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Is There An Association? Exposure (Risk Factor) Outcome

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Target Population Study population Collect data Make comparisons Is there an association? Are the results valid? Chance Bias Confounding Inference Sample Testing Whether a Factor Is Associated With Disease

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Diseased & Exposed Diseased & non-exposed Diseased & non-exposed Non-diseased & non-exposed Non-diseased & non-exposed Non-diseased & exposed Non-diseased & exposed

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All Three Of These Can Be Summarized by a 2x2 Table Yes No Yes No Outcome Exposed? Cohort Clinical Trial Case-Control All three analytical studies rely on a comparison of groups to determine whether there is an association.

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Wound Infection Yes No 1 78 79 7 124 131 Yes No Incidental Appendectomy How many ways can we compare the groups? How would you interpret the comparisons?

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2) Calculate the difference in incidence between the two groups. (Subtract incidence in control group from the incidence in the exposed group). Options For Comparing Incidence 1)Calculate the ratio of the incidences for the two groups. (Divide incidence in exposed group by the incidence in the control group). Or IeI0IeI0 I e - I 0 For Cohort Type Studies

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Yes No Wound Infection 1 78 79 7 124 131Yes No 8 202 210 Subjects RR = 7/131 = 5.3 = 4.2 1/79 1.3 RR = 7/131 = 5.3 = 4.2 1/79 1.3 Cumulative Incidence 5.3% 1.3% (7/131) (1/79) Had Incidental Appendectomy Risk Ratio “Risk Ratio” or “Relative Risk”

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RR = = 5.3% 1.3% = 4.2 Interpretation: “In this study those who had an incidental appendectomy had 4.2 times the risk compared to those who did not have appendectomy.” 5.3% 1.3% Also had appendectomy No appendectomy A ratio; no dimensions. Risk Ratio in Appendectomy Study

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RR = = 5.3% = 1.0 5.3% Exposed group Unexposed group What If Risk Ratio = 1.0 ?

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Yes No Myocardial Infarction Yes No 378 21,693 22,071 subjects 139 10,898 11,037 exposed Aspirin Use 239 10,795 11,034 not exposed RR =.0126 = 0.55.0221 RR =.0126 = 0.55.0221 I exposed = 139/11,037 =.0126 I unexposed = 239/11034 =.0221 I exposed = 139/11,037 =.0126 I unexposed = 239/11034 =.0221 What If Relative Risk < 1.0 ?

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Yes No Myocardial Infarction Yes No 378 21,693 22,071 139 10,898 11,037 Aspirin Use 239 10,795 11,034 RR =.0126 = 0.55.0221 RR =.0126 = 0.55.0221 “Subjects who used aspirin had 0.55 times the risk of myocardial infarction compared to those who did not use aspirin.” Interpretation of Relative Risk < 1.0

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Yes No Disease c - PY 0 a - PY 1 Yes No IR a/PY 1 c/PY 0 Total Disease-free Obs. Time Relative risk = a/PY 1 c/PY 0 Relative risk = a/PY 1 c/PY 0 Exposure “Rate Ratio” or “Relative Risk” Data Summary for Incidence Rate

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Yes No Coronary Artery Disease 60 - 51,477.5 30 - 54,308.7 Yes No 90 105,786.2 Person-Years of Follow Up Incidence In treated group = 30 / 54,308.7 = 55.2 / 100,000 P-Yrs In untreated group = 60 / 51,477.5 = 116.6 / 100,000 P-Yrs Rate Ratio = 55.2 /100,000 P-Yr. = 55.2 = 0.47 116.6 /100,000 P-Yr. 116.6 Rate Ratio = 55.2 /100,000 P-Yr. = 55.2 = 0.47 116.6 /100,000 P-Yr. 116.6 Postmenopausal Hormones

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It is more precise to say that postmenopausal women on HRT had 0.47 times the rate of coronary disease, compared to women not taking HRT. In practice, however, many people interpret it just like a risk ratio.

