9.5 A strategy for stratified analysis

1.: Compute the crude measure and the stratum-specific measures, with confidence intervals.
2.: Judge whether the stratum measures differ materially, by inspection and by a test of homogeneity, bearing in mind its low power.
3.: If they do, report them separately: there is effect modification on this scale. Consider whether another scale is homogeneous.
4.: If they do not, compute a pooled adjusted estimate (Mantel–Haenszel or inverse-variance) and its interval.
5.: Compare the adjusted with the crude estimate. A material difference (a change of \(10\%\) or more is a common working rule) indicates confounding by the stratifying variable, and the adjusted estimate is reported. For the odds ratio, recall that some change can come from non-collapsibility alone (Example 7.4.6).

Stratification runs out of data quickly. With several confounders, each with several levels, the strata multiply and most contain few people; the summary estimators of the next section cope with many small strata, and regression models (Section 12) cope with many confounders at once.

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