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Home , Risk difference, Risk factor

Is There An Association?

Exposure ( Factor) Outcome

Exposures Outcomes “Risk factors” Dependent variable Preventive measures occurrence Management strategy Independent variables

Examples: Lack of exercise Heart disease? Flu Shot Dystonia Disorder?

In analytic studies one enrolls subjects from a population and groupsHypothesis them in some Testingway to make Scheme comparisons that test association between risk factors and outcomes.

Target Population Inference Sample

Study Are the results valid? Population  Chance  Bias 

• Collect data • Make comparisons Is there an association? Various Exposure-Disease Categories 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 …

… those who were Not exposed and Not exposed, Non-diseased But diseased not exposed? All Three Of These Can Be Summarized by a 2x2 Table

Outcome • Cohort Yes No • • Case-Control

Yes 7 124 131

Exposure

No 1 78 79

All three analytical studies rely on a comparison of groups to determine whether there is an association. Incidental Appendectomy A Retrospective and Risk of Wound

Wound Infection Yes No Cumulative

Yes 7 124 131 CIe = 7/131 Incidental = 5.3% Appendectomy 1 78 79 No CI0 = 1/79 = 1.3%

210 Subjects How can we quantify the magnitude of association? For Cohort Type Studies Options For Comparing Incidence

Ie

I0 Or 1. Calculate the ratio of the incidences for 2. theCalculate two groups. the difference (Divide incidence in incidence in exposedbetween group the bytwo the groups. incidence (Subtract in the incidencecontrol in control group group). from the Ie- I0 incidence in the exposed group).

The Risk Ratio A Retrospective (a measure of association) Cohort Study

Wound Infection Yes No Cumulative Incidence

Yes 7 124 131 Ie = 7/131 Incidental = 5.3% Appendectomy 1 78 79 No I0 = 1/79 = 1.3%

“Risk Ratio” or RR = 7/131 = 5.3 = 4.2 “” 1/79 1.3 Association A link between antecedent factors and some outcome –possibly a causal relationship, but not necessarily.

Exposure (Risk Factor) Outcome

Exposures Outcomes “Risk factors” Dependent variable Preventive measures Disease occurrence Management strategy Independent variables

Examples: Lack of exercise Heart disease? Flu Shot Dystonia Disorder? Risk Ratio in the Appendectomy Study

5.3%

Also had appendectomy 5.3% RR = = = 4.2 1.3% 1.3%

(A simple ratio; no No appendectomy 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.” What If Risk Ratio = 1.0 ?

5.3%

Exposed group 5.3% 5.3% RR = = = 1.0 5.3%

Unexposed group The Risk Ratio A Randomized (a measure of association) Clinical Trial

Wound Infection Yes No Cumulative Incidence

Yes 139 10,898 11,037 CIe = 139/11,037 = .0126 Incidental Appendectomy

No 239 10,795 11,034 CI0 = 239/11034 = .0221

RR = .0126 = 0.55 .0221 The Risk Ratio A Randomized (a measure of association) Clinical Trial

Heart Attack Yes No Cumulative Incidence

Yes 139 10,898 11,037CI Low Dose e = 139/11,037 Aspirin = .0126

No 239 10,795 11,034CI = 239/11034 Interpretation: “Subjects who used aspirin had 0 = .0221 0.55 times the risk of compared to those who did not use aspirin.” RR = .0126 = 0.55 .0221 Comparing Incidence Rates or RCT Outcome Yes No Disease-free Incidence Obs. Time Rates

Yes a - PY e IRe = a/PYe Exposure

No b - PY0 IR0 = b/PY0

IR a/PY Rate Ratio = e = e IR0 b/PY0 Comparing Incidence Rates Prospective Cohort Study

Heart Disease Yes No Disease-free Incidence Obs. Time Rates

Yes 30 - 54,308 IRe =30/54,308 Postmenopausal HRT

No 60 - 51,478 IR0 =60/51,478

Rate Ratio = 55.2 /100,000 P-Yr. = 0.47 116.6 /100,000 P-Yr. Best interpretation?

Rate Ratio = 55.2 /100,000 P-Yr. = 0.47 116.6 /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. 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. Multiple Exposure Categories

No Totals Leukemia Leukemia Magnetic High 30 644 674 Field Medium 61 1,408 1,469 Exposure Low 2,264 65,160 67,424

Cumulative Incidence Risk Ratios High 30/674 =.0445 .0415 / .0336 = 1.33 Medium 61/1,469 =.0415 .0445 / .0336 = 1.23 Low 2,264/67,424=.0336 .0336 / .0336 = 1.00

Lowest exposure group is the reference for comparison. Multiple Exposure Categories - An “r x c” (row/column) Table ? Obesity Heart Attack

wgt kg Rate of MI per hgt m2 # MIs Person-years 100,000 P-Yrs. Rate BMI: (non-fatal) of observation (incidence) Ratio <21 41 177,356 23.1 1.0 21-23 57 194,243 29.3 1.3 23-25 56 155,717 36.0 1.6 25-29 67 148,541 45.1 2.0 >29 85 99,573 85.4 3.7 ?

