B6

Vital Statistics

  • Vital statistics is an aspect of statistics concerned with measurements and comparisons of data pertaining to human life.
  • It denotes both the data and the analytical methods used for describing vital events occurring in a community.
  • Raw data for vital statistics can be obtained from several primary sources:
    • Sample surveys
    • Population censuses
    • Vital statistics registers
    • Hospital records
    • Municipalities
  • It includes the counts of births, deaths, and illnesses, from which various rates and ratios may be computed.

Ratios in Biostatistics

  • The ratio is the least complicated form of relative measurement.
  • A ratio represents the relationship between two numbers and does not relate to a particular period of time.
  • For relative comparisons using ratios, both the numerator and denominator must use the same units of measurement, and data must be collected and compared over the same period of time.
  • Ways to write a ratio include:
    • a:ba:b
    • a to ba \text{ to } b
    • ab\frac{a}{b}
  • General Formula for Ratio:   Ratio=Number of cases in a particular event in a period of timeNumber of cases in a particular event in a period of time\text{Ratio} = \frac{\text{Number of cases in a particular event in a period of time}}{\text{Number of cases in a particular event in a period of time}}
  • Examples of ratios include:
    • Sex ratio: Sex ratio=No. of femalesNo. of males\text{Sex ratio} = \frac{\text{No. of females}}{\text{No. of males}}
    • Risk ratio: Risk ratio=Risk of disease in one group (exposed)Risk of disease in another group (unexposed)\text{Risk ratio} = \frac{\text{Risk of disease in one group (exposed)}}{\text{Risk of disease in another group (unexposed)}}

Proportions

  • Proportions are created by dividing a fraction of the population by the total population.
  • In a proportion, the number of cases in a particular event (the numerator) is also included in the total population under study (the denominator).
  • Formula for Proportion:   Proportion=No. of cases in a particular eventTotal population at risk in a period of time\text{Proportion} = \frac{\text{No. of cases in a particular event}}{\text{Total population at risk in a period of time}}
  • A proportion multiplied by 100100 becomes a percentage.

Distinguishing Rates, Proportions, and Ratios

  • The following criteria are used to distinguish between rates, proportions, and ratios:
    • Measure: Rate
    • Is the numerator included in the denominator? Yes
    • Is time included in the denominator? Yes
    • Examples: Incidence rate, Prevalence rate
    • Measure: Proportion
    • Is the numerator included in the denominator? Yes
    • Is time included in the denominator? No
    • Example: Percent Reduction
    • Measure: Ratio
    • Is the numerator included in the denominator? No
    • Is time included in the denominator? No
    • Example: Maternal mortality ratio

Measures of Change and Reduction

  • Percent Reduction (PR)

    • Percent reduction relates to the change after applying a certain treatment.
    • Formula:     Proportion=Original amount−reduced amountOriginal amount×100\text{Proportion} = \frac{\text{Original amount} - \text{reduced amount}}{\text{Original amount}} \times 100

  • Percent Change

    • Percent change is the difference between a new value and an old value, divided by the old value, and multiplied by 100100.
    • In general, change rates can exceed 100%100\%. Because of this possibility, they are not classified as proportions.
    • Formula:     Change rate (%)=New value−Old valueOld value×100\text{Change rate (\%)} = \frac{\text{New value} - \text{Old value}}{\text{Old value}} \times 100

Questions & Discussion

  • Problem 1: HIV Ratio Calculation

    • Question: A hypothetical data shows that for the past 66 months the number of reported male HIV positive cases in Metro Manila was 2020 while that for the females was 4040. Create a ratio representation of reported HIV positive females to HIV positive males in Metro Manila for the Past 66 months. Interpret your answer.
    • Solution:
    • Males = 2020
    • Females = 4040
    • Ratio = 40:2040:20 or 2:12:1
    • Answer: The ratio is 2:12:1.

  • Problem 2: Proportion of Sanitary Toilets

    • Question: According to the National Health Survey of 20102010, out of 12,241,73012,241,730 households surveyed in the Philippines, 9,405,3429,405,342 of them were found to have sanitary toilets. What is the proportion of households having sanitary toilets in the entire number of households surveyed in the Philippines for the year 20102010? Interpret your answers in percentage.
    • Solution:
    • Proportion=9,405,34212,241,730×100=76.83%\text{Proportion} = \frac{9,405,342}{12,241,730} \times 100 = 76.83\%
    • Answer: 76.83%76.83\%

  • Problem 3: Cholestyramine Treatment and Cholesterol Reduction

    • Question: Cholestyramine is a useful drug which lowers the cholesterol level. Suppose four persons with high levels of cholesterol were treated for 66 months with the drug, and their cholesterol levels (measured in g/mLg/mL of blood) before and after treatment were recorded. Compute the percent reduction of cholesterol for each individual. Who among the four had gained a greater amount of reduction of cholesterol?
    • Patient Data & Calculations:
    • Mrs. Magtibay: Before treatment: 295295, After treatment: 245245.
      • Reduction=295−245295×100=16.95%\text{Reduction} = \frac{295-245}{295} \times 100 = 16.95\%
    • Mrs. Manalo: Before treatment: 300300, After treatment: 255255.
      • Reduction=300−255300×100=15.01%\text{Reduction} = \frac{300-255}{300} \times 100 = 15.01\%
    • Mrs. Manalaysay: Before treatment: 315315, After treatment: 275275.
      • Reduction=315−275315×100=12.70%\text{Reduction} = \frac{315-275}{315} \times 100 = 12.70\%
    • Mr. Santos: Before treatment: 320320, After treatment: 280280.
      • Reduction=320−280320×100=12.51%\text{Reduction} = \frac{320-280}{320} \times 100 = 12.51\%
    • Conclusion: Mrs. Magtibay achieved the greatest reduction at 16.95%16.95\%.