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If I'm given an odds ratio table like below in a format that is not a contingency table as such, $$\begin{array}{lll} \text{Duration of Doping} & \text{Cancer Patients} &\text{Controls} \\ \text{Never} & 235 &273\\ <1\text{ year} & 27 & 26\\ 1-2 \text{ years} & 43 & 29\\ >2 \text{ years} & 46 & 23\\ \end{array}$$

Would I just assume that $p=\dfrac{\text{Cancer Patients}}{\text{Cancer Patients}+\text{Controls}}$ and then apply the $\dfrac{p}{1-p}$ formula? And how would I go about finding the $95\%$ confidence interval?

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  • $\begingroup$ You want to determine 95% CI for what? $\endgroup$ – rightskewed Sep 27 '15 at 19:34
  • $\begingroup$ I'm trying to find 95% confidence for the odds. $\endgroup$ – cambelot Sep 27 '15 at 19:37
  • $\begingroup$ You will get three ORs which one's CI do you want? $\endgroup$ – Deep North Sep 28 '15 at 4:45
  • $\begingroup$ Sorry for the confusion. I just want to know how I can find the CI of one and whether the formula I put above is correct. $\endgroup$ – cambelot Sep 28 '15 at 13:21
  • $\begingroup$ Calculate a CI for p and calculate the odds ratio at each endpoint. An "exact" CI for p will be better than the one based on the normal approximation. $\endgroup$ – Russ Lenth Apr 23 '17 at 21:41

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