Epidemiology-Biostatistics Exam Exam 2, 2001 PRINT YOUR LEGAL NAME:

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2 PRINT YOUR LEGAL NAME: 3. Multiple linear regression analysis (multivariate analysis) can be used to: (Select the best statement.) a. adjust for confounding by adding the confounding variable as an independent variable. b. determine if a study result is clinically important. c. adjust for loss to follow-up bias. d. calculate a study s power. e. correct the p-value for multiple comparisons. 4. The standard error of the mean is: (Select the best statement.) a. used to calculate the mean of the sample. b. used whenever the researcher wants to adjust for confounding by the direct or indirect standardization method. c. the sample size divided by the square root of the sample standard deviation. d. a type of sampling bias that can lead to an erroneous study conclusion. e. the standard deviation of the distribution of sample means. 5. Researchers want to make an inference about the average serum (blood) cholesterol levels of students in college B. They will do this by randomly sampling 500 students from college B. The researchers want to be absolutely certain that they sample 250 male students and 250 female students. The researchers should: (Select the best statement.) a. calculate a 50% confidence interval on the sample mean. b. use the methods of stratified sampling. c. conduct a randomized controlled trial to help assure comparability of men and women. d. randomly select 500 subjects, and if there are 252 men and 248 women, discard the men with the highest two serum cholesterol levels and handselect two female students. e. perform a stratified t-test on the average serum cholesterol levels of the males vs. the females.

3 PRINT YOUR LEGAL NAME: 6. Researchers prospectively follow a group of 100 vegetarians and 200 nonvegetarians. After 30 years, 8 of the vegetarians develop heart disease and 20 of the non-vegetarians develop heart disease. The 95% confidence interval on the relative risk of 0.8 extends from 0.6 to 0.9. Alpha was set at Select the best statement: a. Vegetarians were 80% less likely to develop heart disease over 30 years vs. the non-vegetarians. b. The relative risk of 0.8 is not statistically significant as the 95% confidence interval contains the value 0.8. c. Vegetarians were 20% less likely to develop heart disease over 30 years vs. non-vegetarians. d. The study had 95% power to detect a true difference of 20% or more. e. The researchers should have calculated an odds ratio rather than a relative risk. 7. The grades on exam C are normally distributed with a population mean of 75% and a population standard deviation of 5%. Select the best statement: a. The 95% confidence interval on the exam C distribution extends from 65% to 85%. b. 34% of the grades on exam C are between 75% and 80%. c. 65% of the grades on exam C are between 65% and 85%. d. The area under the entire curve of exam C grades could be less than 100%. e. 95% of the grades on exam C are between 75% and 85%. 8. Researchers want to determine if the proportion of men from town A who smoke cigarettes is different than the proportion of women from town A who smoke cigarettes. The researchers randomly select 1,000 men and 1,200 women from town A and they ask them if they smoke cigarettes. Subjects are only permitted to answer yes or no to the question. Select the best statement: a. Smoking could be a confounder in this study. b. Gender could be a confounder in this study. c. The study likely has poor internal validity as there are more women in the study than men. d. The researchers should test their hypothesis with a two-sample t-test. e. The researchers should test their hypothesis with a chi-square test.

4 PRINT YOUR LEGAL NAME: 9. Researchers develop a simple regression model with diastolic blood pressure as the dependent variable and height as the independent variable. They determine that R squared is 68%. Select the best statement: a. 68% of the variability in diastolic blood pressure is accounted for by height. b. 68% of the variability in height is accounted for by diastolic blood pressure. c. One standard deviation below and above R squared contains 68% of the heights. d. The R squared is at the 68 th percentile of the distribution of diastolic blood pressures. e. As diastolic blood pressure is a continuous variable, the researchers should use a logistic regression model. 10. Select the best statement concerning Pearson s correlation coefficient: a. It is an approximation of the mean of two variables. b. It reflects the magnitude of the association for linear and non-linear relationships between two continuous variables. c. A Pearson s correlation coefficient of zero indicates there is no linear association between the two variables. d. A Pearson s correlation coefficient of positive one indicates there is no linear association between the two variables. e. A Pearson s correlation coefficient of negative one indicates there is a non-linear relationship between the two variables. 11. Researchers conduct a randomized controlled trial comparing subjects on Med A vs. Med B in the prevention of strokes. They determine that 200 subjects, 100 subjects in each arm, are required to have a power of 90% to detect a true difference of 5% or more. One percent of the subjects on Med A developed a stroke while 4% of the subjects on Med B developed a stroke. Alpha was set at 0.05 and the resulting P-value was Select the best statement: a. The researchers should reject the null hypothesis. b. Given the null hypothesis is correct, the probability of obtaining a difference of 5% or more due to chance alone is 7%. c. Given the alternative hypothesis is correct, the probability of obtaining a difference of 5% or more due to chance alone is 7%. d. Given the null hypothesis is correct, the probability of obtaining a difference of 3% or more due to chance alone is 90%. e. Given the null hypothesis is correct, the probability of obtaining a difference of 3% or more due to chance alone is 7%.