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Risk Ratios.0336/.0336=1.00.0415/.0336=1.23.0445/.0336=1.33 Cumulative Incidence 2,264/67,424=.0336 61/1,469 =.0415 30/674 =.0445 Low Medium High Magnetic Field Exposure Leukemia No Leukemia Totals 2,26465,16067,424 611,4081,469 30644674 Multiple Exposure Categories

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The Nurse’s Health Study Obesity Non-fatal Myocardial Infarction ? # MIs (non-fatal) 41 57 56 67 85 Person-years of observation 177,356 194,243 155,717 148,541 99,573 Rate of MI per 100,000 P-Yrs (incidence) 23.1 29.3 36.0 45.1 85.4 Rate Ratio 1.0 1.3 1.6 2.0 3.7 Multiple Exposure Categories - An “r x c” (row/column) Table Multiple Exposure Categories - An “r x c” (row/column) Table <21 21-23 23-25 25-29 >29 BMI: wgt kg hgt m 2 ?

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RD = Incidence in exposed - Incidence in unexposed Risk Difference = I e - I 0 The Risk Difference (Attributable Risk)

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Yes No Wound Infection 1 78 79 7 124 131 Yes No 8 202 210 subjects Had Incidental Appendectomy Cumulative Incidence 5.3% 1.3% RD = 0.053 – 0.013 = 0.04 = 4 per 100 Risk Difference in Appendectomy Study

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Even if appendectomy is not done, there is a risk of wound infection (1.3 per 100). … the RD is the excess risk in those who have the factor, i.e., the risk of wound infection that can be attributed to having an appendectomy, assuming there is a cause-effect relationship. Adding an appendectomy appears to increase the risk by (4 per 100 appendectomies), so... 1.3/100 Exposed Not Exposed Excess risk is 4 per 100 5.3/100 Risk Difference Gives a Different Perspective on the Same Information

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Example: Incidence with appendectomy = 5.3% = 0.053 Incidence without appendectomy = 1.3% = 0.013 Risk Difference = 0.040 = 40/1000 i.e., 4 per 100 incidental appendectomies or 40 per 1,000 incidental appendectomies Interpretation: In the group that underwent incidental appendectomy there were 40 excess wound infection per 1000 subjects (or 4 per 100). Interpretation: In the group that underwent incidental appendectomy there were 40 excess wound infection per 1000 subjects (or 4 per 100). Convert % to convenient fractions to interpret for a group of people. Tip #1 for Interpretation of Risk Difference

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The focus is on the excess disease in the exposed group. This implies that if incidental appendectomy were performed on another 1,000 subjects having staging surgery, we would expect 40 excess wound infections attributable to the incidental appendectomy. Interpretation: In the group with incidental appendectomy there were 4 excess wound infections per 100 subjects. Tip #2 for Interpretation of Risk Difference

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Don’t forget to specify the time period when you are describing RD for cumulative incidence. In the appendectomy study the time period was very brief and was implicit (“postoperatively”) it wasn’t necessary to specify the time frame. However, for most cohort studies it is important. Remember that with cumulative incidence, the time interval is described in words. Interpretation: In the group that failed to adhere closely to the Mediterranean diet there were 120 excess deaths per 1,000 men during a two year period of observation. Tip #3 for Interpretation of Risk Difference

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85.4 23.1 # MIs (non-fatal) 41 57 56 67 85 Person-years of observation 177,356 194,243 155,717 148,541 99,573 Rate of MI per 100,000 P-Yrs (incidence) 29.3 36.0 45.1 Relative Risk 1.0 1.3 1.6 2.0 3.7 Risk Difference= 85.4/100,000 - 23.1/100,000 = 62.3 excess cases / 100,000 P-Y in the heaviest group Risk Difference= 85.4/100,000 - 23.1/100,000 = 62.3 excess cases / 100,000 P-Y in the heaviest group Rate Differences <21 21-23 23-25 25-29 >29 BMI: wgt kg hgt m 2

