Relation of the Crude Relative Risk of a Disorder to Relative Risks in Strata of a “Susceptible” Variable

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Abstract

If Td is the relative risk of a disorder in the entire population, and rd, is the relative risk of the disorder in i = I,...m strata, then one may show readily that Td = |GS c1 Td where ci is the product of two terms, Ti the risk ratio of being in the ith stratum, and Pi,unexp d1 the proportion of those with the disorder and unexposed who are in the ith stratum. This formulation is of primary interest in epidemiology when relative risks are available on one or only some strata of a variable that itself may be affected by exposure (what one may define as a “susceptible” covariate) such as mortality or hospitalization. Although relative risks within strata of such a variable may be of some intrinsic clinical interest, only the risk ratio unstratified on such a variate may be pertinent to a causal effect (unlike the case for nonsusceptible variables such as sex, age, etc). In some instances, as for birth defects, one may have data from a few strata or only one (for example, livebirths) of a susceptible covariate (for example, conceptus viability). But one may still be able to draw useful inferences about Td,I the risk ratio in the entire population, because if rd,i |Mg 1/ci (or k/ci), one may conclude that Td is, at least, greater than 1.0 (or k). Similarly, a study of a disorder limited to hospitalized cases and controls may enable investigators to infer, using the same criterion, a positive association in the entire population despite the presence of hospitalization bias of the type described by Berkson. (Epidemiology 1993;4:524529)

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