Is There An Association?
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- Isabel Francis
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1 Is There An Association? Exposure (Risk Factor) Outcome Exposures Risk factors Preventive measures Management strategy Independent variables Outcomes Dependent variable Disease occurrence Lack of exercise Flu Shot Examples: Heart disease? Dystonia Disorder?
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4 In analytic studies one enrolls subjects from a population and groups Hypothesis them in some Testing way to make Scheme comparisons that test association between risk factors and outcomes. Sample Target Population Inference Study Population Collect data Make comparisons Are the results valid? Chance Bias Confounding Is there an association?
5 Various Exposure-Disease Categories
6 Diseased & Exposed Exposed, but Non-diseased Sorted by Exposure & Disease Did those who were exposed to a given dish have a higher probability of disease compared to Not exposed, But diseased those who were not exposed? Not exposed and Non-diseased
7 All Three Of These Can Be Summarized by a 2x2 Table Outcome Yes No Cohort Clinical Trial Case-Control Yes Exposure No All three analytical studies rely on a comparison of groups to determine whether there is an association.
8 Incidental Appendectomy and Risk of Wound Infection Wound Infection Yes No A Retrospective Cohort Study Cumulative Incidence Yes CI e = 7/131 Incidental Appendectomy No CI 0 = 5.3% = 1/79 = 1.3% 210 Subjects How can we quantify the magnitude of association?
9 For Cohort Type Studies Options For Comparing Incidence I e I 0 Or 1. Calculate the ratio of the incidences for 2. the Calculate two groups. the difference (Divide incidence incidence exposed between group the by two the groups. incidence (Subtract in the incidence control in control group). group from the incidence in the exposed group). I e - I 0
10 The Risk Ratio (a measure of association) Wound Infection Yes No A Retrospective Cohort Study Cumulative Incidence Yes I e = 7/131 Incidental Appendectomy No I 0 = 5.3% = 1/79 = 1.3% Risk Ratio or Relative Risk RR = 7/131 = 5.3 = 4.2 1/79 1.3
11 Association Exposure (Risk Factor) A link between antecedent factors and some outcome possibly a causal relationship, but not necessarily. Outcome Exposures Risk factors Preventive measures Management strategy Independent variables Outcomes Dependent variable Disease occurrence Lack of exercise Flu Shot Examples: Heart disease? Dystonia Disorder?
12 Risk Ratio in the Appendectomy Study 5.3% Also had appendectomy 1.3% RR = = 5.3% 1.3% = 4.2 No appendectomy (A simple ratio; no dimensions.) Interpretation: In this study those who had an incidental appendectomy had 4.2 times the risk compared to those who did not have appendectomy.
13 What If Risk Ratio = 1.0? 5.3% Exposed group 5.3% RR = = 5.3% = % Unexposed group
14 The Risk Ratio (a measure of association) Wound Infection Yes No A Randomized Clinical Trial Cumulative Incidence Yes Incidental Appendectomy No ,898 11, ,795 11,034 CI e = 139/11,037 =.0126 CI 0 = 239/11034 =.0221 RR =.0126 =
15 The Risk Ratio (a measure of association) Heart Attack Yes No A Randomized Clinical Trial Cumulative Incidence Low Dose Aspirin Yes ,898 11,037 CI e = 139/11,037 =.0126 No ,795 11,034 CI 0 = 239/11034 Interpretation: Subjects who used aspirin had = times the risk of myocardial infarction compared to those who did not use aspirin. RR =.0126 =
16 Comparing Incidence Rates Outcome Yes No Prospective Cohort Study or RCT Disease-free Obs. Time Incidence Rates Exposure Yes a - PY e IR e = a/py e No b - PY 0 IR 0 = b/py 0 Rate Ratio = IR e a/py e = IR 0 b/py 0
17 Comparing Incidence Rates Prospective Cohort Study Heart Disease Yes No Disease-free Obs. Time Incidence Rates Yes 30-54,308 IR e =30/54,308 Postmenopausal HRT No 60-51,478 IR 0 =60/51,478 Rate Ratio = 55.2 /100,000 P-Yr. = /100,000 P-Yr.
18 Best interpretation? Rate Ratio = 55.2 /100,000 P-Yr. = /100,000 P-Yr. 1. Women using hormone replacement therapy had 0.47 times the risk of coronary disease compared to women who did not use HRT. 2. Women using hormone replacement therapy had 0.47 times more risk of coronary disease compared to women who did not use HRT. 3. Women using hormone replacement therapy had 0.47 times less risk of coronary disease compared to women who did not use HRT.
19 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.
20 Multiple Exposure Categories Magnetic Field Exposure High Medium Low Leukemia No Leukemia Totals ,408 1,469 2,264 65,160 67,424 High Medium Low Cumulative Incidence 30/674 = /1,469 = ,264/67,424=.0336 Risk Ratios.0415 /.0336 = /.0336 = /.0336 = 1.00 Lowest exposure group is the reference for comparison.
