- generate the data, and table them

obese <- sample(c(T,F),size=1000,replace=T)
mi <- factor((obese + sample(c(-1,0,1),prob = c(0.3,0.35,0.35),size=1000,replace=T)) > 0,labels=c("myocardinfarct","non"))
obese <- factor(obese,labels=c("obese","non-obese"))
table(obese,mi)

mi
obese myocardinfarct non
obese 326 187
non-obese 144 343

- use the
`twoby2`

function to get the ratios incl. the confidence intervals

- the risk difference (resp. attributable risk (AR), absolute risk reduction (ARR)) is also calculated

require(Epi)
twoby2(obese,mi)

2 by 2 table analysis:
------------------------------------------------------
Outcome : myocardinfarct
Comparing : obese vs. non-obese
myocardinfarct non P(myocardinfarct) 95% conf. interval
obese 326 187 0.6355 0.5929 0.6760
non-obese 144 343 0.2957 0.2568 0.3378
95% conf. interval
Relative Risk: 2.1491 1.8462 2.5018
Sample Odds Ratio: 4.1525 3.1859 5.4122
Conditional MLE Odds Ratio: 4.1462 3.1584 5.4617
Probability difference: 0.3398 0.2800 0.3959
Exact P-value: 0
Asymptotic P-value: 0
------------------------------------------------------

- so we got a risk of myocard. infarction of 0.6507 for obese and 0.3006 for non-obese

- dividing the first by the second (0.6507/0.3006) gives the risk ratio

- the odds are not given for the groups, calculated by hand it would be

[1] 4.152481

- which you see in the output of
`twoby2()`

(in addition you find the conditional MLE odds)

- the probability difference (as stated above also known as attributable risk (AR) and absolute risk reduction (ARR)) is simply the difference between the two risks

confidence-intervals-for-odds-ratio paired case
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