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. (a) If the patients are assigned with equal numbers in each group. How many patients in each group would be needed? (b) What if the patients are assigned with a 2 to 1 ratio to the standard group and to the new chemical group?

Explanation / Answer

p1 = 0.60 p2=0.75

q1= 0.40 q2 = 0.25

z = 1.96 at 95% CI

Z =0.75 - 0.60 / 0.24/n1 + 0.1875/n2

1.96 = 0.15 / 0.24/n1 + 0.1875/n2

sb.s

3.84 = 0.02 / (0.24/n1 + 0.1875/n2)

for part a n1 = n2 = n

3.84 = 0.02/( 0.42/n)

3.84 = 0.02n / 0.42

n = 80

b) for b

n1 = 2n2

3.84 = 0.02 / (0.24/2n2 + 0.1875/n2)

3.84 = 0.02 /( 0.3/n2)

n2 = 58

n1 = 116

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