BIO STATISTICS FINAL EXAM

·         Question 1

     

Match the following:    

o        

__B __Prognostic Factor           

                         B.  Strongly associated with outcome

__G __Prospective

                         G.  Study looking forward in time

__D __Quasi-experimental

                         D.  No random assignment

__E __Retrospective

                         E.  Study looking backward in time

__I __Stratification

                          I.  Subjects assigned to non overlapping groups

__A __Case control study

                         A.  Subjects identified based on outcome status

__H __Missclassification bias

                        H.  Outcome or exposure classification error

__J __RCT

                        C.  Subjects receive two or more treatments.

__C __Crossover Trial

                        J.  Subject randomly assigned to treatment groups

__F __Washout period

                        F.  Time when no treatment occurs    

·         Question 2

     An 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.

 

Type of study: 

Strengths:

Weaknessess:

         

·         Question 3

     In 1940, 2,000 women working in a factory were recruited into a study.  Half of the women worked in manufacturing and half in administrative offices.  The incidence of bone cancer through 1970 among the 1,000 women working in manufacturing was compared with that of 1,000 women working in administrative offices.  Thirty of the women in manufacturing developed bone cancer as compared to 9 of the women in administrative offices.  This study is an example of a:

 

                             ___ __ study

         

·         Question 4

     A clinical trial is conducted to evaluate the effectiveness of a new drug to prevent preterm delivery.  A total of n=250 pregnant women agree to participate and are randomly assigned to receive either the new drug or a placebo and followed through the course of pregnancy.   Among 125 women receiving the new drug, 24 deliver preterm and among 125 women receiving the placebo, 38 deliver preterm.  Construct a 95% confidence interval for the difference in proportions of women who deliver preterm.  

 

1.  Upper Limit CI=                          

2.  Lower Limt CI =     

                          

·         Question 5

    

  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.  Computed statistic:  

3.  Based on comparing the computed statistics to the critical value which of the following is (are) true?

   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. T here 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.

 

Symptoms Worsened

No Effect

Symptoms Improved

Total

Treatment 1

22

14

14

50

Treatment 2

14

15

21

50

    

 

 

           

·         Question 6

     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 theproportion  of all patients with total cholesterol < 200.  

 

1.  Upper limit of CI:                  

2.  Lower limit of CI:                     

3.  How many patients would be required to ensure that a 95% confidence interval has a margin of error not exceeding 5%?    n= ____314 _____

 

 

 

  New Drug

(n=75) Placebo

(n=75) Total Sample

(n=150)

Mean (SD) Total Serum Cholesterol

185.0 (24.5)

204.3 (21.8)

194.7 (23.2)

% Patients with Total Cholesterol < 200

78.0%

65.0%

71.5%

         

·         Question 7

     Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs.  Patients with asthma or other respiratory conditions often have restricted PEF.  The mean PEF for children free of asthma is 306.  An investigator wants to test whether children with chronic bronchitis have restricted PEF.  A sample of 40 children with chronic bronchitis are studied and their mean PEF is 279 with a standard deviation of 71.  Is there statistical evidence of a lower mean PEF in children with chronic bronchitis?  Apply the appropriate test at alpha=0.05.  

1. Critical z value:    

2. Computed z:    

 

      

3. Based on comparing the critical z value to the computed z value which of the following is (are) true?  

a. There is statistically significant evidence at alpha=0.05 to show a lower mean PEF in children with chronic bronchitis?

b. There is not  statistically significant evidence at alpha=0.05 to show a lower mean PEF in children with chronic bronchitis?

c. There are not enough data points to reach a conclusion.

d. b and c.        

·         Question 8

     Average adult Americans are about one inch taller, but nearly a whopping 25 pounds heavier than they were in 1960, according to a new report from the Centers for Disease Control and Prevention (CDC). The bad news, says CDC is that average BMI (body mass index, a weight-for-height formula used to measure obesity) has increased among adults from approximately 25 in 1960 to 28 in 2002.”   Boston is considered one of America’s healthiest cities – is the weight gain since 1960 similar in Boston?  A sample of n=25 adults suggested a mean increase of 17 pounds with a standard deviation of 8.6 pounds.  Is Boston statistically significantly different in terms of weight gain since 1960?  Apply the appropriate test at a 5% level of significance. 

1.  Critical  t value: +/-  

 

2.  Computed statistic:   

                       

3.  Based on comparing the computed statistic to the critical value which of the following is (are) true?

a. There is significant evidence, alpha=0.05, that the BMI for Boston residents is significantly different than 25.

b. There is not significant evidence, alpha=0.05, that the BMI for Boston residents is significantly different than 25.

c. Statistically speaking the difference between  the BMI for Boston residents and a BMI of 25 . is 0.

d. b and c.        

·         Question 9

     The following table was presented in an article summarizing a study to compare a new drug to a standard drug and to a placebo.

1. Which, if any, baseline characteristics are  significantly different (at the 0.05 level of significance)  between treatment groups?  

a. Disease Stage  

b. Annual Income 

c. % with Insurance

d. Age

e.  a and c

f.  b and d

 

 

Characteristic*

New Drug

Standard Drug

Placebo

p

Age, years

45.2 (4.8)

44.9 (5.1)

42.8 (4.3)

0.5746

% Female

51%

55%

57%

0.1635

Annual Income, $000s

59.5 (14.3)

63.8 (16.9)

58.2 (13.6)

0.4635

% with Insurance

87%

65%

82%

0.0352

Disease Stage

 

 

 

0.0261

  Stage I

35%

18%

33%

 

  Stage II

42%

37%

47%

 

  Stage III

23%

51%

20%

 

*Table entries and Mean (SD) or %
       

·         Question 10

     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. Computed statistics =                     
3. Based on comparing the computed statistic to the critical value which of the following is (are) true?

