Disease and exposure

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Two by two table

Two by two table for disease and exposure
Disease present?
Yes No
Exposed? Yes a b
No c d

Odds ratio

= what you'd expect if disease caused by exposure / what you'd expect if disease NOT caused by exposure
= (a/b)/(c/d) = ad/bc (diagonals)

(Usually used in case control studies: the odds of a person with disease having had the exposure)

Relative risk

= proportion of people with +ve exposure to get disease / proportion of people with ve exposure not to get disease. Also known as risk ratio.
= {a/(a+b)}/{c/(c+d)}

(Usually used in cohort studies: the relative risk in the two groups.)

If disease is uncommon, then a and c are small relative to b and d:

⇒ a/(a+b) ≈ a/b; and c/(c+d) ≈ c/d,
∴ RR = {a/(a+b)}/{c/(c+d)} ≈ (a/b)/(c/d) = ad/bc = OR.

So for uncommon diseases, RR ≈ OR.

While a relative risk (risk ratio) of 1.0 has little meaning so in observational studies are relative risks between 0.5 and 2.0. Essentially a relative risk of greater than 2.0 means that more often than not the observation producing the higher risk will be associated with the outcome, rather than not.

Absolute Risk

Absolute risk is in many cases more important than relative risk, and quoting the wrong one is a favourite tactic of journalists to make a story more interesting, or people wanting to produce action on their topic. If the absolute risk is 1/1 000 000 then a doubling in relative risk is not very compelling. If the absolute risk is 1/10 then an increase of 0.01 in the relative risk might get our attention.

Aetiologic fraction

= (mortality in exposed group - mortality in unexposed group)/mortality in exposed group

Attributable risk

= mortality rate (or incidence) in exposed group - mortality rate (or incidence) in unexposed group

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