Data from The Nurses’ Study The ()

RD = Incidence in exposed - Incidence in unexposed

Risk Difference = Ie - I0 Risk Difference A Retrospective (another measure of association) Cohort Study

Wound Infection Yes No Cumulative Incidence

Yes 7 124 131 Ie = 7/131 Incidental = 5.3% Appendectomy 1 78 79 No I0 = 1/79 = 1.3%

Risk RD = 5.3%-1.3% = 4 per 100 appendectomies Difference = 0.053 – 0.013 = 0.04 = 4 per 100 Risk Difference Gives a Different Perspective

Adding an appendectomy 5.3/100 appears to increase the Even if appendectomy is risk by (4 per 100 appendectomies), so… not done, there is a risk Excess of wound infection (1.3 risk is per 100). 4 per 100

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. 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% = 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

#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). 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. Rate Differences

Rate of MI per wgt kg # MIs Person-years 100,000 P-Yrs Rate 2 hgt m (non-fatal) of observation (incidence rate) Ratio BMI: <21 41 177,356 23.1 1.0 21-23 57 194,243 29.3 1.3 23-25 56 155,717 36.0 1.6 25-29 67 148,541 45.1 2.0 >29 85 99,573 85.4 3.7

Rate Difference = 85.4/100,000 - 23.1/100,000 = 62.3 excess cases / 100,000 P-Y in the heaviest group 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. Flu Vaccine Study

Influenza Vaccination and Reduction in Hospitalizations for Cardiac Disease and 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. Flu Vaccine Study Data

Vaccinated Unvaccinated subjects subjects (N=77,738) (N=62,217) Hospitalized for pneumonia 495 581 or influenza Hospitalized for cardiac 888 1026 disease Death 943 1361

If the exposure is vaccination & outcome of interest is death, what is the risk difference? Vaccinated Unvaccinated subjects subjects (N=77,738) (N=62,217) Hospitalized for pneumonia 495 581 or influenza Hospitalized for cardiac 888 1026 disease Death 943 1361 If the exposure is vaccination & outcome of interest is death, what is the risk difference? Died Not Dead Vaccinated 943 (77,738 - 943) 77,738 Not Vaccinated 1361 (62,217 – 1,361) 62,217

RD = CIe – CIu = (943 / 77,738) - (1,361 / 62,317) = - 0.0097 = - 97/10,000 over a year 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.’ 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 impact. How much impact would prevention have? How many people would benefit? FOBT Screening Example: A study looked at whether fecal occult blood testing (FOBT) decreased mortality from colorectal (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. Calculate RR & RD for Two

Annual Mortality per 100,000 (CI) 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 …. ? Calculate RR & RD for Two Diseases

Annual Mortality per 100,000 (CI) Lung Cancer Cigarette smokers 140 RR= 14 Non-smokers 10 RD= 130 per 100,000

Annual Mortality per 100,000 (CI) Coronary Heart Disease Cigarette smokers 669 RR= 1.6 Non-smokers 413 RD= 256 per 100,000 Smoking is a stronger risk factor for …. ? Smoking is a bigger public health problem for …. ? 800

700

600

500

400

Smokers

300

200

smokers

Smokers

-

smokers -

100 Non Non 0 Lung Cancer Heart Disease Aspirin & Myocardial Infarction (Heart Attack)

Aspirin Placebo Risk Ratio (/10,000) (/10,000) MI 125.9 216.6 0.59

What should we conclude? What should we recommend? Benefits &

Aspirin Placebo Risk (/10,000) (/10,000) Ratio MI 125.9 216.6 0.59

Stroke 107.8 88.8 1.2 Ischemic 82.4 74.3 1.1 Hemorrhagic 20.8 10.9 1.9 Upper GI ulcer 153.1 125.1 1.2 with hemorrhage 34.4 19.9 1.7 Bleeding 2699.1 2037.3 1.3 Transfusion need 43.5 25.4 1.7

What should we conclude? What should we recommend? Benefits & Risks

Aspirin Placebo RR RD (/10,000) (/10,000) (/10,000) MI 125.9 216.6 0.59 -100

Stroke 107.8 88.8 1.2 19 Ischemic 82.4 74.3 1.1 8 Hemorrhagic 20.8 10.9 1.9 10 Upper GI ulcer 153.1 125.1 1.2 28 with hemorrhage 34.4 19.9 1.7 15 Bleeding 2699.1 2037.3 1.3 690 Transfusion need 43.5 25.4 1.7 18 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. Attributable Risk % - (Attributable Proportion) What % of 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. .04 .053 AR% = RD x 100 I e .013 .04 x 100 = 75% Not .053 Exposed Exposed Interpretation: 75% of infections occurring in patients who had the appendectomy could be attributed to the appendectomy. Quiz: A Cohort Study Over One Year

Cumulative Diseased No Disease Totals Incidence Exposed 500 9,500 10,000 0.050 Not Exposed 900 89,100 90,000 0.010 1,400 98,600 100,000 0.014

1. Total risk in exposed group?

2. Excess risk in exposed group?

3. Attributable proportion in exposed group? Quiz: A Cohort Study Over One Year

Cumulative Diseased No Disease Totals Incidence Exposed 500 9,500 10,000 0.050 Not Exposed 900 89,100 90,000 0.010 1,400 98,600 100,000 0.014

1. Total risk in exposed group? 0.050 = 50/1,000

2. Excess risk in exposed group? = 0.050 – 0.10 = 40/1,000 over 1 yr. 3. Attributable proportion in exposed group?

40/1,000 = 80% 50/1,000 A prospective cohort study compared lung cancer mortality in smokers vs. non-smokers.  AmongQuiz: 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. 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.

