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Crude Rates: measures of flows

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Crude Rates: measures of flows. Main definition: No of events in (t,t+1)/Exposure in (t,t+1) (Births in year 1965)/(Midyear pop in 1965x1) (Births 1960-65)/{(Midyear pop 1960-65)*5} To remember: Events: counts from vital stats, surveys etc… Exposure: an abstraction or approximation. - PowerPoint PPT Presentation
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Crude Rates: measures of flows • Main definition: – No of events in (t,t+1)/Exposure in (t,t+1) – (Births in year 1965)/(Midyear pop in 1965x1) – (Births 1960-65)/{(Midyear pop 1960-65)*5} • To remember: – Events: counts from vital stats, surveys etc… – Exposure: an abstraction or approximation
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Page 1: Crude Rates: measures of flows

Crude Rates: measures of flows

• Main definition:– No of events in (t,t+1)/Exposure in (t,t+1)– (Births in year 1965)/(Midyear pop in 1965x1)– (Births 1960-65)/{(Midyear pop 1960-65)*5}

• To remember:– Events: counts from vital stats, surveys etc…– Exposure: an abstraction or approximation

Page 2: Crude Rates: measures of flows

Rates vs Probabilities

• Mortality rate at 4-5:

– Events/exposure• Exposure=units are

persons * unit of time

– Bounded by 0 and infinity

• Probability of dying between 4 and 5:– Events/possible events

• Possible events=units are persons alive at 4

– Bounded by 0 and 1

Page 3: Crude Rates: measures of flows
Page 4: Crude Rates: measures of flows

Nature of crude rates: CDR

• CDR= Deaths/Pop= Dx / Px

• [(Dx/Px)*(Px/Pop)]=(Mx*Cx)

• Weighted average of Mx, with age distribution, Cx, as weights

• Would like to get measures reflecting Mx only

• How does Mx look like? [Figure 1]

Page 5: Crude Rates: measures of flows

Solutions to problems presented by CDR

• Standardization:– SDR1= Csx M1x where Csx is a ‘standard’– SDR2= Csx M2x– Comparison is between SDR1 and SDR2

• Life table: Mx----->S(x) [Figure 2]Life expectancy at birth, Eo

Life expectancy at age x, Ex

Page 6: Crude Rates: measures of flows
Page 7: Crude Rates: measures of flows
Page 8: Crude Rates: measures of flows

CBR

• CBR=Births (t, t+1)/Exposure in (t,t+1)=

• =Bx/Pop= Bx/ Px• =(Bx/Wx)*(Wx/35W15)*(35W15/ Wx)*(Wx/

Px)

• =Fx * Rx*35C15 * w

• A CBR depends on age and sex distributions• We only want to summarize Fx

Page 9: Crude Rates: measures of flows

Rates of Population Increase

r=CBR-CDR

R=r+NMR (met Migration rate)

Doubling time, Td~.69/r

Page 10: Crude Rates: measures of flows

The age profile of Fx

• Age specific fertility rates Fx have a universal shape [Figure 3]

• Synthetic measures of fertility are (all summations are between 15 and 49):– TFR= {15-49} Fx…….total fertility rate

– GRR .45 * TFR…….gross reproduction rate

– NRR .45 {15-49}Fx*S(x)..net reproduction rate

Page 11: Crude Rates: measures of flows
Page 12: Crude Rates: measures of flows
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Page 14: Crude Rates: measures of flows

Models of Mortality

• Summarizing variability in mortality by age:

– Gompertz model (Makeham extension)– Brass logit models– Coale and Demeny Models– United Nations Models

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Page 16: Crude Rates: measures of flows
Page 17: Crude Rates: measures of flows

Model of fertility I

• What would “natural fertility” look like?

• Reproduction span*(1/ Length Average Birth Interval)

• Reproductive span=Menopause-Menarche~35*12=420 months

• Birth Interval:

– Conception time ~5 months

– Pregnancy~9

– Post-partum fecundability~8

– Fetal losses~4

Expected births=420/26 = 16.2

Page 18: Crude Rates: measures of flows

Models of fertility II

• What is natural fertility, Nx? [Figure 4]

• Variability in natural fertility…..K

• Deviations from natural fertility..Vx and m

• A model:• gx =K* Nx*exp(-Vx*m)….marital fertility

• Fx= gx*Gx……………..…general fertility

• [Figures 5 and 6]

Page 19: Crude Rates: measures of flows
Page 20: Crude Rates: measures of flows

Popular standardized measures of fertility: the Princeton Study

• If= births/women 15-49• Ig=births to married women/ max births to

married women • Im=weighted number of married women 15-49/

weighted number of women 15-49 

Page 21: Crude Rates: measures of flows

Historical Strategies: Iso-fertility curves

• Disregarding illegitimate fertility we have:– If= Im*Ig– Two sets of factors operating on each measure– Location of societies in iso-fertility curves

reveals societal strategies for reducing fertility [Figure 7]

Page 22: Crude Rates: measures of flows
Page 23: Crude Rates: measures of flows

Age distributions, Cx

• Cx’s reveal past history of mortality, fertility and migration [Figure 8 and 9]

• Important result: when Fx and Mx are constant we generate a stable population with a unique r. If r=0 we say we have attained a stationary population[Figure 10]

Page 24: Crude Rates: measures of flows
Page 25: Crude Rates: measures of flows
Page 26: Crude Rates: measures of flows

The mathematics of stable populations

• N(x)=B(t-x)*S(x)• B(t-x)=Bo*exp(r*(t-x))• N= N(x)• C(x)=N(x)/N• C(x)=CBR*S(x)*exp(-r*x) • If r=0, C(x)=(1/Eo)*S(x)• a unique relation: NRR=exp(r*T)

• T is the ‘length of a generation’~ Mean age of childbearing

Page 27: Crude Rates: measures of flows

Important results

• Age distributions are heavily affected by changes in fertility

• They are less affected by changes in mortality

• Momentum, M:• M ==(CBR*Eo / r * T) * (NRR-1)/NRR))

Page 28: Crude Rates: measures of flows

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