21 wgt kg hgt m 2 BMI: < >29 Multiple Exposure Categories - An r x c (row/column) Table Obesity # MIs (non-fatal) ? Person-years of observation 177, , , ,541 99,573 Heart Attack Rate of MI per 100,000 P-Yrs. (incidence) Rate Ratio ? Data from The Nurses Health Study
22 The Risk Difference (Attributable Risk) RD = Incidence in exposed - Incidence in unexposed Risk Difference = I e - I 0
23 Risk Difference (another measure of association) Wound Infection Yes No A Retrospective Cohort Study Cumulative Incidence Yes I e = 7/131 Incidental Appendectomy No I 0 = 5.3% = 1/79 = 1.3% Risk Difference RD = 5.3%-1.3% = 4 per 100 appendectomies = = 0.04 = 4 per 100
24 Risk Difference Gives a Different Perspective Even if appendectomy is not done, there is a risk of wound infection (1.3 per 100). 5.3/100 Excess risk is 4 per 100 Adding an appendectomy appears to increase the risk by (4 per 100 appendectomies), so 1.3/100 Not Exposed Exposed Assuming there is a cause-effect relationship the RD is the excess risk in those who have the exposure, i.e., the risk of wound infection that can be attributed to having had the incidental appendectomy.
25 Tips for Interpretation of Risk Difference #1: Convert decimals into a form so that you can interpret for a group of people. Example: Incidence with appendectomy = 5.3% = Incidence without appendectomy = 1.3% = Risk Difference = = 40/1000 i.e., 4 per 100 incidental appendectomies or 40 per 1,000 incidental appendectomies #2: The focus is on excess disease in the exposed group. Interpretation: In the group that underwent incidental appendectomy there were 40 excess wound infection per 1000 subjects (or 4 per 100).
26 Tip #3 for Interpretation of Risk Difference #3 Don t forget to specify the time period when you are describing RD for cumulative incidence. 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. NOTE: 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.
27 Rate Differences wgt kg hgt m 2 BMI: < # MIs (non-fatal) Person-years of observation 177, ,243 Rate of MI per 100,000 P-Yrs (incidence rate) Rate Ratio , , > , Rate Difference = 85.4/100, /100,000 = 62.3 excess cases / 100,000 P-Y in the heaviest group
28 Rate Difference Interpretation Interpretation: 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.) or If 100,000 obese women had remained lean, it would prevent 62 myocardial infarctions per year.
29 Flu Vaccine Study Influenza Vaccination and Reduction in Hospitalizations for Cardiac Disease and Stroke among the Elderly. Kristin Nichol et al.: NEJM 2003;348: 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 flu season.
30 Flu Vaccine Study Data Vaccinated subjects (N=77,738) Unvaccinated subjects (N=62,217) Hospitalized for pneumonia or influenza Hospitalized for cardiac disease Death If the exposure is vaccination & outcome of interest is death, what is the risk difference?
31 Vaccinated subjects (N=77,738) Unvaccinated subjects (N=62,217) Hospitalized for pneumonia or influenza Hospitalized for cardiac disease Death If the exposure is vaccination & outcome of interest is death, what is the risk difference? Died Not Dead Vaccinated 943 (77, ) Not Vaccinated 1361 (62,217 1,361) 77,738 62,217 RD = CI e CI u = (943 / 77,738) - (1,361 / 62,317) = = - 97/10,000 over a year
32 Can a risk difference be a negative number? - 97/10,000 over a year Sure, instead of calling it excess risk, just refer to it as a risk reduction.
33 RR & RD: 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?
34 FOBT Screening Example: A study looked at whether fecal occult blood testing (FOBT) decreased mortality from colorectal cancer (CRC). FOBT decreased mortality from 9 per 1,000 people to 6 per 1,000. Relative Risk Perspective: RR= 0.006/0.009 = 0.67, so FOBT decreased CRC mortality by 33%. The ratio of these two numbers is more impressive than the actual difference. Risk Difference Perspective: The risk difference was 3 per 1,000 people screened.
35 Calculate RR & RD for Two Diseases Annual Mortality per 100,000 (CI) Lung Cancer Cigarette smokers 140 Non-smokers 10 Annual Mortality per 100,000 (CI) Coronary Heart Disease Cigarette smokers 669 Non-smokers 413 Smoking is a stronger risk factor for.? Smoking is a bigger public health problem for.?
36 Calculate RR & RD for Two Diseases Annual Mortality per 100,000 (CI) Lung Cancer Cigarette smokers 140 Non-smokers 10 RR= 14 RD= 130 per 100,000 Annual Mortality per 100,000 (CI) Cigarette smokers 669 Non-smokers 413 Coronary Heart Disease RR= 1.6 RD= 256 per 100,000 Smoking is a stronger risk factor for.? Smoking is a bigger public health problem for.?