100 4900 5000 100/5,000=0.02=20/1,000 over 5 yrs. 20 19980 20000 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% Measuring Association in a Case-Control Study Cohort Type Exposed Cohort & Case-ControlX ModelsX Studies X Compare Time passes Incidence Non-Exposed X To calculate incidence, you need to take a group of initially disease- free people and measure the occurrence of disease over time.

X XX Case-Control X Studies Compare odds of XX DiseasedX exposure to riskCompare factor Prior Exposures Non-Diseased

But in a case-control study we find diseased & non-diseased people and compare the frequency of prior exposures. How many exposed people did it take to generate the 7 cases in the 1st cell?

Retrospective Wound Infection Cohort Study Cumulative Yes No Incidence

Yes 7 124 131 5.3% Had Incidental Appendectomy No 1 78 79 1.3% Case-Control Hepatitis Study CaseYes Control No

Yes 18 7 ? Ate at Deli No 1 29 ?

19 36 How many people had to eat at the Deli in order to generate the 18 cases in the 1st cell? In a true case-control study, you do not know the denominators for exposure groups! 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:

Non- Diseased Total diseased Exposed 7 1,000 1,007 Non- 6 5,634 5,640 exposed

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. 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. Non- Diseased Total diseased Exposed 7 1,000 1,007 Non- 6 5,634 5,640 exposed And since the disease is infrequent, the exposure distribution in non-diseased subjects is similar to that in the total population.

Non- Diseased Total diseased Exposed 7 1,000 1,007 = Non- 6 5,634 5,640 exposed

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 non- diseased people? If I take a reasonable XX XX sample of non-diseased XX X X people, I can estimate the exposure distribution in the overall population. Non- Diseased Total diseased Exposed 7 10 ?

Non-exposed 6 56 ?

(7/1007) = 6.53 = Risk Ratio (6/5640)

(7/6) = 6.53 = (10/56) 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.

Non- Non- Diseased Tot. Diseased Tot. diseased diseased

Exposed 7 1000 1007 Exposed 7 10 ? Non- Non- 6 5634 5640 6 56 ? exposed exposed

(7/1007) = 6.53 = Risk Ratio (7/6) = 6.53 = Odds Ratio (6/5640) (10/56) 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 OR for XX XX XX X X Rick’s Deli Hepatitis

Cases Controls

Ate at Yes 18 7 Yes Rick’s Deli No 1 29

NoOdds = 18/1 Odds = 7/29 Literal: Hepatitis cases were 75 times 18/1 Odds Ratio = more likely to have eaten at the Deli. 7/29 19 36

= 75 Better: Those who ate at Rick’s had 75 times the risk of hepatitis. 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. 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. Ways to Calculate an Odds Ratio

Kid pool 16 108 a b

Not 14 341 c d

Ratio of Odds Ratio of Odds Cross Product of Disease of Exposure Odds = 16/108 Odds = 16/14 Odds = 16x341 Ratio 14/341 Ratio 108/341 Ratio 108x14

= 3.6 = 3.6 = 3.6 a/b a/c a x d c/d b/d b x c With a Common Outcome OR Exaggerates RR

Outcome Yes No

Yes 60 108 168 Ie = 60 exposed 168 Risk Factor

No 45 341 386 I0 = 45 unexposed 386

60 / (60+108) 60 / 108 RR = OR = 45 / (45+341) 45 / 341

RR = 3.06 OR = 4.21 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. 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 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 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. 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. MVC in Elderly Drivers

Percent Death By Age Group

18% 16% 14% 12% 10% 8% 6% Percent Death Percent 4% 2% 0% <25 26-39 40-54 55-69 70+ Age

What measure of disease frequency was used? Elderly Drivers Admitted to BMC after MVC

Mean Mean ISS LOS N Deaths Incidence No Restraint 18.35 13.85 26 8 0.31 Restraint 11.86 9.92 50 5 0.10 Compute risk difference & attributable proportion; interpret them. Elderly Drivers Admitted to BMC after MVC

Mean Mean ISS LOS N Deaths Incidence No Restraint 18.35 13.85 26 8 0.31 Restraint 11.86 9.92 50 5 0.10 Compute risk difference & attributable proportion; interpret them.

Risk Difference = 0.31-0.10 = 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.

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) I just need these two ratios of the exposure But this distribution. rearranges algebraically:

(7 / 1,000) 7 5,634 7 5,634 (7 / 6) = x = x = (6 / 5,634) 1,000 6 6 1,000 (1,000 / 5,634)

Odds of disease in Exposed Odds of exposure in Disease Odds of disease in Unexposed Odds of exposure in Non-Disease