Biostatistics Team Project 1 ? Questions 1. A study is conducted to test a new drug claimed to reduce diastolic blood pressure in adults with a history of coronary heart disease. What is the most efficient study to test whether the drug reduces diastolic blood pressure? Justify your answer. 2. An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs and indicate the pros and cons of each. Then, provide your recommendation for the most efficient design. 3. True or False? The following are all examples of observational study designs: a) Case-control study. b) Prospective cohort study. c) Cross-over trial. d) Retrospective cohort study. 4. A study is run to estimate the incidence of atrial fibrillation (AF) in men and women over the age of 60. Development of atrial fibrillation was monitored over a 10-year follow-up period. The data are summarized below: Developed AF Did not Develop AF Men 120 6453 Women 86 7074 a) Compute the cumulative incidence of AF in men and in women. b) Compute the relative risk of AF incidence comparing men to women. c) Compute the odds ratio of AF incidence comparing men and women. 5. A clinical trial designed to show the efficacy of a new drug in reducing progression to hypertension reports the following: New Drug Placebo Sample size 200 200 Progression to hypertension 14% 19% a) Compute the relative risk of progression to hypertension among patients receiving the new drug as compared to the placebo. b) Compute the difference in proportions of patients progressing to hypertension between the two groups. c) Compute the odds ratio of progression to hypertension among patients receiving the new drug as compared to the placebo. 6. The following are grade point averages measured in a sample of 8 undergraduate students who are applying to graduate schools in public health. 3.28 2.97 3.05 3.61 3.39 2.95 3.00 3.10 a) Compute the sample mean. b) Compute the sample standard deviation. c) Compute the sample median. 7. The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. 25 27 31 33 26 28 38 41 24 32 35 40 a) Compute the mean BMI. b) Compute the standard deviation of BMI. c) Compute the median BMI. d) Compute Q1 and Q3. e) Are there outliers in the distribution of BMI? Justify your answer. 8. A pilot study is run to investigate the effect of a lifestyle intervention designed to increase medication adherence in patients with HIV. Medication adherence is measured as the percentage of prescribed pills that are taken over a one week observation period. Ten patients with HIV agree to participate and their medication adherence before and after the intervention are shown below. Participant ID Before Intervention After Intervention 1 75% 80% 2 82% 84% 3 66% 70% 4 74% 70% 5 88% 90% 6 66% 75% 7 51% 60% 8 93% 90% 9 88% 90% 10 91% 95% a) Compute differences in adherence before versus after the intervention for each participant. b) Compute the mean difference in adherence before versus after the intervention. c) Compute the standard deviation of the difference in adherence before versus after intervention. 9. True or False? For the standard normal distribution, Q3 = 0.675. 10. A random sample of eight adults, aged 30 years, were asked how much they spent on medical costs in the year 2009. The following data were measured. 300 140 5600 520 470 700 640 1200 a) Compute the sample mean. b) Compute the sample standard deviation. c) Compute the sample median. d) Compute the first and third quartiles. 11. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean of 120 and a standard deviation of 16. a) What proportion of patients has glucose levels exceeding 115? b) If a patient has a glucose level of 140, what percentile is this? c) What is the probability that the mean glucose level exceeds 115 in a sample of 12 patients? 12. The following table shows the numbers of patients classified as underweight, normal weight, overweight, and obese, according to their diabetes status. Underweight Normal Weight Overweight Obese Diabetes 8 34 65 43 No Diabetes 12 85 93 40 If a patient is selected at random: a) What is the probability that they are overweight? b) What is the probability that they are obese and diabetic? c) What proportion of the diabetics is obese? d) What proportion of normal-weight patients are not diabetic? e) What proportion of patients is normal weight or underweight? 13. Approximately 30 percent of obese patients develop diabetes. If a physician sees 10 patients who are obese: a) What is the probability that half of them will develop diabetes? b) What is the probability that none will develop diabetes? c) How many would you expect to develop diabetes? 14. The following table shows the distribution of BMI in children living in U.S. and European urban neighborhoods. (The data are in millions.) Neighborhood Normal Weight Overweight Obese US 125 50 40 Europe 101 42 21 Suppose that the probability that a child living in an urban area in the US is obese is 20 percent. A social worker sees 15 children living in urban areas, a) What is the probability that none are obese? b) What is the probability that 5 are obese? 15. BMI in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2. a) A BMI between 25 and 30 is considered overweight. What proportion of children is overweight? b) A BMI of 30 or more is considered obese. What proportion of children is obese? c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25? 16. The following data were collected in a survey of 8th graders and summarize their cell phone status. No cell phone Conventional cell phone user Smart phone user Boys 55 65 35 Girls 31 78 27 a) What proportion of the 8th graders has cell phones? b) What proportion of the boys does not have cell phones? c) Is ownership of a cell phone independent of sex? Justify your answer. d) What proportion of smart phone users are boys? 17. A ferritin test is a popular test to measure a person’s current iron stores. In women, ferritin is approximately normally distributed with a mean of 89 ng/mL and a standard deviation of 23 ng/mL. a) What is the probability that a woman has a ferritin value of 100 or less? b) If a woman has a ferritin of 140, what percentile is this? c) If 50 women are tested, what is the probability that the mean ferritin exceeds 90? 18. With a binomial distribution with n=25 and p=0.48, which is larger: a) P(12 successes). b) P(9 successes). c) P(20 successes). d) P(10 successes). 19. The following table shows the results of a screening test hypothesized to detect persons at risk for side effects of a new cosmetic surgery. Side effects present Side effects absent Screen positive 12 6 Screen negative 85 204 a) Compute the sensitivity of the test. b) Compute the specificity of the test. c) Compute the false positive fraction. d) Compute the false negative fraction. 20. The following table shows the results of a screening test hypothesized to identify persons at risk for a rare blood disease. No Disease Disease Screen Negative 1274 28 Screen Positive 51 45 a) Compute the sensitivity of the test. b) Compute the specificity of the test. c) Compute the false positive fraction. d) Compute the false negative fraction.

