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Example A study is côna ne effectiveness of a new drug in treating the symptoms associated with a certain illness. 2,500 volunteers are selected for the study and they are divided into two groups of 1,250 patients each. During the course of the study some patients withdraw from the study, others are taken out for medical complications, and others die. At the end of the study there were 1,180 patients in the placebo group and 1,047 in the drug group. Interviews with the patients and medical exams were performed to determine if the symptoms improved, or if on the contrary, they worsen or stayed the same. The results are given in Table 4.11. Symptoms\ Group Placebo Drug

Example A study is côna ne effectiveness of a new drug in treating the symptoms associated with a certain illness. 2,500 volunteers are selected for the study and they are divided into two groups of 1,250 patients each. During the course of the study some patients withdraw from the study, others are taken out for medical complications, and others die. At the end of the study there were 1,180 patients in the placebo group and 1,047 in the drug group. Interviews with the patients and medical exams were performed to determine if the symptoms improved, or if on the contrary, they worsen or stayed the same. The results are given in Table 4.11. Symptoms\ Group Placebo Drug

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Repeat the analysis of the clinical study in Example 4.4.8 on page 155 using a confidence level of 95%. What conclusion can you draw about the effectiveness of the drug?

Example 4.4.8. A clinical study is conducted to determine the effectiveness of a new drug in treating the symptoms associated with a certain illness. 2,500 volunteers are selected for the study and they are divided into two groups of 1,250 patients each. During the course of the study some patients withdraw from the study, others are taken out for medical complications, and others die. At the end of the study there were 1,180 patients in the placebo group and 1,047 in the drug group. Interviews with the patients and medical exams were performed to determine if the symptoms improved, or if on the contrary, they worsen or stayed the same. The results are given in Table 4.11. Symptoms\ Group Placebo Drug Improve Worsen or no change 805 785 375 262 Total 1,180 1,047 Table 4.11: Results of Clinical Study CHAPTER 4. STATISTICS 156 Determine, with a confidence level of 99.7%, if the drug is more effective than the placebo. We will estimate what percentage p of patients in the general population respond positively (improve) to the placebo and to the drug. This estimation will be done based on the observed percentage p for the corresponding group. We will do the calculations for both groups side by side. Recall that to have a confidence level of 99.7% for the value of p we need to move 3 standard errors away from p. Placebo Improve Worse or no change = 375 Drug Improve = 785 Worse or no change = 262 = 805 n = 1, 180 n = 1,047 785 1047 805 2 0.6822 2 0.7498 1180 Standard error 2 0.01355 I- 0.01339 p – 3° < p <p+3º 0.6415 < p < 0.7228 0.7096 < p< 0.7899 Because the intervals of possible values for p in both groups overlap, we cannot conclude that p for the drug group is higher than p for the placebo group. In other words, there is not statistically significant evidence that the drug does any better than the placebo.
Transcribed Image Text:Example 4.4.8. A clinical study is conducted to determine the effectiveness of a new drug in treating the symptoms associated with a certain illness. 2,500 volunteers are selected for the study and they are divided into two groups of 1,250 patients each. During the course of the study some patients withdraw from the study, others are taken out for medical complications, and others die. At the end of the study there were 1,180 patients in the placebo group and 1,047 in the drug group. Interviews with the patients and medical exams were performed to determine if the symptoms improved, or if on the contrary, they worsen or stayed the same. The results are given in Table 4.11. Symptoms\ Group Placebo Drug Improve Worsen or no change 805 785 375 262 Total 1,180 1,047 Table 4.11: Results of Clinical Study CHAPTER 4. STATISTICS 156 Determine, with a confidence level of 99.7%, if the drug is more effective than the placebo. We will estimate what percentage p of patients in the general population respond positively (improve) to the placebo and to the drug. This estimation will be done based on the observed percentage p for the corresponding group. We will do the calculations for both groups side by side. Recall that to have a confidence level of 99.7% for the value of p we need to move 3 standard errors away from p. Placebo Improve Worse or no change = 375 Drug Improve = 785 Worse or no change = 262 = 805 n = 1, 180 n = 1,047 785 1047 805 2 0.6822 2 0.7498 1180 Standard error 2 0.01355 I- 0.01339 p – 3° < p <p+3º 0.6415 < p < 0.7228 0.7096 < p< 0.7899 Because the intervals of possible values for p in both groups overlap, we cannot conclude that p for the drug group is higher than p for the placebo group. In other words, there is not statistically significant evidence that the drug does any better than the placebo.
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