Question

A two arm study has been conducted in which participants are randomised to receive a current treatment or a new treatment, with equal number in each treatment arm.

The primary result of the study is the proportion of participants who exhibit at-least a 4-fold rise in serum antibody level from pre-treatment to 28 days post-treatment.

(a) Write down the null and alternative hypothesis to test whether the proportion duffers between treatments. Discuss briefly whether you think a one or two -sided hypothesis would be more appropriate for this study.

Answer 1

Let p1 be the proportion of people in the current treatment who exibit atleast a four fold rise in serum antibody levels from pre to post treatment.

Let p2 be the the proportion of people in new treatment who exibit atleast a four fold rise in serum antibody levels from pre to post treatment.

We are testing,

a) H0: p1= p2 vs H1: p1 not equal p2

(Since we want to test whether the proportion differs between the two)

From H1, we see that this is a non directional two sided hypothesis test. We can use two proportion z test to solve this problem.