8 Standardisation of rates
Proposition 3.5.1 showed that a crude rate is a weighted average of stratum-specific rates, weighted by the population’s own distribution across the strata. Two populations with different age structures therefore have crude rates that differ for two reasons: because their age-specific rates differ, and because their weights differ. In the language of Section 7.4, age confounds the comparison of crude rates. Standardisation removes this by computing, for each population, a summary rate that uses the same weights for both. It is the oldest method of adjusting for confounding and still the standard way of comparing mortality between countries, regions and periods.
Throughout, population \(k\) has person-time \(T_{kj}\), deaths (or cases) \(D_{kj}\) and rate \(I_{kj} = D_{kj}/T_{kj}\) in stratum \(j = 1, \dots , J\).
Example 8.0.1. Two regions have the following deaths, person-years and death rates per \(1000\) person-years in three age groups.
| Region A | Region B
| |||||
| Age | Deaths | Person-yrs | Rate | Deaths | Person-yrs | Rate |
| 0–39 | 30 | 60,000 | 0.5 | 12 | 30,000 | 0.4 |
| 40–64 | 90 | 30,000 | 3.0 | 75 | 30,000 | 2.5 |
| 65+ | 200 | 10,000 | 20.0 | 640 | 40,000 | 16.0 |
| Total | 320 | 100,000 | 3.2 | 727 | 100,000 | 7.27 |
Region B’s crude death rate is more than twice region A’s, yet in every age group its rate is \(20\%\) or so lower. Region B is old: \(40\%\) of its person-time is over \(65\), against \(10\%\) in A. The crude comparison is reversed by confounding by age.
8.2 Indirect standardisation and the SMR
8.3 Comparing SMRs
8.4 Choosing between the methods
8.5 Problems
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