This problem is based on the results of a study by Berman, et al (1991) publishe
ID: 3156051 • Letter: T
Question
This problem is based on the results of a study by Berman, et al (1991) published in the journal Blood. Leukemias are cancers in which the blood-forming cells undergo changes resulting in uncontrolled, malignant growth. Patients with leukemia exhibit excessive numbers of abnormal white blood cells. The main treatment for leukemia is chemotherapy using drugs which target rapidly dividing cells. A randomized comparative experiment was conducted in 1984 to compare the effects of two chemotherapy drugs for treating leukemia. One hundred thirty Leukemia patients at the Memorial Sloan Kettering Cancer Center were randomly assigned to two groups. The 65 patients in the first group received chemotherapy with the newly synthesized drug IDR (idarubicin). The 65 patients in the second group received chemotherapy with the standard drug DNR (daunorubicin). In this example a patient is a unit and the primary outcome "success" for this study is a successful response to the therapy in the sense that the patient achieved complete remission (a complete, but temporary cure) of the leukemia after the chemotherapy. a) Define two relevant (hypothetical) population success proportions p^1 and p^2. Note: These proportions should be defined for this group of 130 patients. b) State a research hypothesis relating the two population proportions p^1 and p^2 defined above relevant for determining whether the new drug IDR is better than the old drug DNR. Provide a clear and complete statement of this hypothesis in words in the context of this problem and explain why your hypothesis is appropriate. At the end of this study, 51 of the 65 patients in the group treated with IDR had achieved complete remission and 38 of the 65 patients in the group treated with DNR had achieved complete remission. c) Perform a hypothesis test to determine whether the data support your theory. Provide the relevant P-value and a complete summary explaining your conclusion in the context of this example. d) Form a 95% confidence interval for the difference between the population proportions p^1 and p^2 from above and provide a summary, in the context of this example, interpreting your confidence interval estimate of this difference and your inference about the effectiveness of the two chemotherapy drugs.Explanation / Answer
c) H0:p1bar=p2bar=0 (There is no difference in effectiveness of two drugs)
H1:p1bar-p2bar > 0 (new drug is better than old drug)
p1bar=51/65, and p2bar=38/65, where p1 and p2 denote sample proportion of patients with IDR who achieved complete remmission and p2 corresponds to sampl eproportion of patients wwith DNR who achieved complete remission.
Perform 2-proportion Z test to calcualte the test statistic and p value.
Z=(p1bar-p2bar)-0/SE(p1bar-p2bar)
SE(p1bar-p2bar)=sqrt[p1barq1bar/n1+p2barq2bar/n2]
=sqrt [51/65(1-51/65)/65+38/65(1-38/65)/65]
=0.08
Z=(51/65-38/65)-0/0.08
=2.51
The p value is 0.012, the p value is less than alpha=0.05. Reject null hypothesi sto conclude that new drug is better than old drug
d) From information given, p1bar=51/65, and p2bar=38/65, where p1 and p2 denote sample proportion of patients with IDR who achieved complete remmission and p2 corresponds to sampl eproportion of patients wwith DNR who achieved complete remission.
SE(p1bar-p2bar)=sqrt[p1barq1bar/n1+p2barq2bar/n2]
=sqrt [51/65(1-51/65)/65+38/65(1-38/65)/65]
=0.08
95% c.i=p1bar-p2bar+-ZSE(p1bar-p2bar), where Z represent z score at alpha=0.05
=(51/65-38/65)+-1.96*0.08
=0.04 to 0.36
The interval does not contain 0, therefore, there is significant difference in the effectiveness of two drugs, new drug is better than old drug.
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