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).
Cheating is not allowed. HRP258
To calculate the odds ratio for breast cancer comparing high-fat diet to low-fat diet, you need to use the formula:
Odds Ratio = (ad) / (bc)
From the given 2x2 table, we can see that:
a = 10 (number of cases on high-fat diet)
b = 5 (number of controls on high-fat diet)
c = 40 (number of cases on low-fat diet)
d = 55 (number of controls on low-fat diet)
Plugging these values into the formula, we get:
Odds Ratio = (10 * 55) / (5 * 40)
Calculating this gives us the odds ratio for breast cancer comparing high-fat diet to low-fat diet.
To calculate the natural log of the odds ratio (lnOR), we simply take the natural logarithm of the odds ratio that we calculated in the previous step.
lnOR = ln(Odds Ratio)
Now, let's calculate the standard error of the lnOR using the given formula:
Standard Error (SE) = sqrt(1/a + 1/b + 1/c + 1/d)
Plugging in the values from the 2x2 table into the formula, we can calculate the SE.
To calculate the 95% confidence interval for the lnOR, we need to consider the normal distribution. The 95% confidence interval can be calculated by multiplying the SE by the appropriate Z-value (usually 1.96 for a 95% confidence interval).
Confidence Interval (CI) = lnOR ± (SE * Z)
To convert the upper and lower confidence limits from lnOR back to odds ratios, we need to exponentiate.
Odds Ratio = e^(lnOR)
This will give us the 95% confidence interval for the odds ratio.