MPH501 2020 January All Exercises Latest

MPH501 Quantitative Methods for Public Health Application

Module 1 Exercise

Question 1An investigator wants to assess whether smoking is a risk factor for pancreatic cancer. Electronic medical records at a local hospital will be used to identify fifty patients with pancreatic cancer.  One hundred patients who are similar but free of pancreatic cancer will also be selected.  Each participant’s medical record will be analyzed for smoking history.  Identify the type of study proposed and indicate its specific strengths and weaknesses.

Question 2What is the most likely source of bias in the study described in Problem 1.

Question 3An investigator wants to assess whether the use of a specific medication given to infants born prematurely is associated with developmental delay. Fifty infants who were given the medication and fifty comparison infants who were also born prematurely but not given the medication will be selected for the analysis. Each infant will undergo extensive testing at age 2 for various aspects of development. Identify the type of study proposed and indicate its specific strengths and weaknesses.

Question 4 A study is planned to assess the effect of a new surgical intervention for gallbladder disease. One hundred patients with gallbladder disease will be randomly assigned to receive either the new surgical intervention or the standard surgical intervention. The efficacy of the new surgical intervention will be measured by the time is takes a patient to return to normal activities, measured in days. Identify the type of study proposed and indicate its specific strengths and weaknesses.

 

MPH501 Quantitative Methods for Public Health Application

Module 2 Exercise

Question 1 A cohort study is conducted to assess the association between clinical characteristics and the risk of stroke.  The study involves n=1,250 participants who are free of stroke at the study start.  Each participant is assessed at study start (baseline) and every year thereafter for five years.  The following table displays data on hypertension status measured at baseline and hypertension status measured two years later.

             2 Years: Not Hypertensive           2 Years: Hypertensive

Baseline: Not Hypertensive         850       148

Baseline: Hypertensive   45         207

a.          Compute the prevalence of hypertension at baseline.

b.          Compute the prevalence of hypertension at 2 years.

c.           Compute the cumulative incidence of hypertension over 2 years.

Question 2A randomized trial is conducted to evaluate the efficacy of a new cholesterol lowering medication.  The primary outcome is incident coronary artery disease.  Participants are free of coronary artery disease at the start of the study and randomized to receive either the new medication or a placebo.  Participants are followed for a maximum of 10 years for the development of coronary artery disease.  The following data are observed.

             Number of Participants  Number with Coronary Artery Disease

Cholesterol Medication  400       28

Placebo 400       42

Some patients were not followed for a total of 10 years.  Some suffered events (i.e., developed coronary artery disease during the course of follow-up) while others dropped out of the study.  The following table displays the total number of person-years of follow-up in each group.

             Number with Coronary Artery Disease   

Total Years of Follow-Up

Cholesterol Medication  28         3,451

Placebo 42         2,984

a.          Compute the incidence rate of coronary artery disease in patients receiving the new medication.

b.          Compute the incidence rate of coronary artery disease in patients receiving placebo.

Question 3A study is run to estimate the mean total cholesterol level in children 2-6 years of age.  A sample of 9 participants is selected and their total cholesterol levels are measured as follows.

185      225      240      196      175      180      194      147      223

X           X2

147       21,609

175       30,625

180       32,400

185       34,225

194       37,636

196       38,416

223       49,729

225       50.625

240       57,600

1765     352,865

a.          Compute the sample mean.

b.          Compute the sample standard deviation.

c.           Compute the median.

d.          Compute the first and third quartiles.

e.          Which measure, the mean or median, is a better measure of a typical value?  Justify.

f.           Which measure, the standard deviation or the interquartile range, is a better measure of dispersion?  Justify.

Question 4 The following data were collected as part of a study of coffee consumption among graduate students.  The following reflect cups per day consumed:

3          4          6          8          2          1          0          2

X           X2

0           0

1           1

2           4

2           4

3           9

4           16

6           36

8           64

26         134

a.          Compute the sample mean.

b.          Compute the sample standard deviation.

c.           Compute the median.

d.          Compute the first and third quartiles.

e.          Which measure, the mean or median, is a better measure of a typical value?  Justify.

f.           Which measure, the standard deviation or the interquartile range, is a better measure of dispersion?  Justify.

