Vital Statistics

Abdullah Al Mahmud

Concept of Vital Statistics

That branch of biometry which deals with data and laws of human mortality, morbidity, and demography.

Arthur Newsholme \(\downarrow\)

the whole study of mankind as affected by heredity or environment in so far as the results of this study can be arithmetically stated.

Rates & Ratios

  • Dependency Ratio
  • Sex ratio
  • Population density
  • Crude Birth Rate (CBR)
  • General Fertility Rate (GFR)
  • Age-Specific Fertility Rate (ASFR)
  • Total Fertility Rate (TFR)
  • Gross Reproduction Rate (GRR)
  • Net Reproduction Rate (NRR)
  • Net Fertility Rate (NFR)
  • Crude Death Rate (CDR)
  • Age-Specific Death Rate (ASDR)

Rate vs Ratio

Dependency Ratio

\[d = \frac{P_{0-14}+P_{65+}}{P_{15-64}}\times100\] Where

  • \(P_{0-14}\) = The no. of children aged between 0 & 14
  • \(P_{65+}\) = The no. of people aged 65 or older
  • \(P_{15-64}\) = The no. of people aged between 15 and 64

Sex Ratio

\(SR = \frac MF \times 100\)

Population Density

\(D = \frac PA\)

P = Density

A = Area

Crude Birth Rate

\(CBR = \frac BP\times 100\)

B = Total no. of alive children in a year

P = Average population of that region in that time

General Fertility Rate

\(\displaystyle GFR = \frac{B}{F_{15-49}}\times 1000\)

B = Total number of live births in a year

\(F_{15-49}\) = Total number of women in reproductive age group (15-49)

Age-Specific Fertility Rate

\(\displaystyle ASFR_i = \frac{B_i}{F_i}\times 1000\)

\(B_i\) = Total number of live births in a year by the women in ith age group

\(F_i\) = No. of women in ith age group

Total Fertility Rate

Total Fertility Rate (TFR) of a population is the average number of children that are born to a woman over her lifetime if:

  1. they were to experience the exact current age-specific fertility rates (ASFRs) through their lifetime.
  2. they were to live from birth until the end of their reproductive life.

\(\displaystyle TFR = 5 \sum_{i=1}^7ASFR_i = 5 \sum_{i=1}^7 \frac{B_i}{F_i}\times 1000\)

5 for class interval

Gross Reproduction Rate

\(\displaystyle GRR = 5 \sum_{i=1}^7\frac{G_i}{F_i}\times 1000\)

\(G_i =\) Total number of girl babies born in a year by the women in ith age group

Net Reproduction Rate

\(\displaystyle NRR = 5 \sum_{i=1}^7\frac{G_i}{F_i}\times S_i\times 1000\)

\(S_i =\) Survival rate of women of reproductive age group (15-49)

Net Fertility Rate

\(\displaystyle NFR = 5 \sum_{i=1}^7\frac{B_i}{F_i}\times S_i\times 1000\)

Implications

  • GRR > 1: Number of potent women increasing
  • GRR = 1: Number of potent women remains constant. There is no change in population
  • NRR > 1: The number of potent women more than that of previous year; population increasing
  • NRR = 1: No change in population
  • GRR = NRR: No new-born girls dies before reaching last potent age

Numerical Problem

Find CBR, GFR, ASFR, TFR, GRR, & NRR

Age # Women # Newborn # Baby boys Survival probability
15-19 7806000 521435 272342 0.980
20-24 6781000 846256 422247 0.977
25-29 5840000 412342 206122 0.972
30-34 5434000 326268 183134 0.960
35-39 5675000 211810 111440 0.942
40-44 6083000 69750 34380 0.895
45-49 5361000 42354 22462 0.854

Total population = 109,027,142

Solutio to Rates

Age Group # Women \(F_i\) # Newborn \(B_i\) # Baby boys # Baby girls \(G_i\) Survival probability \(S_i\) \(ASFR_i =\) \(\frac{B_i}{F_i}\times 100\) \(\frac{G_i}{F_i}\) \(\frac{G_i}{F_i}\times S_i\)
15-19 7806 521435 272342 0.980
20-24 6781 846256 422247 0.977
25-29 5840 412342 206122 0.972
30-34 5434 326268 183134 0.960
35-39 5675 211810 111440 0.942
40-44 6083 69750 34380 0.895
45-49 5361 42354 22462 0.854

Natural Growth Rate (NGR)

NGR = CBR - CDR

\(\displaystyle \frac BP \times 1000-\frac DP \times 1000 = \frac {B-D}P \times 1000\)

Growths

Geometric Growth

\(P_o =\) Initial population

\(P_n =\) Final population

\(n =\) Number of period (year, month, etc)

\(r =\) Rate of increase

  • Population after 1 year, \(P_1 = P_o + P_or = P_o(1+r)\)
  • Population after 2 years, \(P_2 = P_1 + P_1r = P_1(1+r) = P_o(1+r)^2\)
  • Population after n years, \(P_n = P_o(1+r)^n\)

Growth Problems

  • Time required for population to get doubled/tripled in certain rate
  • Rate required for population to get doubled/tripled in certain time

Exponential Growth

Geometric: \(P_n = P_o(1+r)^n\)

If n is fragmented in smaller periods

Like 100 % in 1 year \(\rightarrow\) 50 % in each half-year

\(P_n = P_o(1+\frac{r}{n})^n\)