Biostatistics Team Project 1 ? Questions

1. A study is conducted to test a new drug claimed to reduce diastolic blood pressure in adults with a history of coronary heart disease. What is the most efficient study to test whether the drug reduces diastolic blood pressure? Justify your answer.

2. An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs and indicate the pros and cons of each. Then, provide your recommendation for the most efficient design.

3. True or False? The following are all examples of observational study designs:
a) Case-control study.
b) Prospective cohort study.
c) Cross-over trial.
d) Retrospective cohort study.

4. A study is run to estimate the incidence of atrial fibrillation (AF) in men and women over the age of 60. Development of atrial fibrillation was monitored over a 10-year follow-up period. The data are summarized below:

Developed AF Did not Develop AF
Men 120 6453
Women 86 7074

a) Compute the cumulative incidence of AF in men and in women.
b) Compute the relative risk of AF incidence comparing men to women.
c) Compute the odds ratio of AF incidence comparing men and women.

5. A clinical trial designed to show the efficacy of a new drug in reducing progression to hypertension reports the following:

New Drug Placebo
Sample size 200 200
Progression to hypertension 14% 19%

a) Compute the relative risk of progression to hypertension among patients receiving the new drug as compared to the placebo.
b) Compute the difference in proportions of patients progressing to hypertension between the two groups.
c) Compute the odds ratio of progression to hypertension among patients receiving the new drug as compared to the placebo.

6. The following are grade point averages measured in a sample of 8 undergraduate students who are applying to graduate schools in public health.
3.28 2.97 3.05 3.61 3.39 2.95 3.00 3.10
a) Compute the sample mean.
b) Compute the sample standard deviation.
c) Compute the sample median.

7. The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.
25 27 31 33 26 28 38 41 24 32 35 40
a) Compute the mean BMI.
b) Compute the standard deviation of BMI.
c) Compute the median BMI.
d) Compute Q1 and Q3.
e) Are there outliers in the distribution of BMI? Justify your answer.

8. A pilot study is run to investigate the effect of a lifestyle intervention designed to increase medication adherence in patients with HIV. Medication adherence is measured as the percentage of prescribed pills that are taken over a one week observation period. Ten patients with HIV agree to participate and their medication adherence before and after the intervention are shown below.