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.        

·         Question 11

     An investigator conducts a study to investigate whether there is a difference in mean PEF in children with chronic bronchitis as compared to those without.  Data on PEF are collected and summarized below.  Based on the data, is there statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without?  Apply the two sample t test at alpha=0.05.  

1.  Z 95% Confidence Interval:  

               

2.  Upper Limit 95% CI:                       

3.  Lower Limit 95% CI:                       

4 . Based on comparing the critical the upper and lower limits of the confidence interval for the mean PEF for children with No Chronic Bronchitis to the mean PEF for children With Bronchitis which of the following is (are) true. (4 points)

a. There is statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without.  

b. There is not statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without.  

c. The confidence interval contains the mean PEF for the No Chronic Bronchitis group.

d. a and c.

 

Group

Number of Children

Mean PEF

Std Dev PEF

Chronic Bronchitis

25

281

68

No Chronic Bronchitis

25

319

74

       

·         Question 12

     The table below summarizes baseline characteristics on patients participating in a clinical trial. 

 

1.  Which, if any, baseline characteristics are  significantly different (at the 0.05 level of significance)  between treatment groups?  (10 points)

a. Age

b. Total Cholesterol 

c. Diabetes

d. % Female

e.  a and b

f.  c and d

Characteristic Placebo

(n=125) Experimental

(n=125)

P

Mean (+ SD) Age

54 + 4.5

53 + 4.9

0.7856

% Female

39%

52%

0.0289

% Less than High School Education

24%

22%

0.0986

% Completing High School

37%

36%

 

% Completing Some College

39%

42%

 

Mean (+ SD) Systolic Blood Pressure

136 + 13.8

134 + 12.4

0.4736

Mean (+ SD) Total Cholesterol

214 + 24.9

210 + 23.1

0.8954

% Current Smokers

17%

15%

0.5741

% with Diabetes

8%

3%

0.0438

 

 

 

         

·         Question 13

     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=__5 ___

2.  Critical value: As this is a left tailed test so critical value = -t(0.05,df = 5) = -2.015; From t-table  

3.  Computed statistic: As we can see that this is a paired sample test so we need to find out the difference and the mean and standard deviation of the differences. The differences are -2, -3, -4, 5, 1 and -1 which is giving mean = -0.6667 and sample standard deviation = 3.2660.

So test statistic =  = -0.50

4.  Based on comparing the computed statistic to the critical value which of the following is (are) true?

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.

Subject

Initial Weight

Weight after 6 Weeks

1

155

157

2

142

145

3

176

180

4

180

175

5

210

209

6

125

126

 

 

 

 

 

         

·         Question 14

     The graph below shows what kind of relationship between the independent and dependent variables:

  

The graph shows a positive relationship between the independent and dependent variables.

         

·         Question 15  (IGNORE THIS QUESTION)

     

Which of the following is NOT  true concerning scatterplots?     

D.   The unit of measure on the X and Y axis must be the same.  

 

     

·         Question 16

    

  Examine the above graphs below and answer the following questions.

 

1.  Which of the above graphs indicates a negative relationship between the

    graphed variables? (Include all that are negative)      

           D, E and F

                                           

2.  On which axis is the dependent variable graphed?                                                

3.  Which of the above graphs indicated the highest correlation?                               

 

 

             

·         Question 17

     The following data were collected in a study relating hypertensive status measured at baseline to incident stroke over 5 years.

 

1.  Compute the cumulative incidence of stroke in the study.

 

Cumulative Incidence =

 

2.  Compute the cumulative incidence of stroke in patients classified as hypertensive at baseline.

 

Cumulative Incidence Hypertensive =    

                               

3.  Compute the cumulative incidence of stroke in patients free of hypertension at baseline.

 

Cumulative Incidence Not Hypertensive =                             

 

4.  Compute the risk difference of stroke in patients with hypertension as compared to patients free of hypertension.

 

Risk Difference =    

 

                                       

5.  Compute the relative risk of stroke in patients with hypertension as compared to patients free of hypertension.

 

Relative Risk =  

                                              

6.  Compute the population attributable risk of stroke due to hypertension.

 

PAR =                                             

         

·         Question 18

     The survival curve below depicts survival times and rates for a particular cancer diagnosed at various stages of progression.

 

1.  At what time (to the nearest year) does 12 year survival appear certain for Stages II cancer?

2.  For Stage I cancer what is the minimum survival time (to the nearest year)? 1 year

3.  What is the median survival time for Stage IV cancer (to the nearest year)? 1 year 

       

·         Question 19

     In a 10 year study of CAD 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.

 

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

 

Incidence Rate New Medication =  per 1,000 person years.

 

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

 

Incidence Rate Placebo =   per 1,000 person years.

 

       

·         Question 20

     A small cohort study is conducted in 13 patients with an aggressive cellular disorder linked to cancer.  The clinical courses of the patients are depicted graphically below.

 

1.  Compute the prevalence of cancer at 12 months.

 

    Prevalence =                               

2.  Compute the cumulative incidence of cancer at 12 months.

 

    Cumulative Incidence 12 Months =         

3.  Compute the incidence rate (per month) of cancer.

 

    Incidence Rate =

4.  Compute the incidence rate (per month) of death.

 

    Incidence Rate =

.