PubHlth Introductory Biostatistics Fall 2011 Examination 1 Due Monday October 31, 2011

Transcription

1 PubHlth Exam I Page 1 of 13 PubHlth Introductory Biostatistics Fall 2011 Examination 1 Due Monday October 31, 2011 Before you begin: This is a take-home exam. You are welcome to use any reference materials you wish. You are welcome to use the computer as you wish, too. However, you MUST work this exam by yourself and you may not consult with anyone. Instructions and Checklist: 1. Start each problem on a new page. 2. Write your name on every page. 3. Make a photo-copy of your exam for safekeeping prior to submission 4. Complete the signature page How to submit your exam: Worcester In-Class Section You may submit your exam in EITHER of 2 ways: 1. Bring your completed exam to class on Monday October 31, 2011, being sure that you have made a copy for safe keeping; OR 2. Mail your completed exam to me with post mark October 31, 2001 to my address below. ONLINE Section You may submit your exam in EITHER of 2 ways: 1. Upload your completed exam to the ASSIGNMENT tab no later than 11:59 pm on Monday October 31, This must be a single pdf and be named using the convention lastname_exam1.pdf. 2. Mail your completed exam to me with post mark October 31, 2001 to my address below. Address and telephone number for mailing Carol Bigelow School of Public Health/402 Arnold House University of Massachusetts/Amherst 715 North Pleasant Street Amherst, MA Tel

2 PubHlth Exam I Page 2 of 13 PubHlth Introductory Biostatistics Fall 2011 Examination I DUE: 11:59 PM Monday October 31, 2011 Signature This is to confirm that in completing this exam, I worked independently and did not consult with anyone. Signature: Printed Name: Date:

3 PubHlth Exam I Page 3 of (10 points total) 1a. (5 points) The figure below is an example of a clustered bar chart. It summarizes data on in-hospital mortalilty (Y-axis) in hospital in relationship to assessed risk of death (X-axis) using the APACHE II scale in two groups of patients: (1) nonoperative group- these patients were admitted into a medical intensive care unit without surgery; and (2) postoperative these patients underwent surgery and were then admitted to the intensive care unit. APACHE II scores have valid range 0 to 71, with 0=least risk of death and 71=greatest risk of death. In 1-2 sentences, interpret this clustered bar chart, focusing on a comparison of the two groups of patients.

4 PubHlth Exam I Page 4 of 13 1b. (5 points) The figure below is a comparison of two cumulative frequency polygons. It is a summary of data on total cholesterol (mmol/l) in a randomized controlled trial that investigated the effectiveness of health checks (intervention group) relative to standard care (control group). In 1-2 sentences, comment on the two total cholesterol distributions. Speculate on the comparison of the two groups with respect to the benefit of intervention.

5 PubHlth Exam I Page 5 of (10 points total) The following table summarizes the distribution of n=1000 cases of acute gastroenteritis in a hypothetical community over the course of one calendar year. Cases of Acute Gastroenteritis (Number) in 2010 in a Hypothetical Community Period Number of cases January 1, 2010 March 31, April 1, 2010 June 30, July 1, 2010 July 31, August 1, 2010 September 30, October 1, 2010 December 31, a. (5 points) By hand or by any means you like, construct an appropriate graphical summary of the distribution of cases of acute gastroenteritis over one calendar year. Tip!! Notice that the calendar periods are NOT of equal duration. 2b. (5 points) In 1-2 sentences, state in words the findings of this surveillance.

6 PubHlth Exam I Page 6 of (10 points total) Suppose that each value in a data set is changed by adding a constant c. 3a. (2 points) What is the effect on the median? 3b. (2 points) What is the effect on the mean? 3c. (2 points) What is the effect on the mode? 3d. (2 points) What is the effect on the variance? 3e. (2 points) What is the effect on the range?

7 PubHlth Exam I Page 7 of (15 points total) The Irish Department of Public Health publishes health care information on its websites. An issue in the development of these materials is their reading level. The recommended reading level is that of year olds. The following is a stem and leaf plot of the reading levels of health information postings on n=46 websites a. (2 points) Which measures of location and spread would you use to describe these data? In 1-2 students, state your preference and explain your selection. 4b. (3 points) Calculate the mean and standard deviation of these data. 4c. (10 points) By hand or by any means you like, construct a box-plot summary of these data. In developing your answer, fill in the following table. P25 = (1.5)* IQR = P50 = Lower Fence = P75 = Upper Fence = Interquartile Range (IQR) = Extreme values (if any) =

8 PubHlth Exam I Page 8 of (10 points total) Questions #5a, #5b and #5c pertain to the following three events: A = {serum cholesterol = } B = {serum cholesterol > 300} C = {serum cholesterol < 280} 5a. (2 points) Are the events A and B mutually exclusive? 5b. (2 points) Are the events A and C mutually exclusive? 5c. (2 points) Suppose Pr(A)=.2 and Pr(B)=.1. What is Pr(serum cholesterol > 250)? Questions #5d and #5e pertain to the following. Suppose that the gender of successive offspring in the same family are independent events and that the probability of a male or female offspring is.5 5d. (2 points) What is the probability that exactly one of two successive children will be female? 5e. (2 points) Suppose that three successive offspring are male. What is the probability that the fourth child will be male?

