Question

Subjects with pre‑existing cardiovascular symptoms who were receiving subitramine, an appetite suppressant, were found to be at increased risk of cardiovascular events while taking the drug. The study included 9844 overweight or obese subjects with preexisting cardiovascular disease and/ or type 2 diabetes. The subjects were randomly assigned to subitramine (4899 subjects) or a placebo (4945 subjects) in a double‑blind 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 568 subjects in the subitramine group and 505 subjects in the placebo group.

find the test statistic

Answer 1

It is a test for proportion difference, where we want to test that there is an increased risk of cardiovascular events in sample 1 as compared to sample 2

let  subitramine group is sample 1 and placebo group is sample 2

then, sample proportion for  subitramine group is and sample proportion for placebo group

n1 = 4899 and n2 = 4945 (n1 and n2 are sample sizes)

test statistics formula is

where

setting the values, we get

Therefore, test statistics is 2.20(rounded to 2 decimals)