Crude OR = (400*2550)/(450*1100) = 2.06

1. 1. Which one of the following would NOT be expected to increase the statistical power of a clinical trial to test a new medical treatment? • treating a more clinically homogeneous group of patients • lengthening the trial to allow enrollment of more patients • adopting a more stringent standard of evidence to prove the new treatment works • adopting stronger measures to ensure compliance with therapy • testing only a subgroup of patients for whom the new drug would be expected to have the greatest advantage

2. 2. Two researchers conduct separate randomized clinical trials comparing the same new therapy and publish their results in consecutive New England Journal of Medicine papers. The first study found a difference in favor of the new therapy and reported p=.02 to support their contention that this difference was real. The second study used twice as many patients as the first and also observed a difference in favor of the experimental therapy, but reported that p=.21 and therefore that observed difference was not statistically significant. Which statement below is NOT a possible explanation of the different results?  • One of the reported p-values must be incorrect, since larger sample sizes generate smaller p-values.  • The observed difference favoring the new therapy was smaller in the second clinical trial than in the first. • Because of differences in designs of the two clinical trials, measurement error and biological variability were greater in the second trial than in the first. • The first trial included an adjustment for confounding variables, while the second examined the crude difference between therapies. • The first study was not blinded, and diagnostic suspicion bias contaminated the results. 

3. 3. You conduct a case-control study examining the relationship between drinking soda and colon cancer and find that among 1500 who have colon cancer, 400 drink soda, while among the 3000 controls who don’t have colon cancer, 450 drink soda. • Draw a 2x2 table and calculate the crude OR. Crude OR = (400*2550)/(450*1100) = 2.06

4. 3. (continued) Now you stratify by gender and find the following: • Among women, 200 of 1000 who have colon cancer drink soda, while among the 2000 who don’t have colon cancer, 300 drink soda. • Among men, 200 of the 500 who have colon cancer drink soda, but only 150 of the 1000 who don’t have colon cancer drink soda. • Draw out the stratified 2x2 tables and calculate their respective ORs. • Is this an example of effect modification or confounding? OR = (200*1700)/(300*800) = 1.42 OR = (200*850)/(150*300) = 3.78 The stratum-specific ORs are substantially different (> 20% different). Therefore this is an example of Effect Modification.

5. Explain in lay terms what this conclusion means. • What do you do now? There is a natural, inherent difference between how drinking soda affects risk of developing colon cancer in men versus women. Men who drink soda have a greater increase in risk of colon cancer than women do because of something intrinsic to the male body’s response to the soda. We cannot report the crude (combined) OR because it falsely elevates the risk in women and falsely reduces the risk in men. It is misleading. We instead report the separate, stratified ORs that we calculated.

6. 4. You conduct a case-control study to examine the relationship between eating margarine and depression. You find that among the 185 patients who suffer from depression, 65 eat margarine, while 50 of the 230 controls eat margarine. • Draw a 2x2 table and calculate the crude OR. Crude OR = (65*180)/(50*120) = 1.95

7. 4. (continued) Among the 100 women in this group who suffer from depression, 25 eat margarine. Among the 50 female controls, 5 eat margarine. Among the 85 male cases, 40 eat margarine. Among the 180 male controls, 45 eat margarine. • Draw out the stratified 2x2 tables and calculate their respective ORs. • Is this an example of effect modification or confounding? OR = (25*45)/(5*75) = 3 OR = (40*135)/(45*45) = 2.67 The stratum-specific ORs are very similar (they don’t differ by >20%), but they differ from the crude OR. This is an example of confounding.

8. Explain in lay terms what this conclusion means. • What do you do now? The relationship between eating margarine and depression is distorted by gender. Gender is a variable associated with both eating margarine and with developing depression. For example, maybe more men burn their toast, and burnt toast is also associated with an increase in depression. We cannot report the crude (combined) OR because it falsely represents the risk. We instead need to conduct a Mantel-Haenszel adjustment to calculate a combined OR that controls for the effect of gender. Good news for you guys is that you do not need to know how to do this!

9. 5. Ahh, the fun of the matched case-control adjustment... Consider the following matched case-control study examining the relationship between eating peanut butter for breakfast and developing peptic ulcer disease: Pair: 1 2 3 4 5 6 7 8 9 10 PUD (+): + + + - - - + + + + Controls: + + - + + - + - - - Draw a regular 2x2 table and calculate a summary OR. Crude OR = (7*5)/(3*5) = 2.33

10. 5. (continued) Let’s approach the same question differently. Consider the following matched case-control study examining the relationship between eating peanut butter for breakfast and developing peptic ulcer disease: Pair: 1 2 3 4 5 6 7 8 9 10 PUD (+): + + + - - - + + + + Controls: + + - + + - + - - - Calculate the matched OR. To approach this type of question, first select only the discordant pairs. Now, we make one ratio: Discordant pairs with case exposed Discordant pairs with case unexposed = 4/2 = 2.0 The strength of association between exposure and disease changes when we use matched cases and controls. Remember that this method increases statistical power (a more homogenous population) but may decrease generalizability to the population at large.

11. 6. In an "outcomes" analysis of coronary bypass surgery, health services researchers identify charts of all patients diagnosed with three vessel disease at three major clinical centers during the past ten years. These patients are separated into those who initially were treated surgically and those who were initially treated medically, with surgery used if medical treatment was unsuccessful. Aggregate results for mortality and a variety of other outcome variables were compiled for each group, to produce prognostic profiles for those initially treated medically vs. those who received immediate surgery. This study was a: • prospective cohort study • retrospective cohort study • cross-sectional survey • hospital-based case-control study • controlled clinical trial

12. 7. Consider the following study: • In a study examining the relationship between oral contraceptives and bacteriuria, you follow women who do and do not use oral contraceptives over a three-year period, and find that 70 of the 500 individuals who use OC acquired bacteriuria, while 150 of 3000 individuals who don’t use OC acquired bacteriuria. • Is this a cohort or case-control study? • What is the incidence among the exposed? • What is the incidence among the unexposed? • What is the relative risk? • What is the attributable risk? • What is the attributable risk %? Cohort Ie = 70/500 = 0.14 Io = 150/3000 = 0.05 RR = Ie/Io = 2.8 AR = Ie-Io = 0.09 AR% = (Ie-Io)/Ie = 0.64 • Now suppose that the prevalence of use of OC in the population is 20%. • What is the expected incidence of bacteriuria in our population? • What is our population attributable risk? • What is our population attributable risk %? It = (Pe)(Ie) + (1-Pe)(Io) = (0.2)(0.14) + (0.8)(.05) = 0.068 PAR = (It-Io) = 0.018 PAR% = (It-Io)/It = 0.26