37 800 Non-smokers Smokers Non-smokers Smokers Lung Cancer Heart Disease
38 Aspirin & Myocardial Infarction (Heart Attack) Aspirin Placebo (/10,000) (/10,000) MI Risk Ratio 0.59 What should we conclude? What should we recommend?
39 Benefits & Risks Aspirin Placebo Risk (/10,000) (/10,000) Ratio MI Stroke Ischemic Hemorrhagic Upper GI ulcer with hemorrhage Bleeding Transfusion need What should we conclude? What should we recommend?
40 Benefits & Risks Aspirin Placebo RR RD (/10,000) (/10,000) (/10,000) MI Stroke Ischemic Hemorrhagic Upper GI ulcer with hemorrhage Bleeding Transfusion need
41 Rare Outcomes RR or RD? 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.
42 Attributable Risk % - (Attributable Proportion) What % of infections in the exposed group can be attributed to having had the exposure? 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 exposure. AR% = RD x I e.04 x 100 = 75% Not Exposed Exposed Interpretation: 75% of infections occurring in patients who had the appendectomy could be attributed to the appendectomy.
43 Quiz: A Cohort Study Over One Year Diseased No Disease Totals Cumulative Incidence Exposed 500 9,500 10, Not Exposed ,100 90, ,400 98, , Total risk in exposed group? 2. Excess risk in exposed group? 3. Attributable proportion in exposed group?
44 Quiz: A Cohort Study Over One Year Diseased No Disease Totals Cumulative Incidence Exposed 500 9,500 10, Not Exposed ,100 90, ,400 98, , Total risk in exposed group? = 50/1, Excess risk in exposed group? 3. Attributable proportion in exposed group? = = 40/1,000 over 1 yr. 40/1,000 = 80% 50/1,000
45 A prospective cohort study compared lung cancer mortality in smokers vs. non-smokers. Among Quiz: 20,000 Smoking non smokers & Lung there CA were Death 20 deaths from lung cancer during 5 years of study. Among 5,000 smokers there were 100 deaths from lung cancer during the 5 year study period. 1) Organize this information in a 2x2 table. 2) Calculate the cumulative incidence of death (per 1,000) due to lung cancer in smokers and non-smokers. 3) Calculate the relative risk; interpret it in words. 4) Calculate the risk difference; interpret it in words. 5) Calculate the attributable fraction in the exposed; interpret it in words.
46 A prospective cohort study compared lung cancer mortality in smokers vs. non-smokers. Among 20,000 non smokers there were 20 deaths from lung cancer during 5 years of study. Among 5,000 smokers there were 100 deaths from lung cancer during the 5 year study period. 1) Organize this information in a 2x2 table. 2) Calculate the cumulative incidence of death (per 1,000) due to lung cancer in smokers and non-smokers. 3) Calculate the relative risk; interpret it in words. 4) Calculate the risk difference; interpret it in words. 5) Calculate the attributable fraction in the exposed; interpret it in words /5,000=0.02=20/1,000 over 5 yrs. 20/20,000=0.001=1/1,000 over 5 yrs. RR = 20/1 RD = 19/1,000 over 5 yrs. AF in exposed = 19/20 x 100 = 0.95 = 95%
47 Measuring Association in a Case-Control Study
48 Cohort Type Studies Non-Exposed Exposed Cohort & Case-Control Models Time passes X X X X Compare Incidence To calculate incidence, you need to take a group of initially diseasefree people and measure the occurrence of disease over time. Compare odds of exposure to risk Compare factor Prior Exposures X X X X X Diseased Case-Control Studies Non-Diseased But in a case-control study we find diseased & non-diseased people and compare the frequency of prior exposures.
49 How many exposed people did it take to generate the 7 cases in the 1 st cell? Retrospective Cohort Study Wound Infection Yes No Cumulative Incidence Yes Had Incidental Appendectomy No % 1.3%
50 Hepatitis Case Yes Control No Case-Control Study Yes 18 7? Ate at Deli No 1 29? 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!
51 A Rare Outcome If I somehow had exposure and outcome information on all of the subjects in the source population and looked at the association using a cohort design, it might look like this: Diseased Total Exposed 7 1,000 1,007 Nondiseased Nonexposed 6 5,634 5,640 The risk ratio is calculated as (7/1,007) / (6/5,640) = 6.53, i.e., the key information is in the four numbers in the four highlighted numbers.
