The November 6, 2003, issue of the New England Journal of Medicine reported on a study of the effectiveness of letrozole in postmenopausal women with breast cancer who had completed five years of tamoxifen therapy. Over 5000 women were enrolled in the study; they were randomly assigned to receive either letrozole or a placebo. The primary response variable of interest was disease-free survival. The article reports that 7.2% of the 2575 women who received letrozole suffered death or disease, compared to 13.2% of the 2582 women in the placebo group.

Fill in the two by two table below.

letrozole placebo total
death or disease 185 341 526
no death or disease 2390 2241 4631
total 2575 2582 5157

Using the numbers from the table above, calculate the odds ratio of death or disease in the placebo group versus the treatment group

(341 / 2241) / (185 / 2390)
## [1] 1.965797

The odds of death or disease are 1.97 times higher in the placebo group compared to the treatment group.

Using the same table, calculate the odds ratio of no death or disease in the treatment group versus the placebo group

(2390 / 185) / (2241 / 341)
## [1] 1.965797

The odds of no death of disease are 1.97 times higher in the treatment group compared to the placebo group.

Using the same table, calculate the odds ratio of death or disease in the treatment group versus the placebo group

(185 / 2390) / (341 / 2241)
## [1] 0.5086995

The odds of death or disease in the treatment group are 0.5 times that in the placebo group.