Question 5 In the study of a new anti-hypertensive medication, systolic blood pressures are measured at baseline (or the start of the study before any treatment is administered).  The data are as follows:

120      112      138      145      135      150      145      163    

148      128      143      156      160      142      150

a.          Compute the sample mean.

b.          Compute the sample median.

c.           Compute the sample standard deviation.

d.          Compute the sample range.

e.          Are there any outliers?  Justify.

 

MPH501 Quantitative Methods for Public Health Application

Module 3 Exercise

Question 1Hyperlipidemia in children has been hypothesized to be related to high cholesterol in their parents.  The following data were collected on parents and children.

CHILD   Both Parents Hyperlipidemic       One Parent Hyperlipidemic         Neither Parent Hyperlipidemic

Not Hyperlipidemic        13         34         83

Hyperlipidemic  45         42         6

a.          What is the probability that one or both parents are hyperlipidemic?

b.          What is the probability that the child and both parents are hyperlipidemic?

c.           What is the probability that a child is hyperlipidemic IF neither of his/her parents are hyperlipidemic?

d.          What is the probability that a child is hyperlipidemic IF both of his/her parents are hyperlipidemic?

Question 2 A national survey of graduate students is conducted to assess their consumption of coffee.  The following table summarizes the data.

             Do not drink coffee         Drink Decaffeinated Only            Drink Caffeinated Coffee

Male     145       94         365

Female 80         121       430

a.          What proportion of students drink decaffeinated coffee only?

b.          What proportion of coffee drinkers (caffeinated and decaffeinated) are female?

c.           What proportion of the females do not drink coffee?

Question 3 Investigators wanted to assess the accuracy of self-reported smoking status.  Participants are asked whether they currently smoke or not.  In addition, laboratory tests are performed on hair samples to determine presence or absence of nicotine.  The laboratory assessment is considered the gold standard, or truth about nicotine.  The data are as follows:

             Nicotine Absent Nicotine Present

Self-Reported Non-Smoker          82         14

Self-Reported Smoker    12         52

a.          What is the sensitivity of self-reported smoking status?

b.          What is the specificity of self-reported smoking status?

Question 4 The following table displays blood pressure status by sex.

             Optimal             Normal Hypertension     Total

Male     22         73         55         150

Female 43         132       65         240

Total     65         205       120       390

a.          What proportion of the participants have optimal blood pressure?

b.          What proportion of men have optimal blood pressure?

c.           What proportion of participants with hypertension are male?

d.          Are hypertensive status and male gender independent?

Question 5 Suppose BMI at 16 weeks gestation has a mean 28.5 with a standard deviation of 3.6 and BMI is assumed to follow a normal distribution.  Find the following:

a.          The proportion of women with BMI> 30.

b.          The proportion of women with BMI>40.

c.           The BMI that separates the top 10% from the rest.

Question 6 Diastolic blood pressures are approximately normally distributed with a mean of 75 and a standard deviation of 10.

a.          What is the 90th percentile of diastolic blood pressure?

b.          If we consider samples of 20 patients, what is the 90th  percentile of the mean diastolic blood pressure?

 

 

 

 

MPH501 Quantitative Methods for Public Health Application

Module 4 Exercise

Question 1 A study is run to estimate the mean total cholesterol level in children 2-6 years of age.  A sample of 9 participants is selected and their total cholesterol levels are measured as follows.

185      225      240      196      175      180      194      147      223

Generate a 95% confidence interval for the true mean total cholesterol levels in adults with a history of hypertension.

X	X2
185	34,225
225	50,625
240	57,600
196	38,416
175	30,625
180	32,400
194	37,636
147	21,609
223	49,729
1,765	352,865

Question 2 The main trial is conducted and involves a total of 200 patients.  Patients are enrolled and randomized to receive either the experimental medication or the placebo.  The data shown below are data collected at the end of the study after 6 weeks on the assigned treatment.

Generate a 95% confidence interval for the difference in mean systolic blood pressures between groups.

Question 3 The following data are collected as part of a study of coffee consumption among undergraduate students.  The following reflect cups per day consumed:

3          4          6          8          2          1          0          2

X	X2
3	9
4	16
6	36
8	64
2	4
1	1
0	0
2	4
26	134

 

Compute the sample mean

Compute the sample standard deviation

Construct a 95% confidence interval for the mean number of cups of coffee consumed among all undergraduates.

Question 4 The following table displays descriptive statistics on the participants involved in a study.

