as the Sullivan method) are based on externalinformation on the proportion in each state. Life tables can also be extended to show lifeexpectancies in different labour force states or marital status states.

3.7.1. Types of life tables

Life tables differ according to the reference year or the table, the age detail and number of factorscomprehended by table. There are two types of life tables according to the reference year of thetable.

a. The current period or period life table andb. Cohort life table.

The first type of table is based on the experience over a short period of time, such as a year, threeyear or an intercensal period, in which mortality has remained substantially the same. The deathstatistics used for a current life table relate to the period of one to three years, and the populationdata use relate to the middle of that period. By this table, the combined mortality experience by ageof the population in a particular short period of time; it does not represent the mortality experienceof an actual cohort. It assumes a hypothetical cohort that is subject to the age-specific death reatesof served in the particular period. Therefore a current life table may be viewed as a “Snapshot” ofthe current mortality. It is an excellent summary description of mortality in a year of a short period.

The second type of life table, the generation life table, is based on the mortality rates experiencedby a particular birth cohort. (eg: all persons born in the year 1900). According to this type of table,the mortality experience of the persons in the cohort would be observed from their moment of birththrough each consecutive age in successive calendar year until all of them die. Obviously, data overa long period of year are needed to complete a single table and it is not possible wholly on the basisof actual data to construct generating tables for cohorts born in this century. This type of table



useful for projections of mortality, for studies of mortality trends, and for the measurement offertility and reproductivity.

Again life tables are also classified into two types according to the length of the age interval in whichthe data are presented.

a. Complete andb. Abridged

A complete life table contains data for every single year of age from birth to the last applicable age.An Abridged life table, on the other hand contains data by intervals of 5 or 10 years of age. Thesimple abridged life table is usually prepared rather than the more elaborate complete life table.Values for 5 or 10 years interval are sufficiently accurate for most purposes and the abridged table isless burdensome to prepare and it is more convenient to use. Sometimes it is observed or presentedthat the basic values from a complete life table are presented only for every fifth age in order toeconomize on space.

We may also distinguish a standard life table, which is concerned only with the general mortalityexperience of a cohort by age, from a multiple decrement table, which describes the separate andcombined effects of more than one factor. Mortality is always involved. Multiple decrement tablesare in several forms. The mortality factors may be applied in terms of component death rates ormortality may be combined with change in one or more socio economic characteristics of thepopulation.

3.7.2. Life tables functions

The basic life table’s functions are

S,No Functions Explanation1 X Age

2 Is the number of persons living at any specified age x in any year out of an assumed number ofbirths. usually called the cohort or radix of the life table.

3 Is the number of persons among the persons who die before reaching the age (x+1)

4 Is the probability that a person of exact age x will die within one year following the attainmentof that age,

5 The probability that a person aged x survives up to age x+n.

6 The central mortality rate, is the probability that a person whose exact age is not known but liesin between x and (x+1)

7 The force of mortality at age x, a ratio of instantaneous rate of decrease in ℎ8 Is the number of years lived in the aggregate by the cohort of persons between age x and

(x+1)9 Is the total number of years lived by the cohort after attaining the age x

10 Complete expectation of life, the average number of years a person of given age can beexpected to live under the prevailing mortality conditions.

11 Crude expectation of life, the average number of complete years of life lived by the cohortafter age x by each of persons attaining that age.

The above discussed functions are generally calculated and used for life tables. However in somecases due to limitations of space, some of the columns may be omitted. This is done without asignificant loss of information since the functions are interrelated and some can be directlycalculated from the others. In general, the mortality rate is the basic function in the table, that is theinitial function from which all other life table functions are derived.



3.7.3. Construction of a simple life table

The complete life table can be constructed if we can compute the quantities for all ≥ 0. Theonly other data which is needed is the radix . he column is called the pivotal column of the lifetable.

3.7.4. Interpretation of a simple life table

Life table functions are subject to two different interpretations depending on the interpretationgiven to the life table as a whole. In more common practice, the life table is viewed as depicting thelifetime mortality experience of a single cohort of new born babies, who are subject to the age-specific mortality rates on which the table is based. In second interpretation of the life tables isviewed as a stationary population resulting from the unchanging schedule of age-specific mortalityrates shown and a constant annual number of births.

a. The life table as the mortality experience of a Cohort:

Under this first interpretation the life table model conceptually traces a cohort of newborn babiesthrough their entire life under the assumption that they are subject to the current observedschedule of age-specific mortality rates. The Cohort of new born babies called the radix of the table,is usually assumed to numbers 100,000. In this case, the interpretation of the life table functions inan abridged table would be as follows:

X to x+n: the period of life between two exact ages.

: the proportion of the persons in the cohort alive at the beigining of an indicated age interval (x)who will die before reaching the end of that age interval (x+n)

: The number of persons living at the beginning of the indicated age interval (x) out of the totalnumber of births assumed as the radix of the table.

: The number of persons who would die within the indicated age interval (x,x+n)out of the totalnumber of births assumed in the table.

: the number of peron-yearsthat would be lived within the indicated age interval (x,x+n) by thecohort of 100,000 new born babies.

: the total number of person-years that would be livied after the beginning of the indicated ageinterval by the cohort of 100,000 births assumed.

: The average remaining lifetime in years for a person who survies to the beginning of theindicated age interval. This function is also called the complete expectation of life or simply lifeexpectancy.

The interpretation of the function in a complete life table is the same as in the abridged table exceptthat , , − . ℎ , values have thesame interpretation as in the abridged table since they are not “Interval” values but pertain to exactage x.



b. The life table as a Stationary population:

An alternate interpretation of life table is the one associated with the concept of a stationarypopulation. A stationary population is defined as a population whose total number anddistribution by age do not change with time. Such, a hypothetical population could be obtainedif the number of births per year remained constant (usually assumed at 100,000) for a longperiod of time and each cohort of births experienced the current observed mortality ratesthroughout life. The annual number of deaths would thus equal 100,000 also and there would beno change in the size of the population. In this case, the interpretation of x to x+n, , and

would be as previously indicated, but for the other life table functions it would be as follows:

: The number of persons who reach the beginning of the age interval each year. Thus if birthsremained constant at 100,000 per year.

: The number of persons that die each year within the indicated age interval. Thus if birthsremained constant at 100,000 per year.

: The number of persons in the population who at any moment are living within the indicatedage interval. Thus if births remained constant at 100,000 per year.

: The number of persons in the population who at any moment are living within the indicated ageinterval and all higher age intervals.

Each interpretation has its particular application. The interpretation of the life table as a stationarypopulation is used in the comparative measurement of mortality and in studies of populationstructure.

c. Life Span and Life expectancy

In measuring longevity two concepts should be distinguished- life span and life expectancy.

The first concept tries to establish numerically the extreme limit of age in life. That is the maximumage that human beings as a species could reach under optimum conditions. There is no known exactfigure for this concept. For purposes of defining the concept more precisely and of excluding rarecases, we might define life span as the age beyond which less than about 0.1 percent of the originalcohort lives.

demography ch3

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