Vital statistics are the data and methods used to study the dynamic phenomena of human population such as births, deaths, marriages, divorces, fertility, mortality and migration.
Spiegelman: "The branch of biometry which deals with the data and the laws of human mortality, morbidity and demography."
The science behind it is demography.
In India the primary source for vital rates is the Sample Registration System (SRS) run by the Office of the Registrar General & Census Commissioner.
The number of deaths per 1 000 population in a given calendar year.
where \(D\) = total deaths in the year, \(P\) = mid-year population.
Merits: easy to compute, single number, comparable across regions.
Demerits: ignores age structure — populations with many elderly will show high CDR even if mortality at each age is low.
City A had 12 500 deaths in a year; mid-year population was 1 250 000. CDR = (12 500/1 250 000) × 1000 = 10 per 1 000.
A crude death rate mixes mortality with age structure. A country with a young population can have a lower CDR than a country with an old one, even when its people die younger at every age. This is why CDRs of different populations are compared only after standardisation (Section 3.3).
The death rate for a specific category — age, sex, cause of death, occupation, etc. Most common is the Age-Specific Death Rate (ASDR).
where \(D_x\) = deaths in age group \(x\), \(P_x\) = mid-year population of age group \(x\).
Other specific rates: sex-specific death rate, cause-specific death rate, infant mortality rate, etc.
In age group 50–59: deaths 800, population 80 000. ASDR = (800/80 000) × 1000 = 10 per 1 000.
Infant deaths = 4 500 in a year; live births = 150 000. IMR = (4 500/150 000) × 1000 = 30 per 1 000 live births.
Used to compare mortality across populations with different age structures. Two methods: Direct and Indirect.
Apply the ASDRs of the population being studied to a standard population:
\[ \text{SDR}_{\text{direct}} \;=\; \dfrac{\sum P_x^{\text{std}} \cdot m_x}{\sum P_x^{\text{std}}}, \]where \(P_x^{\text{std}}\) = standard-population age distribution, \(m_x\) = ASDR of the study population for age group \(x\).
The result is what the death rate would have been if the study population had the same age structure as the standard.
Used when age-specific death rates of the study population are not available, but its age distribution and total deaths are.
where \(M_x^{\text{std}}\) = ASDRs of the standard population, \(P_x\) = age structure of the study population.
\[ \text{SMR} \;=\; \dfrac{\text{Actual deaths}}{\text{Expected deaths}}, \qquad \text{SDR}_{\text{indirect}} \;=\; \text{SMR} \times \text{CDR}^{\text{std}}. \]SMR = Standardised Mortality Ratio. If SMR > 1, study population has higher mortality than standard.
Compute standardised death rate of City X using the standard population below:
| Age group | City X population (Px) | City X deaths (Dx) | ASDR mx per 1000 | Std. pop. (Pxstd) |
|---|---|---|---|---|
| 0–14 | 20 000 | 100 | 5 | 30 000 |
| 15–59 | 50 000 | 250 | 5 | 55 000 |
| 60+ | 30 000 | 900 | 30 | 15 000 |
| Total | 100 000 | 1 250 | — | 100 000 |
City X CDR = 1 250/100 000 × 1 000 = 12.5 per 1 000.
Direct standardised = (30 000 × 5 + 55 000 × 5 + 15 000 × 30)/100 000 = (150 000 + 275 000 + 450 000)/100 000 = 875 000/100 000 = 8.75 per 1 000.
Conclusion: After removing the effect of age structure, City X's "true" mortality is 8.75 — lower than its crude rate of 12.5.
City Y total deaths 800. Age distribution: 0–14 = 25 000, 15–59 = 60 000, 60+ = 15 000. Standard ASDRs (per 1 000): 4, 6, 25.
Expected deaths = 25 000(0.004) + 60 000(0.006) + 15 000(0.025) = 100 + 360 + 375 = 835.
SMR = 800/835 = 0.958.
If standard CDR = 8 per 1 000, indirect SDR = 0.958 × 8 = 7.66 per 1 000.
| Aspect | Direct | Indirect |
|---|---|---|
| Data required from study population | ASDRs + total population | Age distribution + total deaths |
| Data required from standard | Age distribution | ASDRs and CDR |
| Output | Standardised rate | SMR; then standardised rate |
| Use when | Reliable ASDRs available | ASDRs of study pop. missing |