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To compare apples and apples, we must express the multiplicative measures on an additive scale (or the additive ones on a multiplicative scale).
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We can use Bayes' theorem to obtain additive analogues of (1.4) – (1.6), which are here displayed along with their multiplicative counterparts: Notice how each additive measure is obtained by multiplying H's unconditional probability, expressed on the relevant scale, P, O or B, by the associated multiplicative measure diminished by 1.
The ATM is a single multiplicative measure that includes both the proportion and intensity scores.
This table shows that there are two differences between each multiplicative measure and its additive counterpart.
If we settle on the point of probabilistic independence PE(H) = P(H) as a natural common zero, and so subtract 1 from each multiplicative measure,[13] then equivalent likelihood terms appear in both columns.
First, the likelihood term that appears in a given multiplicative measure is diminished by 1 in its associated additive measure.
The index could be a multiplicative measure like RR or OR, or an additive measure like the risk difference (RD).
We tested our hypothesis under two different interaction models, a biological model that measures on an additive scale the risk difference between different exposures, and a statistical model on a multiplicative scale that considers the difference in the relative risk of a disease in the presence of both factors [18].
These three multiplicative effect measures are sometimes referred to under the generic term of relative risk.
A high SIR does not necessarily imply a high disease burden, as incidence rates for specific age-groups may be low and the SIR is measured on a multiplicative scale.
In a joint-effects analysis of the effect of both a positive family history of prostate cancer and self-reported ever use of coumaphos in association with prostate cancer (age-adjusted only), we observed the joint effect of both exposures in excess of the expected joint effect of the two independent exposures, measured on the multiplicative scale.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com