Participant ID Before Intervention After Intervention
1 75% 80%
2 82% 84%
3 66% 70%
4 74% 70%
5 88% 90%
6 66% 75%
7 51% 60%
8 93% 90%
9 88% 90%
10 91% 95%
a) Compute differences in adherence before versus after the intervention for each participant.
b) Compute the mean difference in adherence before versus after the intervention.
c) Compute the standard deviation of the difference in adherence before versus after intervention.

9. True or False? For the standard normal distribution, Q3 = 0.675.

10. A random sample of eight adults, aged 30 years, were asked how much they spent on medical costs in the year 2009. The following data were measured.
300 140 5600 520 470 700 640 1200
a) Compute the sample mean.
b) Compute the sample standard deviation.
c) Compute the sample median.
d) Compute the first and third quartiles.

11. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean of 120 and a standard deviation of 16.
a) What proportion of patients has glucose levels exceeding 115?
b) If a patient has a glucose level of 140, what percentile is this?
c) What is the probability that the mean glucose level exceeds 115 in a sample of 12 patients?

12. The following table shows the numbers of patients classified as underweight, normal weight, overweight, and obese, according to their diabetes status.

Underweight Normal Weight Overweight Obese
Diabetes 8 34 65 43
No Diabetes 12 85 93 40

If a patient is selected at random:
a) What is the probability that they are overweight?
b) What is the probability that they are obese and diabetic?
c) What proportion of the diabetics is obese?
d) What proportion of normal-weight patients are not diabetic?
e) What proportion of patients is normal weight or underweight?

13. Approximately 30 percent of obese patients develop diabetes. If a physician sees 10 patients who are obese:
a) What is the probability that half of them will develop diabetes?
b) What is the probability that none will develop diabetes?
c) How many would you expect to develop diabetes?

14. The following table shows the distribution of BMI in children living in U.S. and European urban neighborhoods. (The data are in millions.)

Neighborhood Normal Weight Overweight Obese
US 125 50 40
Europe 101 42 21

Suppose that the probability that a child living in an urban area in the US is obese is 20 percent. A social worker sees 15 children living in urban areas,
a) What is the probability that none are obese?
b) What is the probability that 5 are obese?

15. BMI in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2.
a) A BMI between 25 and 30 is considered overweight. What proportion of children is overweight?
b) A BMI of 30 or more is considered obese. What proportion of children is obese?
c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?

16. The following data were collected in a survey of 8th graders and summarize their cell phone status.

No cell phone Conventional cell phone user Smart phone user
Boys 55 65 35
Girls 31 78 27

a) What proportion of the 8th graders has cell phones?
b) What proportion of the boys does not have cell phones?
c) Is ownership of a cell phone independent of sex? Justify your answer.
d) What proportion of smart phone users are boys?

17. A ferritin test is a popular test to measure a person’s current iron stores. In women, ferritin is approximately normally distributed with a mean of 89 ng/mL and a standard deviation of 23 ng/mL.
a) What is the probability that a woman has a ferritin value of 100 or less?
b) If a woman has a ferritin of 140, what percentile is this?
c) If 50 women are tested, what is the probability that the mean ferritin exceeds 90?

18. With a binomial distribution with n=25 and p=0.48, which is larger:
a) P(12 successes).
b) P(9 successes).
c) P(20 successes).
d) P(10 successes).

19. The following table shows the results of a screening test hypothesized to detect persons at risk for side effects of a new cosmetic surgery.

Side effects present Side effects absent
Screen positive 12 6
Screen negative 85 204

a) Compute the sensitivity of the test.
b) Compute the specificity of the test.
c) Compute the false positive fraction.
d) Compute the false negative fraction.

20. The following table shows the results of a screening test hypothesized to identify persons at risk for a rare blood disease.

No Disease Disease
Screen Negative 1274 28
Screen Positive 51 45

a) Compute the sensitivity of the test.
b) Compute the specificity of the test.
c) Compute the false positive fraction.
d) Compute the false negative fraction.

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