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
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
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
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]
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
• A model:• gx =K* Nx*exp(-Vx*m)….marital fertility
• Fx= gx*Gx……………..…general fertility
• [Figures 5 and 6]
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
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]
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]
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
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))