Characteristic	Experimental Medication (n=100)	Placebo (n=100)
Mean (SD) Age, years	47.2 (4.3)	46.1 (5.1)
% Males	46%	58%
Mean (SD) Educational Level, years	13.1 (2.9)	14.2 (3.1)
Mean (SD) Annual Income, $000s	$36.560 ($1,054)	$37.470 ($998)
Mean Body Mass Index	24.7 (2.7)	25.1 (2.4)

 

Generate a 95% confidence interval for the mean age among participants assigned to the placebo.

Generate a 95% confidence interval for the difference in mean ages in participants assigned to the experimental versus the placebo groups.

Generate a 95% confidence interval for the difference in mean body mass index in participants assigned to the experimental versus the placebo groups.

Question 5 A crossover trial is conducted to compare an experimental medication for migraine headaches to a currently available medication.  A total of 50 patients are enrolled in the study and each patient receives both treatments.  The outcome is the time, in minutes, until the headache pain resolves.  Following each treatment, patient’s record the time it takes until pain is resolved.  Treatments are assigned in random order (i.e., some patients receive the currently available medication first and then the experimental medication and others receive the experimental medication first and then the currently available medication).  The mean difference in times between the experimental and currently available medication is -9.4 minutes, with a standard deviation of 2.8 minutes.  Construct a 95% confidence interval for the mean difference in times between the experimental and currently available medication.

Question 6 A clinical trial is run to assess the efficacy of a new pacemaker device in patients with atrial fibrillation (AF).  Two hundred participants are randomized to receive the new pacemaker or a currently available pacemaker.  There are two primary outcomes of interest – the number of days in a three month period with an atrial fibrillation event and hospitalization for atrial fibrillation over the three month follow-up period.  Data on baseline characteristics and the outcomes are shown below.

 

Baseline Characteristics	New Pacemaker (n=100)	Available Pacemaker (n=100)
Mean (SD) Age, years	67.3 (5.9)	66.9 (5.6)
% Male	48%	52%
Outcomes
Mean (SD) Number of days with AF event	8.4 (3.2)	14.9 (3.9)
% Hospitalized for AF	4%	9%

 

Compute a 95% confidence interval for the difference in mean number of days with an AF event between participants receiving the new pacemaker as compared to the available pacemaker.

Compute a 95% confidence interval for the mean number of days with an AF event among participants receiving the new pacemaker.

 

 

 

 

 

 

MPH501 Quantitative Methods for Public Health Application

Module 5 Exercise

Question 1 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.

Question 2 The main trial in Problem 7 is conducted and involves a total of 200 patients.  Patients are enrolled and randomized to receive either the experimental medication or the placebo.  The data shown below are data collected at the end of the study after 6 weeks on the assigned treatment.

	Experimental (n=100)	Placebo (n=100)
Mean (SD) Systolic Blood Pressure	120.2 (15.4)	131.4 (18.9)
% Hypertensive	14%	22%
% With Side Effects	6%	8%

a.          Test if there is a significant difference in mean systolic blood pressures between groups using []=0.05.

Question 3Suppose a secondary outcome is recorded in the trial described in Problem 10 reflecting asthma symptom severity measured on a scale of 0-100 with higher scores indicating more severe symptoms.  In the participants who receive the experimental medication the mean symptom score is 74 with a standard deviation of 5.6 and in the placebo group the mean symptom score is 85 with a standard deviation of 6.0.  Is there a significant difference in mean symptom scores between groups?  Run the appropriate test at a 5% level of significance.

Question 4 Recent recommendations suggest 60 minutes of physical activity per day.  A sample of 50 adults in a study of cardiovascular risk factors report exercising a mean of 38 minutes per day with a standard deviation of 19 minutes.  Based on the sample data, is the physical activity significantly less than recommended?  Run the appropriate test at a 5% level of significance.

Question 5 A study is conducted to compare mean cholesterol levels for individuals following a low carbohydrate diet for at least 6 months to individuals following a conventional (low-fat, low calorie) diet for at least 6 months.  The data are summarized below:

Diet Program     Sample Size       Mean Cholesterol           Std Dev Cholesterol

Low Carbohydrate          50         225.4    24.5

Conventional     75         203.8    21.6

Test if there is a significant difference in mean cholesterol levels between the diet programs using a 5% level of significance.

Question 6 The mean lifetime for cardiac stents is 8.9 years.  A medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer.  A study of 40 new devices reveals a mean lifetime of 9.7 years with a standard deviation of 3.4 years.  Is there statistical evidence of a prolonged lifetime of the stents?  Run the test at a 5% level of significance.

