Kitagawa Component Decomposition
Split the difference between two crude rates into an age-composition effect and a rate effect using Kitagawa's two-component decomposition with averaged compositions and rates.
Description
Split the difference between two crude rates into an age-composition effect and a rate effect using Kitagawa's two-component decomposition with averaged compositions and rates.
Split the difference between two crude rates into an age-composition effect and a rate effect using Kitagawa's two-component decomposition with averaged compositions and rates.1
When to use Kitagawa Component Decomposition
Use standardization to compare populations with different age compositions after aligning age-specific rates and standard weights exactly.
- Population 1
- Population counts by age group in population 1.
- Rates 1
- Age-specific rates in population 1.
- Population 2
- Population counts by age group in population 2.
- Rates 2
- Age-specific rates in population 2.
How the method works
- Crude rate 1
- Crude rate of population 1, sum of composition-weighted rates.
- Crude rate 2
- Crude rate of population 2.
- Composition effect
- Composition effect: composition differences weighted by average age-specific rates.
- Rate effect
- Rate effect: rate differences weighted by average population composition.
- Difference
- Crude rate 1 minus crude rate 2, the decomposed total.
Limitations and assumptions
The standardized result is a weighted summary, not an observed crude rate. It changes with the reference population, and incompatible age bands or rate denominators invalidate the comparison.
Alternative or Complementary measures
Report crude and age-specific rates alongside the standardized value, and repeat the calculation with another accepted standard population when comparisons could depend on the chosen weights.
References
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Age adjustment — Wikipedia contributors
Similar or alternative tools
- Age Standardized Prevalence Weighted
Compute the age-standardized prevalence as the standard-weight weighted average of age-specific prevalences, sum(w_i * p_i) / sum(w_i).
- Direct Standardized Rate SDR
Compute the directly age-standardized rate as the standard-population-weighted average of age-specific rates, SDR = sum(m_i * W_i) / sum(W_i).
- Indirect Standardized SMR
Apply indirect standardization: compute expected deaths from standard age-specific rates and study exposure, divide observed by expected deaths for the SMR, and multiply that ratio by the standard population's crude rate to obtain an indirectly standardized rate.