The standard treatment of cancer by a standard chemical substantially shrinks or

Question

The standard treatment of cancer by a standard chemical substantially shrinks or eliminates tumors in about 60% of patients, i.e., the response rate is 60%. To verify the improvement of a newly developed chemical, a clinical trial is conducted to randomly assign patients to the standard chemical and to the newly developed chemical. The objective of this clinical trial is to identify a 15% higher response rate for the new chemical (i.e., 75%), at 95% confidence level. If the patients are assigned with equal numbers in each group. How many patients in each group would be needed? What if the patients are assigned with a 2 to 1 ratio to the standard group and to the new chemical group?

Explanation / Answer

Solution:

Given that p = 0.60, E = 0.75 and a = 1 - 0.95 = 0.05

Using Z-tables, the critical value is

Z (a/2) = Z (0.05/2) = Z (0.025) = 1.96

a. The sample size is given by:-

N = [Z/E]^2*p*(1 – p)

N = [1.96/0.75]^2*0.6*0.4

N = 6.83*0.6*0.4

N = 1.64 ~ 2

b. If the patients are assigned with a ratio of 2 to 1, the patients in standard group would be 2 x 2 = 4 and the patients in new chemical group would be 2.

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