52 So all of the information we need in in those 4 numbers. But RR = (7/1,007) can be rearranged algebraically (6/5,640) To (7/6) (1,007/5,640) = 6.53 In a sense this is comparing the exposure distribution (odds of exposure) in the diseased people to the exposure distribution in the overall population. Diseased Total Exposed 7 1,000 1,007 Nondiseased Nonexposed 6 5,634 5,640
53 And since the disease is infrequent, the exposure distribution in non-diseased subjects is similar to that in the total population. Diseased Total Exposed 7 1,000 1,007 Nondiseased Nonexposed = 6 5,634 5,640 So, if all I need to estimate the risk ratio is the exposure distribution in in the cases and the exposure distribution in non-diseased people, why not just take a sample of nondiseased people?
54 X X X X X X Diseased Nondiseased If I take a reasonable sample of non-diseased people, I can estimate the exposure distribution in the overall population. Total Exposed 7 10? Non-exposed 6 56? (7/1007) (6/5640) (7/6) (10/56) = 6.53 = Risk Ratio = 6.53 = Odds Ratio
55 So, if I want to estimate a risk ratio for a rare disease, it is more efficient to find cases, but then just take a sample of non-diseased controls in order to estimate the exposure distribution in the entire population. Diseased Tot. Exposed Nonexposed Nondiseased Nonexposed Diseased Tot. Exposed 7 10? Nondiseased 6 56? (7/1007) (6/5640) = 6.53 = Risk Ratio (7/6) (10/56) = 6.53 = Odds Ratio
56 Case-control Method for Sampling Find diseased people & non-diseased people; compare their odds of having been exposed. (Esp. useful for rare outcomes, e.g., birth defects.) Outcome Sick Not Sick Yes Exposure Status No Odds of exposure = 6/4; odds of exposure =8/24
57 OR for Rick s Deli X X X X X X Hepatitis Cases Controls Ate at Rick s Deli Yes Yes No No Odds = 18/1 Odds = 7/29 Odds Ratio = 18/1 7/29 = 75 Literal: Hepatitis cases were 75 times more 19 likely to have 36 eaten at the Deli. Better: Those who ate at Rick s had 75 times the risk of hepatitis.
58 An Odds Ratio Is Interpreted Like a 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.
59 You can always calculate an odds ratio, but 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.
60 Ways to Calculate an Odds Ratio Ratio of Odds of Disease Odds = 16/108 Ratio 14/341 = 3.6 a/b c/d Kid pool Not a b c d Ratio of Odds of Exposure Odds = 16/14 Ratio 108/341 = 3.6 a/c b/d Cross Product Odds = 16x341 Ratio 108x14 = 3.6 a x d b x c
61 With a Common Outcome OR Exaggerates RR Outcome Yes No Risk Factor Yes No exposed unexposed I e = I 0 = RR = 60 / (60+108) 45 / (45+341) OR = 60 / / 341 RR = 3.06 OR = 4.21
62 You should be able to calculate these measures of disease frequency and measures of association using a simple hand calculator. Epi_Tools.XLS will also do them, but you need to be able to do them without Epi_Tools for the exams.
63 What does one measure and compare in a case-control study? 1. Cumulative incidence 2. Incidence rate 3. Risk of disease 4. Frequency of past exposures 5. Risk difference
64 In a cohort study one may measure the degree of association between an exposure and an outcome by calculating either a relative risk or an odds ratio? 1. True 2. False 3. I m not sure
65 In a case-control study one may measure the degree of association between an exposure and an outcome by calculating either a relative risk or an odds ratio. 1. True 2. False 3. I don t know.
66 When is an odds ratio a legitimate estimate of relative risk? 1. Whenever one is conducting a case-control study. 2. When the exposure is relatively uncommon. 3. When the outcome is relatively uncommon. 4. When the sample size is large.
67 Percent Death MVC in Elderly Drivers Percent Death By Age Group 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% < Age What measure of disease frequency was used?
68 Elderly Drivers Admitted to BMC after MVC Mean ISS Mean LOS N Deaths Incidence No Restraint Restraint Compute risk difference & attributable proportion; interpret them.
69 Elderly Drivers Admitted to BMC after MVC Mean ISS Mean LOS N Deaths Incidence No Restraint Restraint Compute risk difference & attributable proportion; interpret them. Risk Difference = = 0.21 = 21 excess deaths/100 injured drivers Attributable Proportion = (0.21/0.31) x 100 = 68% 68% of the deaths in unrestrained elderly drivers could be attributed to their lack of restraint.
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72 Diseased Non-diseased Total Exposed 7 1,000 1,007 Non-exposed 6 5,634 5,640 (7/1,000) = Odds Ratio (7/1,007) = Risk Ratio (6/5,634) (6/5,640) But this rearranges algebraically: I just need these two ratios of the exposure distribution. (7 / 1,000) (6 / 5,634) = 7 5, ,634 (7 / x = x = 1, ,000 (1,000 6) / 5,634) Odds of disease in Exposed Odds of disease in Unexposed Odds of exposure in Disease Odds of exposure in Non-Disease
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