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.