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Among the heaviest women there were 62 excess cases of heart disease per 100,000 person-years of follow up that could be attributed to their excess weight. This suggests that if we followed 50,000 women with BMI > 29 for 2 years we might expect 62 excess myocardial infarctions due to their weight. (Or one could prevent 62 deaths by getting them to reduce their weight.) Rate Difference Interpretation If 100,000 obese women had remained lean, it would prevent 62 myocardial infarctions per year. or

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Influenza Vaccination and Reduction in Hospitalizations for Cardiac Disease and Stroke among the Elderly. Kristin Nichol et al.: NEJM 2003;348:1322-32. These investigators used the administrative data bases of three large managed care organizations to study the impact of vaccination in the elderly on hospitalization and death. Administrative records were used to whether subjects had received influenza vaccine and whether they were hospitalized or died during the year of study. The table below summarizes findings during the 1998-1999 flu season.

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Vaccinated subjects (N=77,738) Unvaccinated subjects (N=62,217) Hospitalization for pneumonia or influenza 495581 Hospitalization for cardiac disease 8881026 Death9431361 DiedNot Dead Vaccinated943(77,738 - 943) Not Vaccinated1361(62,217 – 1,361) If the exposure is vaccination & outcome of interest is death, what is the risk difference? RD = CI e – CI u = (943 / 77,738) - (1,361 / 62,317) = -0.0097 = - 97/10,000 over a year 77,738 62,217

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-97/10,000 over a year Instead of calling it ‘excess risk’, just refer to it as a ‘risk reduction.’ Can a risk difference be a negative number?

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RR & RD Provide Different Perspectives Relative Risk: shows the strength of the association. RR = 1.0 suggests no association RR close to 1.0 suggests weak association RR >> 1.0 or RR << 1.0 suggests a strong association Risk Difference: a better measure of public health impact. How much impact would prevention have? How many people would benefit?

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FOBT A large study looked at whether fecal occult blood testing (FOBT) could decrease mortality from colorectal cancer (CRC). Relative Risk Perspective: FOBT decreased mortality from CRC by 33% ! (RR =.67 for FOBT compared to no screening) Risk Difference Perspective: FOBT decreased mortality from 9 per 1,000 people to 6 per 1,000. So, RR= 0.67 (i.e., 0.006/0.009 BUT The risk difference was only 3 per 1,000 people screened. The ratio of these two numbers is more impressive than the actual difference. The ratio of these two numbers is more impressive than the actual difference.

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Lung Cancer Cigarette smokers140 Non-smokers 10 Coronary Heart Disease Cigarette smokers669 Non-smokers413 Annual Mortality per 100,000 (CI) RR= 14 RD= 130 per 100,000 RR= 14 RD= 130 per 100,000 RR= 1.6 RD= 256 per 100,000 RR= 1.6 RD= 256 per 100,000 Calculate RR & RD for Two Diseases Annual Mortality per 100,000 (CI) Smoking is a stronger risk factor for …. ? Smoking is a bigger public health problem for …. ?

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Non-smokers Smokers Non-smokers

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MI125.9216.6 Aspirin Placebo RR (/10,000) 0.59 What should we conclude? What should we recommend? Aspirin & MI

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Stroke107.888.81.2 Ischemic82.474.31.1 Hemorrhagic20.810.91.9 Upper GI ulcer153.1125.11.2 with hemorrhage34.419.91.7 Bleeding2699.12037.31.3 Transfusion need43.525.41.7 Aspirin Placebo RR (/10,000) MI125.9216.6 0.59 What should we conclude? What should we recommend? Benefits & Risks

