Assignment
Question 1
The following data are collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo the extent of wound healing is measured and the data are shown below.
|
|
Wound Healing: % Reduction in Size of Wound
|
|
Treatment
|
None
|
1-25%
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26-50%
|
51-75%
|
76-100%
|
|
New Compound (n=125)
|
4
|
11
|
37
|
32
|
41
|
|
Placebo (n=125)
|
12
|
24
|
45
|
34
|
10
|
Suppose that clinicians feel that if the percent reduction in the size of the wound is greater than 50% then the treatment is a success.
a. Generate a 95% confidence interval for the percent success in patients receiving the new compound.
b. Generate a 95% confidence interval for the difference in the percent success between the new compound and placebo
c. Generate a 95% confidence interval for the relative risk of treatment success between treatments
d. Generate a 95% confidence interval for the odds ratio of treatment success between treatments.
Question 2
The following table displays descriptive statistics on the participants involved in the study described in Problem 1.
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Characteristic
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New Compound
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Placebo
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p-value
|
|
Mean Age, years
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47.2
|
46.1
|
0.7564
|
|
% Males
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44%
|
59%
|
0.0215
|
|
Mean Educational Level, years
|
13.1
|
14.2
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0.6898
|
|
Mean Annual Income, $000s
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$36,560
|
$37,470
|
0.3546
|
|
Mean Body Mass Index
|
24.7
|
25.1
|
0.0851
|
Are any of the characteristics significantly different between groups? Justify briefly. (Hint: No calculations, just interpret above.)
Question 4
An investigator hypothesizes that cholesterol levels in children might be affected by educating their parents on proper nutrition and exercise. A sample of 40 families with a child between the ages of 10-15 who has been diagnosed with high cholesterol agree to participate in the study. All parents are provided educational information on nutrition and exercise. After following the prescribed program, their child's total cholesterol level is measured. The children's mean cholesterol level is 175 with a standard deviation of 19.5. Is there significant evidence of a reduction in total cholesterol in the children? Run the appropriate test at the 5% level of significance and assume that the null value for total cholesterol is 191.
Step 1. Set up hypotheses and determine level of significance
Step 2. Select the appropriate test statistic.
Step 3. Set up decision rule.
Step 4. Compute the test statistic.
Step 5. Conclusion.
Question 3
Use the data in Tables 1 and 2 to conduct tests of hypothesis to determine whether the father's diagnosis of ADHD is a confounding factor. (Hint: Test if there is a relationship between the father's diagnosis and the child's exposure and between the father's diagnosis and the child's diagnosis.) Is father's diagnosis of ADHD a confounder? Justify your conclusion.
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Table 1.
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Father's diagnosis and child's exposure
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Exposed to Lead Paint
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Not Exposed to Lead Paint
|
|
Father with ADHD
|
66
|
44
|
|
Father without ADHD
|
39
|
251
|
Step 1. Set up hypotheses and determine level of significance
Step 2. Select the appropriate test statistic.
Step 3. Set up decision rule.
Step 4. Compute the test statistic.
Step 5. Conclusion.
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Table 2.
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|
Father's diagnosis and child's diagnosis
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Child with ADHD
|
Child without ADHD
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|
Father with ADHD
|
34
|
76
|
|
Father without ADHD
|
29
|
261
|
Step 1. Set up hypotheses and determine level of significance
Step 2. Select the appropriate test statistic.
Step 3. Set up decision rule.
Step 4. Compute the test statistic.
Step 5. Conclusion.
Is father's diagnosis a confounding factor? State your final answer below and provide an explanation why you came to this conclusion.
Question 4
A study is run to evaluate risk factors for incident hypertension. All participants are free of hypertension at the start of the study and are followed for 4 years at which time they are re-assessed for hypertension. Risk factors are measured in all participants at the start of the study. A total of n=3182 participants enroll and 1123 develop hypertension over 4 years. A multiple logistic regression model is run and the results are as follows:
|
Risk Factor
|
Regression Coefficient
|
Chi-Square
|
P-value
|
|
Intercept
|
-18.416
|
746.103
|
0.0001
|
|
Age, years
|
0.0533
|
95.004
|
0.0001
|
|
Male Gender*
|
-0.2524
|
6.189
|
0.0129
|
|
Systolic Blood Pressure
|
0.0629
|
141.417
|
0.0001
|
|
Diastolic Blood Pressure
|
0.0752
|
80.237
|
0.0001
|
|
BMI
|
0.0637
|
29.209
|
0.0001
|
|
Current Smoker*
|
0.3270
|
10.116
|
0.0015
|
Male gender is coded 1=male, 0=female. Current smoker is coded 1=yes, 0=no.
a. What is the relative importance (statistical significance) of the risk factors? Justify your answer.
b. Estimate adjusted odds ratios to quantify the effect of gender and current smoking status on incident hypertension.
c. Who is more likely to develop hypertension, a man or a woman? Justify your answer.
Question 5
The following table displays the numbers of participants who develop hypertension by gender and age group in the study described in Problem 13.
|
Women
|
Develop Hypertension
|
Do Not Develop Hypertension
|
Total
|
|
Age 50+ Years
|
255
|
237
|
492
|
|
Age < 50 Years
|
241
|
916
|
1157
|
|
Total
|
496
|
1153
|
1649
|
|
Men
|
Develop Hypertension
|
Do Not Develop Hypertension
|
Total
|
|
Age 50+ Years
|
283
|
188
|
471
|
|
Age < 50 Years
|
344
|
718
|
1062
|
|
Total
|
627
|
906
|
1533
|
a. What is the relative risk for hypertension in women 50+ years versus women < 50 years of age?
b. What is the relative risk for hypertension in men 50+ years versus men < 50 years of age?
Question 15
Use the data in Problem 14 to estimate the relative risk for hypertension in participants < 50 years of age versus 50 years of age and older, adjusted for gender using the Cochran-Mantel-Haenszel method.