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The following data were collected from a case-control study of breast cancer and fat intake:

case control
High-fat diet 10 5
Low-fat diet 40 55
50 60
Statistical inferences for odds ratios are based on the natural log of the odds ratio, rather than the odds ratio itself (because the distribution for an odds ratio does not follow a normal distribution). The sampling distribution of the natural log of the odds ratio (lnOR) follows a normal distribution, with standard error

=1a+1b+1c+1d−−−−−−−−−−−−−√
(where a, b, c, and d are the cells in the 2x2 table).

Calculate the odds ratio for breast cancer (comparing high-fat diet to low-fat diet) from the 2x2 table above.

Take the natural log of the odds ratio that you calculated

Calculate the standard error of the lnOR, according to the formula given above.

Calculate the 95% confidence interval for the lnOR.

Convert the upper and lower confidence limits that you calculated in (e) back to odds ratios by exponentiating (i.e., calculate the 95% confidence interval for the OR).

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