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Stroke107.888.81.2 19 Ischemic82.474.31.1 8 Hemorrhagic20.810.91.9 10 Upper GI ulcer153.1125.11.2 28 with hemorrhage34.419.91.7 15 Bleeding2699.12037.31.3 690 Transfusion need43.525.41.718 MI125.9216.60.59 -100 Aspirin Placebo RR RD (/10,000) (/10,000) (/10,000) Benefits & Risks

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If we are going to discuss rare, but serious possible complications of influenza vaccine, would it be better to look at the Risk Ratio or the Risk Difference? Observed frequency in: Exposed people: 2 / 100,000 Unexposed people: 1 / 100,000 Risk Ratio = 2; those exposed had two times the risk! (OMG!) Risk Difference = 1 per 100,000; assuming that the exposure is a cause of the outcome, the exposed group had an excess risk of 1 case per 100,000 subjects.

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The proportion (%) of disease in the exposed group that can be attributed to the exposure, i.e., the proportion of disease in the exposed group that could be prevented by eliminating the risk factor. AR% = RD x 100 I e.04 x 100 = 75%.053 What % of infections in the exposed group can be attributed to having the exposure? Exposed Not Exposed.013.053.04 Interpretation: 75% of infections in the exposed group could be attributed to doing an incidental appendectomy. Attributable Risk % - The Attributable Proportion

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DiseasedNo DiseaseTotals Incidence (Risk) Exposed5009,50010,000 0.050 Not Exposed90089,10090,000 0.010 1,40098,600100,000 0.014 Total risk in exposed group? Excess risk in exposed group? Attributable proportion in exposed group? 0.050 = 50/1,000 0.050 – 0.10 = 40/1,000 over 1 yr. 40/1,000 = 80% 50/1,000 Consider this cohort study conducted over 1 year:

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The Population Attributable Proportion DiseasedNo DiseaseTotals Incidence (Risk) Exposed5009,50010,000 0.050 Not Exposed90089,10090,000 0.010 1,40098,600100,000 0.014 Of the 1,400 diseased people, only 500 were exposed (35.7%). Of these only 80% can be attributed to the exposure. So, in the total population the fraction of cases that can be attributed to the exposure is 0.357 x 0.80 = 0.286, or 28.6%.

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Measuring Association in a Case-Control Study

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To calculate incidence, you need to take a group of disease-free people and measure the occurrence of disease over time. Odds of having the risk factor prior to disease? controls cases (Already have disease) (No disease) But in a case-control study we find diseased and non-diseased people and we measure and compare the prevalence of prior exposures.

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Yes No Wound Infection 1 78 79 7 124 131 Yes No Had Incidental Appendectomy Cumulative Incidence 5.3% 1.3% How many exposed people did it take to generate the 7 cases in the 1 st cell? Probability that an exposed person had disease? Odds that an exposed person had disease? Cohort Study

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Yes No Hepatitis 1 29 18 7 Yes No 19 36 Ate at Deli Case Control How many people had to eat at the Deli in order to generate the 18 cases in the 1 st cell? In a true case-control study, you do not know the denominators for exposure groups! ? ? Case-Control Study

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If the outcome is uncommon, the odds of exposure among non-disease subjects will be similar to the odds of exposure among the total population… So the odds ratio will be a good estimate of the risk ratio. (7/1,000) = Odds Ratio (7/1,007) = Risk Ratio (6/5,634) (6/5,640) Diseased Non-diseasedTotal Exposed71,0001,007 Non-exposed65,6345,640

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Diseased Non-diseasedTotal Exposed71,0001,007 Non-exposed65,6345,640 (7/1,000) = Odds Ratio (7/1,007) = Risk Ratio (6/5,634) (6/5,640) (7 /1,000) (6 /5,634) 7 x 1,0006 5,634 (7/ (1,000 6) /5,634) 7 x 1,0006 5,634 = Odds of disease in Exposed Odds of disease in Unexposed Odds of exposure in Disease Odds of exposure in Non-Disease But this rearranges algebraically: ==

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Yes No Hepatitis 1 29 18 7 Yes No Ate at Deli Case Control In cases =18/1 In controls =7/29 = 75 Odds of Exposure Deli =18/7 No Deli =1/29 = 75 Odds of Disease

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An Odds Ratio Is Interpreted Like Relative Risk “Individuals who ate at the Deli had 75 times the risk of hepatitis A compared to those who did not eat at the Deli.” An odds ratio is a good estimate of relative risk when the outcome is relatively uncommon. The odds ratio exaggerates relative risk when the outcome is more common.