9 PubHlth Exam I Page 9 of (10 points total) The following are excerpts from journal articles. In each, the authors describe the method of sampling that was used to obtain the analysis sample. For each, indicate whether the sample obtained is unbiased or potentially biased. If your answer is potentially biased, explain your reasoning. 6a. (2 points) An advertisement was placed in a university newspaper to recruit participants. The resulting sample consisted of 49 individuals: 30 females with a mean age of 24.4 years (SD=5.76) and 19 males with a mean age of 26.3 years (SD=7.61). Thirty eight were university students, whereas the other 11 subjects were employed 6b. (2 points) Students enrolled in introductory psychology courses volunteered to participate in the research. There were 40 females and 40 males in the final sample. The participants ranged in age from 18 to 37 years, with an average age of 22 years. Only two of the participants were married. 6c. (2 points) Participants were 247 seventh-grade students who studied in four junior high schools. Three classrooms (N=99) implemented IMPROVE [a math program with no ability tracking] and five homeroom classes (N=148) served as a non-treatment control group. Experimental classrooms were randomly selected from the entire pool (10 junior high schools) of seventh grade classes using IMPROVE, whereas the non-treatment control classes were randomly selected from a different district where students were tracked by ability.

10 PubHlth Exam I Page 10 of (10 points total) - continued 6d. (2 points) City directories were used to obtain a random sample of 300 residential addresses from each city. The scale [ie a questionnaire], a letter explaining the study, and a stamped self-addressed envelope were mailed to each of the 600 addresses. At the end of a 4-week period, 90 questionnaires, 78 useable, had been received from New Madrid (26%). Ninety two questionnaires, 84 useable, had been received from Garnett (28%) 6e. (2 points) Questionnaires were mailed to all female students (n=236) and a random sample of male students (n=348) [enrolled in a college of engineering] who met the following criteria: (a) entered college directly from high school, (b) declared a major in engineering upon enrolling, (c) were enrolled in the university as 3 rd, 4 th, or 5 th year students at the time of the study and (d) were American citizens or residents. The final sample comprised all 278 eligible participants who returned their questionnaires through the mail.

11 PubHlth Exam I Page 11 of (15 points total) The following table shows the annual incidence rates of colon cancer, lung cancer and stomach cancer among males aged 50 years and older from a state tumor registry. Average Annual Incidence per 100,000 males For Colon, Lung and Stomach Cancer Ages, in years Type of Cancer Colon Lung Stomach a. (5 points) Using the information in the table, what is the estimated probability that a 57-year old, disease free male, will develop lung cancer over the next one year? 7b. (5 points) Using the information in the table, what is the estimated probability that a 55-year old, disease free male, will develop colon cancer over the next five years? 7c. (5 points) Suppose there is a cohort of year old men who have never had cancer. How many colon cancers would be expected to develop in this cohort over a 15 year period?

12 PubHlth Exam I Page 12 of (10 points total) Pulmonary embolism is a relatively common condition that necessitates hospitalization and also often occurs in patients hospitalized for other reasons. An oxygen tension (arterial P O2 ) <90 mm Hg is one of the important criteria used in diagnosing this condition. Suppose that the sensitivity of this test is 95%, the specificity is 75% and the estimated prevalence of pulmonary embolism is 20%. 8a. (5 points) What is the predictive value positive of the oxygen tension test? 8b. (5 points) In 1-2 sentences, explain the meaning of the predictive value positive that you obtained in #8a.

13 PubHlth Exam I Page 13 of (10 points total) The following are hypothetical data. The prevalence of diabetes in males 20 years of age and older has been studied in Worcester. The following table shows the age-specific prevalence (per 1000). Age Specific Prevalence of Diabetes in Worcester By Gender (per 1000) Age group (years) Males Females Suppose that we plan a new study in Amherst. Suppose further that Amherst consists of 48% males and 52% females. Of the males, 40% are ages 20-39, 32% are and 28% are 55+. Of the females, 44% are ages 20-39, 37% are and 19% are 55+. Assuming that the Worcester prevalence rates hold in Amherst, calculated the expected prevalence of diabetes in Amherst.