Abstract
AbstractThe relationship between the commonly used indiréctly standardized comparative mortality indices, the standardized mortality ratio (SMR) and the standardized proportional mortality ratio (SPMR) is well known; whereas, the relationship between their less commonly used directly adjusted counterparts, the standardized risk ratio (SRR) and the recently proposed externally standardized proportional mortality ratio (SePMR) has been heretofore not developed. This paper fills this void by demonstrating the algebraic and statistical relationship between the SRR and the SePMR and showing how, under some modest assumptions, valid inferences about the SRR can be based on analysis of SePMR's. More specifically, an asymptotic prediction interval has been developed for the SePMRi which, with high probability, contains the ratio RSRRi = SRRi/SRR. The utility of the SePMRi is supported empirically using data from a recent retrospective cohort study of mineral fiber workers.
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