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In cohort studies and clinical trials you can calculate incidence, so you can calculate either a relative risk or an odds ratio. In a case-control study, you can only calculate an odds ratio. You can always calculate an odds ratio, but…

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Yes No Got Giardiasis 14 341 355 16 108 124 Yes No Exposed to Kiddy Pool Cohort Design: Calculate RR or OR I can compute either RR or OR here. Why? Compare frequency of Giardia Not Kid pool

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Not vs. Yes No Giardia 16108 14341 Risk Ratio = 3.3 Risk Ratio = 3.3 16 / (16+108) = 12.9% 14 / (14+341) = 3.9% Cumulative Incidence Odds = 16/14 Ratio 108/341 = 3.6 Odds = 16/14 Ratio 108/341 = 3.6

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Odds = 16/14 Ratio 108/341 = 3.6 Odds = 16/14 Ratio 108/341 = 3.6 a/c b/d a x d b x c = 16108 14341 Kid pool Not vs. a b c d Odds = 16x341 Ratio 108x14 = 3.6 Odds = 16x341 Ratio 108x14 = 3.6 Calculation of the Odds Ratio Odds = 16/108 Ratio 14/341 = 3.6 Odds = 16/108 Ratio 14/341 = 3.6 = a/b c/d Ratio of Odds of Disease Ratio of Odds of Exposure Cross Product

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With a Common Outcome OR Exaggerates RR I e = 60 168 I 0 = 45 386 Yes No Outcome 14 341 386 unexposed 16 108 168 exposed Yes No Risk Factor 16 / (16+108) 14 / (14+341) RR = 3.3 16 / (16+108) 14 / (14+341) RR = 3.3 RR = 16 / 108 14 / 341 OR = 3.6 16 / 108 14 / 341 OR = 3.6 OR =

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With a Common Outcome OR Exaggerates RR I e = 60 168 I 0 = 45 386 Yes No Outcome 45 341 386 unexposed 60 108 168 exposed Yes No Risk Factor 60 / (60+108) 45 / (45+341) RR = 3.06 60 / (60+108) 45 / (45+341) RR = 3.06 RR = 60 / 108 45 / 341 OR = 4.21 60 / 108 45 / 341 OR = 4.21 OR =

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You should be able to calculate these measures of disease frequency and measures of association using a simple hand calculator. Stat Tools will also do them, and there is one question on Quiz 3 for which you are asked to hand calculate an odds ratio and then check your answer using Stat Tools.

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N. Engl. J. Med. Abstract N. Engl. J. Med. Abstract Racial Disparities in Health Care

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Yes No Referral for Cardiac Cath 326 34 360 305 55 360 Black White What was the odds ratio ? (Calculate and compare your answer with your neighbor’s.)

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Yes No Referral for Cardiac Cath 326 34 360 305 55 360 Black White Incidence What was the probability that a black patient would be referred for catheterization (cumulative incidence)? What was the probability that a white patient would be referred for catheterization? (Calculate and compare your answer with your neighbor’s.)

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Yes No Black 163 17 180 90.5% Referral for Cath. White Incidence Yes No Black 163 17 180 90.5% 142 38 180 78.9% Referral for Cath. White Incidence What does the stratified analysis suggest? MalesFemales Stratified by Gender

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If you were writing the abstract for the Shulman study, how would you report the major findings?

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