Question

A two-arm study is used to compare treatment A and treatment B, with subjects randomly assigned to either treatment arm. The outcome is the proportion of subjects with at least a four-fold increase in the response parameter from pre-treatment to post-treatment.

1. If previous experience suggests that with treatment A the proportion of subjects who demonstrate the required response is 0.67, and there are 450 subjects available for the current study (alpha = 0.05).
   1. What is the power of this study to detect a 0.1 difference in proportions between treatments?
   2. What sample size is needed to achieve 80% power?
2. It was decided that a difference in proportion of 0.07 is more plausible. What sample size is necessary to detect this difference (alpha = 0.05)?

Answer 1

(a) The formula is:

Sample Size, n = 450

Type I error rate, α = 0.05

True Proportion, p = 0.67

Null Hypothesis Proportion, p0 = 0.77 or 0.57

By plugging in all the values in the formula, we get:

Power, 1−β = 0.9947

(b) The formula is:

Type I error rate, α = 0.05

True Proportion, p = 0.67

Null Hypothesis Proportion, p0 = 0.74 or 0.60

By plugging in all the values in the formula, we get:

Power, 1−β = 0.80

Sample Size, n = 450