Standardization using the harmonically weighted ratios: internal and external comparisons

Standardization of rates is a basic tool for epidemiologists. The most frequently used methods are the 'direct standardization' (with summary index of comparative mortality figure, CMF) and the 'indirect standardization' (with summary index of standardized mortality ratio, SMR). The CMF facilitates a valid comparison between populations or across time periods, yet, it suffers from the problem of instability. By contrast, the SMR is stable and can be used for external comparison. However, it cannot guarantee a valid internal comparison. In this paper, the author proposes a new standardized measure, the 'harmonically weighted ratio' (HWR). The HWR can be used for external as well as internal comparisons--with the assumption of rate-ratio homogeneity, or with heterogeneity but dominance of one population over another. Simulation shows that its performance in terms of pairwise comparisons is the best among the three methods or compares favourably to that of the SMR. The author also examines the behaviours of the HWR when used for hypothesis testing (the 'HWR test'). The HWR can be considered for standardization when the purpose of the standardization is solely for comparison and when the universe of the comparisons can be clearly defined.