 

MPH501 Quantitative Methods for Public Health Application

Module 6 Exercise

Question 1 The following data was 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.

Percent Wound Healing
Treatment	0-25%	26-50%	51-75%	76-100%
New Compound (n=125)	15	37	32	41
Placebo (n=125)	36	45	34	10

Is there a difference in the extent of wound healing by treatment?  (Hint:  Are treatment and the percent wound healing independent?)  Run the appropriate test at a 5% level of significance.

Question 2The following data were collected in an experiment designed to investigate the impact of different positions of the mother during ultrasound on fetal heart rate.  Fetal heart rate is measured by ultrasound in beats per minute.  The study includes 20 women who are assigned to one position and have the fetal heart rate measured in that position.  Each woman is between 28-32 weeks gestation.  The data are shown below.

Back	Side	Sitting	Standing
140	141	144	147
144	143	145	145
146	145	147	148
141	144	148	149
139	136	144	145
Mean = 142.0	Mean = 141.8	Mean = 145.6	Mean =146.8

Is there a significant difference in mean fetal heart rates by position?  Run the test at a 5% level of significance.

Question 3In this study patients were recruited from 3 different clinical sites.  Use the following data to test if there is a difference in the proportions of hypertensive patients across clinical sites.

Site 1	Site 2	Site 3
Hypertensive	10	14	12
Not Hypertensive	68	56	40

Question 4 Suppose more detail is actually recorded in the primary outcome in the clinical trial described in Problem 10.  The data are recorded as follows.

Change in Symptoms
Treatment	Much Worse	Worse	No change	Better	Much Better
Experimental	10	17	35	28	10
Placebo	12	25	42	12	9

 

Is there a difference in change in symptoms by treatment group?  Run the appropriate test at a 5% level of significance.

Question 5An investigator wants to estimate caffeine consumption in high school students. How many students would be required to ensure that a 95% confidence interval estimate for the mean caffeine intake (measured in mg) is within 15 mg of the true mean? Assume that the standard deviation in caffeine intake is 68 mg.

Question 6 A crossover trial is planned to evaluate the impact of an educational intervention program to reduce alcohol consumption in patients determined to be at risk for alcohol problems. The plan is to measure alcohol consumption (the number of drinks on a typical drinking day) before the intervention and then again after participants complete the educational intervention program. How many participants would be required to ensure that a 95% confidence interval for the mean difference in the number of drinks is within 2 drinks of the true mean difference? Assume that the standard deviation of the difference in the mean number of drinks is 6.7 drinks and that 20% of the participants will drop out over the course of follow up.

 

MPH501 Quantitative Methods for Public Health Application

Module 7 Exercise

Question 1 A clinical trial is run to evaluate the efficacy of a new medication to relieve pain in patients undergoing total knee replacement surgery.  In the trial, patients are randomly assigned to receive either the new medication or the standard medication.  After receiving the assigned medication, patients are asked to report their pain on a scale of 0-100 with higher scores indicative of more pain.  Data on the primary outcome are shown below.

 

 

 

 

Sample Size	Mean Pain Score	Standard Deviation of Pain Score
New Medication	60	30.31	7.52
Standard Medication	60	53.85	7.44

Because procedures can be more complicated in older patients, the investigators are concerned about confounding by age.  For analysis, patients are classified into two age groups, less than 65 and 65 years of age and older.  The data are shown below.

Age < 65 Years	Sample Size	Mean Pain Score	Standard Deviation of Pain Score
New Medication	40	25.30	2.46
Standard Medication	25	45.51	1.83
Total: Age < 65 Years	65	33.07	10.16
Age 65+ Years	Sample Size	Mean Pain Score	Standard Deviation of Pain Score
New Medication	20	40.33	2.16
Standard Medication	35	59.80	2.49
Total: Age 65+	55	52.72	9.74

 

Is there a statistically significant difference in mean pain scores between patients assigned to the new medication as compared to the standard medication?  Run the appropriate test at ?=0.05.  (Ignore age in this analysis.)

Question 2 Use the data in Problem 7 to determine whether age a confounding variable.   Run the tests of hypothesis to determine whether the age is related to treatment assignment and whether there is a difference in mean pain scores by age group.  Is age a confounder?  Justify your conclusion.

 

 

 

Age Group and Treatment	New Medication	Standard Medication
Age < 65	40	25
Age 65+	20	35