Deep sea diving and osteonecrosis of the femoral head
In this fictional example, a study-group of 450 subjects over the age of 50 was identified. All subjects were asked if they had been deep-sea diving below a level of 10 metres for at least once in their lives. Furthermore, all subjects had a pelvic radiograph taken that has been scrutinised by a radiologist for signs of osteonecrosis (example of a cross-sectional study).
In our example, we assume that 150 subjects have been deep-sea diving and 300 have not. Of the 150 subjects who have been deep-sea diving, 15 had signs of osteonecrosis on the radiographs whilst 135 did not. In the group of 300 non deep-sea divers, only 2 people had signs of osteonecrosis on the radiographs.
We can now construct a two by two table as follows:
| Osteonecrosis | No Osteonecrosis | |
|---|---|---|
| Deep Sea Diving | 15 | 135 |
| No Deep Sea Diving | 2 | 298 |
Absolute Risk Deep Sea Diving
Absolute Risk No Deep Sea Diving
Relative Risk
Risk of exposed individuals getting the disease as compared to non exposed individuals:
Odds Ratio
The odds ratio is the ratio of the odds of a disease occurring among exposed individuals to that of it occurring in unexposed individuals:
Or in the JGR / R console:
Use the epiR 1 library:
library(epiR)
Create a matrix for use by epiR:
mat<-matrix(c(15,2,135,298),ncol=2)
Perform the calculations:
epi.2by2(mat)
Outcome + Outcome – Total Inc risk * Odds
Exposed + 15 135 150 10.000 0.11111
Exposed – 2 298 300 0.667 0.00671
Total 17 433 450 3.778 0.03926
Point estimates and 95 % CIs:
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Inc risk ratio 15.00 (3.48, 64.74)
Odds ratio 16.46 (3.75, 150.22)
Attrib risk * 9.33 (4.44, 14.22)
Attrib risk in population * 3.11 (1.12, 5.10)
Attrib fraction in exposed (%) 93.33 (71.23, 98.46)
Attrib fraction in population (%) 82.35 (35.59, 95.17)
———————————————————
* Cases per 100 population units
The package epiR 1 should be installed.
The odds ratio provided is the maximum likelihood estimate that is different from the cross product ratio. To obtain the cross product ratio :
summary(epi.tests(mat))
est lower upper
aprev 0.33333333 0.28988788 0.3789871
tprev 0.03777778 0.02215822 0.0597982
se 0.88235294 0.63559084 0.9854207
sp 0.68822171 0.64225778 0.7315911
diag.acc 0.69555556 0.65074125 0.7377768
diag.or 16.55555556 3.73358392 73.4110779
nnd 1.75261905 1.39467728 3.5990822
youden 0.57057465 0.27784862 0.7170118
ppv 0.10000000 0.05705743 0.1595679
npv 0.99333333 0.97612650 0.9991916
plr 2.83006536 2.26446054 3.5369439
nlr 0.17094355 0.04643069 0.6293616