Question

In a randomized clinical trial to determine the most effective timing of the administration of chemotherapeutic drugs to lung cancer patients, 26 patients were given four drugs simultaneously, while 15 patients were given the same four drugs sequentially. Objective response to the treatment (defined as the shrinkage of the tumor by at least 50%) was observed in 16 of the patients treated simultaneously and in 4 of the patients treated sequentially. (By Hand Calculation)

a. Carry out the appropriate test to determine if there is a difference in effectiveness between the two different treatments. Include all steps for full credit.

b. Quantify the difference in effectiveness of the two treatments with the appropriate measure and interpret it in the context of the problem.

Answer 1

In a randomized clinical trial to determine the most effective timing of the administration of chemotherapeutic drugs to lung cancer patients, 26 patients were given four drugs simultaneously, while 15 patients were given the same four drugs sequentially. Objective response to the treatment (defined as the shrinkage of the tumor by at least 50%) was observed in 16 of the patients treated simultaneously and in 4 of the patients treated sequentially. (By Hand Calculation)

a. Carry out the appropriate test to determine if there is a difference in effectiveness between the two different treatments. Include all steps for full credit.

Two sample proportion test used

This is a two sided test.

p1=16/26 =0.6154

p2=4/15 = 0.2667

P = (x1+x2)/(n1+n2)

=20/41 = 0.4878

=2.1517

Table value of z at 0.05 level = 1.96

Rejection Region: Reject Ho if z < -1.96 or z > 1.96

Calculated z =2.1517 , falls in the rejection region

The null hypothesis is rejected.

We conclude that there is a difference in effectiveness between the two different treatments.

b. Quantify the difference in effectiveness of the two treatments with the appropriate measure and interpret it in the context of the problem.

The difference in proportion of success in the simultaneously treated and the sequentially treated is

p1-p2= 0.6154-0.2667 = 0.3487

34.87% more successfully treated in the simultaneously treated than the sequentially treated.

This difference is significant at 0.05 level of significance.