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Biostatistics POPH90013 Assignment 2, 2014
This assignment assesses material presented throughout the subject but primarily from Lecture/Tutorial 6 to Lecture/Tutorial 10.
Due: 27th May, 2014, 12.00pm
The maximum mark for this assignment is 40. It forms 40% of the final grade. Your assignment should be submitted via LMS as a Microsoft Word document and should not be longer than 8 pages. Please put your student ID number and tutor’s name in the header of the document. Please do not put your name on the assignment. Make sure that you format any results you want to show in a way that would be suitable for inclusion in a consulting report or research paper.
Question 1 [Total 12 marks] Table 1.1 (see below) presents information from a hypothetical study investigating the association between smoking and the risk of heart disease for women. The data come from 1012 women who were part of a case-control study. There were 419 women who had heart disease (cases) and 593 women who did not have heart disease (controls). The controls were randomly selected from 25,500 women enrolled in the Melbourne Collaborative Cohort Study (MCCS) who were alive at the end of follow-up. All of the relevant exposure variables (smoking and BMI (see Question 2)) were measured at the beginning of the MCCS. The Cancer Council of Victoria provided the original data on which this example is based. The investigators of this case-control study stated the following research question: Is there an association between smoking and the risk of heart disease for women? Table 1.1
Heart disease Smoking Yes No Total Case 240 179 419 Control 275 318 593 Total 515 497 1012
a) [2 marks] From the data in Table 1.1, calculate and interpret the odds ratio (OR) for the association between the risk of heart disease and smoking. b) [3 marks] From the data in Table 1.1, calculate the standard error (s.e.) of the log odds ratio (loge(OR)) and a 95% confidence interval (95% CI) for the corresponding population odds ratio. Provide an interpretation of the 95% CI for the population odds ratio. c) [3 marks] From the data in Table 1.1, calculate the risk ratio (RR; also called the relative risk) the standard error (s.e.) of the log risk ratio (loge(RR)) and a 95% confidence interval for the corresponding population risk ratio. d) [4 marks] Compare the risk ratio calculated in (c) and its 95% confidence interval to the odds ratio and its 95% confidence interval that you calculated in parts (a) and (b) above. Give reasons for any differences, and whether, based on the data in Table 1.1, you prefer the odds ratio or the risk ratio as a measure of association between the risk of heart disease and smoking. Would your preference for either the odds ratio or the risk ratio change if you were told that the data in Table 1.1 came directly from a cohort study rather than a nested case-control study?
Question 2 [Total 8 marks] Following on from Question 1, the investigators were concerned that obesity (body mass index (BMI) greater than 30 kg/m2) may confound the association between smoking and the risk of heart disease. The data were therefore stratified by obesity in Table 2.1 (see below). The investigators amended the research question to the following: “Is the association between smoking and the risk of heart disease for women confounded by obesity? If so, what is the magnitude of the association adjusted for obesity?” Table 2.1
Obese Smoking Yes No Heart disease Case 50 81 Heart disease Control 125 223 Non-obese Heart disease Heart disease Case Control 190 150 98 95
a) [2 marks] From the data in Table 2.1, calculate the odds ratio for the association between smoking and the risk of heart disease separately for obese and non-obese individuals. b) [2 marks] The Mantel Haenszel weights for each strata are d0*h1/n = 81*125/(50+125+81+223) = 21.14 (for those obese) and 98*150/(190+150+98+95) = 27.58 (for those non-obese). Use these weights and the stratum-specific odds ratios to calculate the Mantel-Haenszel estimate of the pooled odds ratio (ORMH). c) [2 marks] Is there evidence that obesity is a confounder of the association between smoking and the risk of heart disease for women? d) [2 marks] Finally, assume that the standard error (s.e.) of the natural logarithm of the Mantel-Haenszel estimate of the pooled odds ratio (loge(ORMH)) calculated in part (b) is 0.14. Based on this measure of precision, is there evidence of an association at the population level between smoking and the risk of heart disease for women having either adjusted for obesity?
Question 3 [Total 10 marks] Write a short abstract for a research report (250 words) that responds to the investigators’ two research questions by summarising the results of your investigations in Questions 1 and 2. Question 4 [Total 10 marks] Table 4.1 below gives the results for two randomised controlled trials comparing oral ibuprofen versus placebo for children suffering from a migraine. The outcome measure was pain relief at two hours following administration of oral ibuprofen or placebo. An absolute difference in the proportion of children with pain relief at two hours of 0.15 or more corresponds to a clinically important difference. Table 4.1
Trial 1 2 n per group 55 180 Difference in sample proportions (oral ibuprofen – placebo) 0.15 0.25 95% confidence interval for difference in population proportions -0.03 to 0.33 ?? p-value 0.074 ??
For trial 2, the authors presented their results in table 4.2 below but did not present a confidence interval for the difference in population proportions nor a p-value. Table 4.2: Results for Trial 2
Group Oral ibuprofen Placebo Number of children in group 180 180 Number with pain relief at 2 hours 99 54
a) b)
c)