So far we have only considered that persons could be either exposed or not, but exposure can frequently be quantified and a gradient established. Examples may include the number of glasses (or volume) of water consumed per day, the number of pizza slices eaten, or the degree of completion of a vaccination course etc. The risk of illness can then be calculated according to amount drunk, eaten or completed.
|
Amount drunk
|
Exposed
|
Cases
|
Risk (%)
|
RR
|
|
None
|
100
|
5
|
5
|
ref
|
|
1 glass
|
100
|
11
|
11
|
2.2
|
|
2 glasses
|
100
|
16
|
16
|
3.2
|
|
3 glasses
|
100
|
22
|
22
|
4.4
|
|
≥4 glasses
|
100
|
28
|
28
|
5.7
|
|
|
500
|
82
|
82
|
|
The Χ2 test for trend across these strata = 23.24, p≤0.001 - indicating that there is a trend across the exposure strata.
If instead a case control study had been conducted (note the similarity between the OR and the RR above):
|
Amount drunk
|
Exposed
|
Cases
|
OR
|
|
None
|
5
|
30
|
ref
|
|
1 glass
|
11
|
30
|
2.2
|
|
2 glasses
|
16
|
30
|
3.2
|
|
3 glasses
|
22
|
30
|
4.4
|
|
≥4 glasses
|
28
|
30
|
5.6
|
|
|
82
|
150
|
|
For which the Χ2 test for trend = 12.77, p≤0.001
In the above examples, the risk of disease occurring increases with the amount of water consumed (i.e. with the dose of water). This is frequently called a dose response or a dose effect relationship.
To compute the risk ratio or the odds ratio the same reference level of exposure is used. Here the non exposed group is used as a reference. Alternatively the group with the lowest incidence could be used.
Dose response is particularly interesting when in an outbreak (often in water borne or a food borne outbreak) everybody is exposed to the same factor but the level of exposure differs among individuals. Choosing the lowest category of exposure as a reference still allows identification of a food item or a beverage as the vehicle for the outbreak. To test that the trend observed in risk or odds ratio differs from no trend, we can use a chi square for trend [1-3]. Dose response is also an important criterion to consider when providing evidence for causality proposed by Bradford Hill [4].
References
1. J.J.Schlesselman. Case-control studies: design, conduct, analysis. New York: Oxford University Press; 1982.
2. B.R.Kirkwood, J.A.C.Sterne. Medical Statistics. Second ed. Massachusetts: Blackwell Science Ltd; 2003.
3. K.J.Rothman, S.Greenland, T.L.Lash. Modern Epidemiology. Third ed. Philadelphia, USA: Lipincott Williams and Wilkins; 2008.
4. A.Bradford Hill. The Environment and Disease: Association or Causation? Proceedings of the Royal Society of Medicine 1965;58:295-300.
