9 Some Demographic Topics

Transcription

1 9 Some Demographic Topics 9.1 Single Figure Indices How do we compare the mortality eperience of two or more populations? A single figure that summarises the mortality eperience of a population enables easy comparison. Single Figure indices are formulas for calculating such a single figure: Notes on single figure indices: theyareeasytoassimilate,ratherthanarangeofage-specificrates;but thereisalossofinformationinsummarisingandsocareneedstobetakeninthe construction and application of the indices 286

2 Crude Death Rate(CDR) Where: CDR = = Total deaths Total eposure d E c In the handout eample we have: d = numberofdeathsinagegroup E c = populationinagegroup RegionA: CDR = 175 7,900 = RegionB: CDR = 267 7,900 =

3 Country: CDR = 5, ,000 = Notes: (a) CDR = = d E c ( = E c d E c Total population E c Total population ) µ = w µ Hence, the CDR is a weighted average of the age-specific forces of mortality, where the weights reflect the population structure. (b) Strengths of the CDR: CDRiseasytocalculate 288

4 thedatarequirementsareminimal(justthetotaldeathsandthetotal population). (c) Weaknesses of the CDR: CDRisheavilyinfluencedbytheagestructureofthepopulation. In the handout eample the CDRs imply that: RegionBhasheaviermortalitythanRegionA Both regions have heavier mortality than the country However, the age specific mortality indicate that: Mortality Region A Mortality Region B Mortality of Country CDR for Region A is influenced by the relatively high proportion of young people. 289

5 The country has, relatively, an even younger population than either Region A or B. We need to develop an inde which is less influenced by differences in age structures. Standardised Death Rate(SDR) SDR = w µ (neversmr!) Where: w = s E c s E c are based on a standard population We note that: 290

6 (a) ForRegionA,(withagespecific A µ ): SDR A = s E c A µ s E c In the handout eample(taking the country s population structure as standard), we haveforsdr A : 20 2,000 55, ,50050, ,000 55, , ,000 = SDR B = (b) TheSDRisnotveryinfluencedbythepopulationstructureasshownby: SDR A SDR B (c) The data requirements are: 291

7 age specific mortality rates of the region age specific structure of the standard population(weights) However, the weights(age specific structure of the standard population) may be unknown or unreliably estimated. Weconsiderthecasewheretheweightsareonlyreliablyknownatspecifictimes(eg census times). Indirectly Standardised Death Rate The calculation of the SDR is an eample of direct standardisation. However the age specific structure of a standard population may only be known at census dates. ThisgivesproblemsifweneedtocalculatetheSDRatdatesinbetweenthese censuses. 292

8 Assumption: Thenwehavethat: SDR(at census) = SDR(non-census) CDR(atcensus) CDR(non-census) SDR(non-census) = SDR(atcensus) CDR(at census) CDR(non-census) = F CDR(non-census) and the data requirements for CDR(non-census) are easily met even at non-census times. 293

9 F is called the area comparability factor, and: s E c µ F = s E c d E c F iscalculatedatthecensusandassumedtoremainconstantuntilthenetcensus when it is updated. Standardised Mortality Ratio TheSMRisaratio(notrate)of: actual deaths in region epected deaths in region 294

10 The epected deaths are calculated using the age specific mortality rates for the standard population. Therefore,theSMRforregion Arelativetoastandardpopulation S,is: Notes: SMR A = (a) SMRisthemostcommonratiofoundin demographic studies. (b) Inoureample,SMR A : = 1.022(= 102.2%) 2, ,000 SMR B = 1.009(= 100.9%) (c) The data requirements are: A µ A E c s µ A E c ,50050, ,000 2,

11 totalnumberofdeathsintheregion populationateachagegroupintheregion age-specific mortality rates in standard population This information is more likely to be known more reliably than the information for the SDR(in particular the age specific population structure). (d) TheSMRisusuallyepressedasapercentageand: aregionwhichhasthesamemortalityasthestandardpopulationwillhavean SMRof100% ifthesmrisgreaterthan100%thentheregionhasheaviermortalitythan the standard population. ifthesmrislessthan100%thentheregionhaslightermortalitythanthe standard population. 296

12 Data for eamples on single figure indices Table 1: Mortality statistics Age RegionA RegionA RegionB RegionB Country Country Group population deaths population deaths population deaths Totals

13 Table 2: Age-specific mortality rates Age group Region A Region B Country Models for Population Projections Projections of the population are needed to assist in the planning for: 298

14 demand for food, power, services, transport housing welfare services taes labour costs national insurance contributions We consider mathematical models and component models for population projections. Mathematical Models Mathematical models: are projections based on the total populations takenoaccountof 299

15 fertility rates mortality rates migration rates The advantages of mathematical models: data requirements are minimal eplicitassumptionscanbekepttoaminimum makes comparisons easy The Eponential Model Definition: P t =Sizeofpopulationattimet (t 0) Then for the eponential we have: P t = P 0 e r t For some growth parameter r. 300

16 Notes: (a) Therateofgrowisproportionaltoitscurrentsize: d dt P t = d dt P 0e r t = r (P 0 )e r t = r P t (b) Thisisaverysimplemodelwithonly1 parameter (c) The model can be realistic, particularly over a short time period. (d) Ittakesaccountofonlythemostbasic information about a population its size. (e) Since P t = P 0 e r t thenas t : if r > 0,then P t (population will continue rising indefinately) if r < 0,then P t 0 301

17 (population can become etinct after some time) Neither of these is considered realistic. The Logistic Model Populations do not normally increase indefinitely due to limitations of resources. We adjust the eponential model by introducing a factor that slows down the population growth as the population increases. For the logistic model we have: Notes: d dt P t = r P t k P 2 t (a) The differential equation is satisfied by: P t = 1 c 1 e r t + c 2 = e r t c 1 + c 2 e r t 302

18 (b) Themodelhas3parameters: r, c 1 and c 2.Thereforeisshouldgiveabetterfit than the eponential model with only 1 parameter. (c) Wehave: Also: 1 c 2 P t lim P t = 1 < t c 2 P 0 = 1 c 1 + c c 1 + c 2 t (d) The parameters can be estimated from data by least squares estimation or any other method. 303

19 Problem with mathematical models Projection of the components of the population separately(eg males, females) may not give the same value as projecting the population as a whole. Component Projection Method This method projects the population size and structure on the basis of: the eisting population future births future deaths future immigration/emigration The scheme would proceed as follows: (i) Start with an estimated population at time 0 subdivided by age, gender, etc. 304

20 (ii) Project mortality, fertility, migration rates for each age, gender etc. for each year into the future. (iii) Buildupthepopulationyearbyyearby applying mortality, fertility, migration rates to successively projected populations. In projecting the rates: (a) Note that even though mortality rates are relatively stable, future mortality rates are difficult to predict. Future deaths may depend on future births, immigration/emigration. (b) Future births are difficult to predict. They depend on: number of women of childbearing age trends in number of children(fashion, economics) ageofmotheratbirthoffirstchild trends in marriage/co-habiting 305

21 (c) Future national immigration/emigration will depend on future economic conditions and politics. Future local movements could depend on employment prospects. End 306