Table 1
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Examples of accumulative risk functions |
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| Accumulative Risk Function, ƒ(x) |
Interpretation |
Relative Risk, RR |
Example |
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Relative risk depends only on current exposure, with no contribution from past exposure. |
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Instantaneous poisoning as a result of exposure to high levels of toxic chemicals; injuries or death in accidents due to binge drinking; infection with Hepatitis B or C as a result of an infected injection |
| ƒ(x) = 1 |
Relative risk depends on the accumulated exposure (or average exposure if normalized with respect to exposure time), without any effects from the temporal distribution of exposure. |
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Cancer risk from life-time exposure to carcinogens which have no threshold level |
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Relative risk depends on current and past exposures. But the role of past exposure lasts for a limited time, K, and decline as a linear function of time. |
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| ƒ(x) = ea(t-T) |
Relative risk depends on current and past exposures. But the role of past exposure decays as an exponential function of time. |
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For simplicity of notation, in all these cases we assume that: 1) L = 0. Including a lag is straightforward and can be done by replacing t with (t - L) in the corresponding formulas; and 2) there is no threshold for exposure. Including the threshold level is also straightforward using the TRUE (x (t) ≥ X) function. In scenarios 1, 3, and 4, where the effects of past exposure declines over time, risk reversibility can take place if exposure is reduced or removed. In 1 there is immediate risk reversibility; in 3, there is full reversibility after time K; in 4, risk reversibility asymptotically reaches 100%. In scenario 2 there is no risk reversibility and the effects of past exposure remain for an indefinite period. | |||
Murray et al. Population Health Metrics 2003 1:1 doi:10.1186/1478-7954-1-1 |
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