Question

(23.18) Subjects with pre-existing cardiovascular symptoms who were receiving sibutramine, an appetite suppressant, were found to be at increased risk of cardiovascular events while taking the drug. The study included 9804 overweight or obese subjects with pre-existing cardiovascular disease and/or type 2 diabetes. The subjects were randomly assigned to sibutramine (4906 subjects) or a placebo (4898 subjects) in a doubleblind fashion. The primary outcome measured was the occurrence of any of the following events: nonfatal myocardial infarction or stroke, resuscitation after cardiac arrest, or cardiovascular death. The primary outcome was observed in 561 subjects in the sibutramine group and 490 subjects in the placebo group Step 1: Find the proportion of subjects experiencing the primary outcome for both the sibutramine and placebo groups. (Round your answers to 4 decimal places.) For the sibutramine group, pˆ1p^1 = __Answer 1__. For the placebo group, pˆ2p^2 = __Answer 2__. Answer 1_ Answer 2_ Step 2: Can we safely use the large-sample confidence interval for comparing the proportions of sibutramine and placebo subjects who experienced the primary outcome? Yes No Step 3: Give a 95% confidence interval for the difference between the proportions of sibutramine and placebo subjects who experienced the primary outcome. (Round your answers to 4 decimal places.) __Answer 1__ to __Answer 2__ Answer 1 Answer 2

Answer 1

The given information is:

Sibutramine group:

Total number of subjects (n1) is 4906.

Total number of subjects in which primary outcome was observed (x1) is 561.

Placebo group:

Total number of subjects (n2) is 4898.

Total number of subjects in which primary outcome was observed (x2) is 490.

Step 1: The proportion of subjects experiencing the primary outcome for both the sibutramine and placebo groups can be calculated as,

For the sibutramine group is given by,

For the placebo group is given by,

Answer 1: 0.1143

Answer 2: 0.1000

Step 2: Conditions to perform confidence interval for two proportion:

1: Subjects are randomly assigned to each of the group.

2. The sample size of both the groups is large and it can be proved as,

and

From the above, it is clear that conditions are satisfied.

Yes, we can safely use the large-sample confidence interval for comparing the proportions of sibutramine and placebo subjects who experienced the primary outcome.

Step 3: The confidence level © is 0.95.

The significance level is 1 – c = 1 – 0.95 = 0.05

The two-tailed critical value obtained at the significance level 0.05 using the z-table is +/- 1.96.

The 95% confidence interval for the difference between the proportions of sibutramine and placebo subjects who experienced the primary outcome can be calculated as:

Therefore, the required confidence interval is (0.0021, 0.0265).

Answer 1: 0.0021

Answer 2: 0.0265