5 PRINT YOUR LEGAL NAME: 12. Referring to question 11 above: (Select the best statement.) a. The probability that a Type II Error occurred is 7%. b. The study might have insufficient power to detect a true difference of 3% or more. c. The probability that a Type II Error occurred is 3%. d. The researchers should reject the null hypothesis. e. The probability that a Type I Error occurred is 3%. FOR QUESTIONS 13 25, WRITE THE ANSWERS IN THE SPACES PROVIDED. 13. When is it appropriate to use a non-parametric test for continuous data? 14. Researchers develop the following regression equation: Diastolic Blood Pressure in mm Hg = constant + (slope) (age in years) If the slope is 0.50, how will each additional year of age affect the diastolic blood pressure? 15. Under what circumstances might a researcher decide to transform continuous data?

6 PRINT YOUR LEGAL NAME: 16. What is the difference between a statistic and a parameter? 17. A researcher records the serum (blood) HDL level from 100 randomly selected subjects from town A. The researcher then places the 100 subjects on med A, an experimental medicine to lower serum HDL, for six months and again records the serum HDL levels of the 100 subjects. Assume the serum HDL levels are normally distributed. What statistical test should the researcher use to determine if med A lowered the HDL levels in the subjects? 18. The prevalence of Disease X is known to be 10% in town A. The sensitivity of a test for Disease X is 90% and the specificity of a test for Disease X is 70%. Calculate the predictive value negative of a test for Disease X in town A. Show your work. 19. A researcher conducts a randomized controlled trial for subjects assigned to med A vs. med B in the prevention of heart disease. Because the researcher intends to perform multiple outcome comparisons, alpha is set at The researcher determined that a minimum of 100 subjects would be necessary to have a power of 80% to detect a true difference of 3% or more. The researcher reports that 10% of the subjects on med A developed heart disease while 15% of the subjects on med B developed heart disease with a resulting P-value of What should the researcher s decision be regarding the null hypothesis? Explain your answer.

7 PRINT YOUR LEGAL NAME: 20. Referring to question # 19 above, write a complete sentence interpreting the P- value and containing the appropriate data from the results. It is not acceptable to simply state that the P-value is or is not statistically significant. 21. Two hospitals choose to compare their CABG mortality rates over a one-year period. The hospitals have agreed to look at the mortality data considering patients with or without a diagnosis of hypertension (high blood pressure) at the time of the operation. The data for Hospital A are shown in the following table: Hospital A CABG Number Deaths Hypertension Diagnosis No Hypertension Diagnosis The data for Hospital B are shown in the following table: Hospital B CABG Number Deaths Hypertension Diagnosis No Hypertension Diagnosis The hospital officials report that the CABG mortality rates are the same between the two hospitals. Using the data from these tables only, was the diagnosis of hypertension a confounder in the comparison between Hospital A and Hospital B such that an adjustment would be required? Explain your answer.

8 PRINT YOUR LGAL NAME: 22. Researchers want to determine if there is a difference in the average height between Tufts medical students and Harvard medical students. They randomly select 100 students from each school. The heights are normally distributed in each group. What statistical test should the researchers use to test the hypothesis? 23. There are pros and cons to the various types of epidemiology studies. List one pro and one con of a randomized controlled trial. (Do not list more than one pro and one con.) 24. The scores on an exam are normally distributed with a population mean of 80% and a population standard deviation of 5%. A student scores 75% on the exam. What percent of the exam scores were higher than the student s exam score? Show your work. 25. Researchers want to make an inference about the average systolic blood pressure of Tufts medical students. The researchers report that the systolic blood pressures are normally distributed. They randomly select 100 students and report that the sample mean is 120 mm Hg with a 95% confidence interval extending from 115 mm Hg to 125 mm Hg. Write a sentence interpreting this confidence interval. END OF EXAM

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