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2. A clinical trial is conducted to evaluate the efficacy of a new drug for prevention of hypertension in patients with pre-hypertension (defined as systolic blood pressure between 120–139 mmHg or diastolic blood pressure between 80–89 mmHg). A total of 20 patients are randomized to receive the new drug or a currently available drug for treatment of high blood pressure. Participants are followed for up to 12 months, and time to progression to hypertension is measured. The experiences of participants in each arm of the trial are shown below.
New Drug | Currently Available Drug | |||
Hypertension | Free of Hypertension | Hypertension | Free of Hypertension | |
7 | 8 | 6 | 8 | |
8 | 8 | 7 | 9 | |
10 | 8 | 9 | 11 | |
9 | 10 | 11 | ||
11 | 11 | 12 | ||
12 | ||||
12 |
Estimate the survival (time to progression to hypertension) functions for each treatment group using the Kaplan-Meier approachNew Drug
Complete the table below.
Time, Months | Number at Risk
Nt |
Number of Events (Hypertension)
Dt |
Number Censored
Ct |
Survival Probability
S_{t+1 }= S_{t}*((N_{t}-D_{t})/N_{t}) |
0 | 10 | 0 | ||
7 | 1 | |||
8 | 1 | |||
9 | 0 | |||
10 | 1 | |||
11 | 0 | |||
12 | 0 |
Currently Available Drug
Complete the table below.
Time, Weeks | Number at Risk
Nt |
Number of Events (Hypertension)
Dt |
Number Censored
Ct |
Survival Probability
S_{t+1 }= S_{t}*((N_{t}-D_{t})/N_{t}) |
0 | 10 | |||
6 | ||||
7 | ||||
8 | ||||
9 | ||||
10 | ||||
11 | ||||
12 |
To answer the question as to whether or not there is a difference in time to progression, a Chi square statistic is computed. The critical value for rejection of the null hypothesis is 3.84. The computed Chi square is 0.335.
Based on comparing the computed Chi square and the critical Chi square, which of the following is (are) true?
- There is not statistically significant evidence to show that the time to progression is different between groups.
- There is statistically significant evidence to show that the time to progression is different between groups.
- The time to progression is essentially the same for each group.
- a and c.
The hazard ratio risk of progression to hypertension is 0.658. Based on this computation, which of the following is (are) true?
- The risk of progression to hypertension is reduced by 34.2% in patients assigned to the new drug as compared to the currently available drug.
- The risk of progression to hypertension is 1.52 times higher in patient’s current drug as compared to the new drug.
- The risk of progression to hypertension is 5.12 times higher in patient’s current drug as compared to the new drug
- a and b
The mean BMI in patients free of diabetes was reported as 28.2. The investigator conducting the study hypothesizes that the BMI in patients free of diabetes is higher. Based on the data given below is there evidence that the BMI is significantly higher that 28.2? Use a 5% level of significance. 25 27 31 33 26 28 38 41 24 32 35 40Critical t value: (2 points)Computed t = (2 points)Based on comparing the critical t value to the computed t value which of the following is (are) true?
a. There is statistically significant evidence at alpha=0.05 to show the BMI is significantly higher than 28.2. b. There is not statistically significant evidence at alpha=0.05 to show the BMI is significantly higher that 28.2. c. There are not enough data points to reach a conclusion.d. b and c.
A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children. A total of 250 children are randomized to either the new drug or placebo (125 per group). The mean age of children assigned to the new drug is 12.4 with a standard deviation of 3.6 years. The mean age of children assigned to the placebo is 13.0 with a standard deviation of 4.0 years. Is there a statistically significant difference in ages of children assigned to the treatments? Apply the two sample z test at a 5% level of significance.
1. Critical z value = +/- (2 points)
2. Computed statistic= (2 points)
3. Based on comparing the computed statistic to the critical value which of the following is (are) true? (6 points)
a. There is significant evidence, alpha=0.05, that there is a difference in ages of children assigned to the treatments.
b. There is not significant evidence, alpha=0.05, that there is a difference in ages of children assigned to the treatments.
c. Statistically speaking the difference in initial weights and weights after 6 weeks is 0.
d. b and c.
A small pilot study is conducted to investigate the effect of a nutritional supplement on total body weight. Six participants agree to take the nutritional supplement. To assess its effect on body weight, weights are measured before starting the supplementation and then after 6 weeks. The data are shown below. Is there a significant increase in body weight following supplementation? Use a paired t-test at a 5% level of significance.
1. df=_____ (2 points)
2. Critical value: ______ (2 points)
3. Computed statistic:_____ (2 points)
4. Based on comparing the computed statistic to the critical value which of the following is (are) true? (4 points)
a. There is significant evidence, alpha=0.05, to show that body weight increased following supplementation?
b. There is not significant evidence, alpha=0.05, to show that body weight increased following supplementation?
c. Statistically speaking the difference in initial weights and weights after 6 weeks is 0.
d. b and c.
A study is designed to investigate whether there is a difference in response to various treatments in patients with rheumatoid arthritis. The outcome is patient’s self-reported effect of treatment. The data are shown below. Is there a statistically significant difference in the proportions of patients who show improvement between treatments 1 and 2. Apply the test at a 5% level of significance.
1. Critical value: (2 points)
2. Computed statistic: (2 points)
3. Based on comparing the computed statistics to the critical value which of the following is (are) true? (6 points)
a. There is significant evidence, alpha=0.05, to show that there is a difference in the proportions of patients who show improvement between treatments 1 and 2.
b. There is not significant evidence, alpha=0.05, to show that there is a difference in the proportions of patients who show improvement between treatments 1 and 2.
c. There is significant evidence, alpha=0.05, to show that there is a no difference in the proportions of patients who show improvement between treatments 1 and 2.
d. a and c.
A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children. A total of 250 children are randomized to either the new drug or placebo (125 per group). There are 63 boys assigned to the new drug group and 58 boys assigned to the placebo. Is there a statistically significant difference in the proportions of boys assigned to the treatments? Apply the appropriate test at a 5% level of significance.1. Critical value= +/- (2 points)2. Computed statistics= (2 points)3. Based on comparing the computed statistic to the critical value which of the following is (are) true? (6 points)
a. There is significant evidence, alpha=0.05, that there is a difference in the proportions of boys assigned to the treatments.b. There is not significant evidence, alpha=0.05, that there is a difference in the proportions of boys assigned to the treatments.c. Statistically speaking the difference in the proportions of boys assigned to the treatments is 0.d. b and c.
The following data were collected in a clinical trial to compare a new drug to a placebo for its effectiveness in lowering total serum cholesterol. Generate a 95% confidence interval for the difference in mean total cholesterol levels between treatments.
1. Upper limit of CI: (2 points)
2. Lower limit of CI: (2 points)
3. Based on the confidence interval which of the following is (are) true? (4 points)
a. There is significant evidence, alpha=0.05, to show that there is a difference in Total Serum Cholesterol between treatments New Drug and Placebo.
b. There is not significant evidence, alpha=0.05, to show that there is a difference in Total Serum Cholesterol between treatments New Drug and Placebo.
c. The difference between Total Serum Cholesterol between treatments New Drug and Placebo is essentially 0.
d. b and c.